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{"url":"https:\/\/planetmath.org\/IsotropicQuadraticSpace","text":"# isotropic quadratic space\n\nA vector $v$ (an element of $V$) in a quadratic space $(V,Q)$ is isotropic if\n\n1. 1.\n\n$v\\neq 0$ and\n\n2. 2.\n\n$Q(v)=0$.\n\nOtherwise, it is called anisotropic. A quadratic space $(V,Q)$ is isotropic if it contains an isotropic vector. Otherwise, it is anisotropic. A quadratic space $(V,Q)$ is totally isotropic if every one of its non-zero vector is isotropic, or that $Q(V)=0$.\n\nSimilarly, an isotropic quadratic form is one which has a non-trivial kernel, or that there exists a vector $v$ such that $Q(v)=0$. The definitions for that of an anisotropic quadratic form and that of a totally isotropic quadratic form should now be clear from the above discussion (anisotropic: $\\operatorname{ker}(Q)=0$; totally isotropic: $\\operatorname{ker}(Q)=V$).\n\nExamples.\n\n\u2022 Consider the quadratic form $Q(x,y)=x^{2}+y^{2}$ in the vector space $\\mathbb{R}^{2}$ over the reals. It is clearly anisotropic since there are no real numbers $a,b$ not both $0$, such that $a^{2}+b^{2}=0$.\n\n\u2022 However, the same form is isotropic in $\\mathbb{C}^{2}$ over $\\mathbb{C}$, since $1^{2}+i^{2}=0$; the complex numbers are algebraically closed.\n\n\u2022 Again, using the same form $x^{2}+y^{2}$, but in $\\mathbb{R}^{3}$ over the reals , we see that it is isotropic since the $z$ term is missing, so that $Q(0,0,1)=0^{2}+0^{2}=0$.\n\n\u2022 If we restrict $Q$ to the subspace consisting of the $z$-axis ($x=y=0$) and call it $Q_{z}$, then $Q_{z}$ is totally isotropic, and the $z$-axis is a totally isotropic subspace.\n\n\u2022 The quadratic form $Q(x,y)=x^{2}-y^{2}$ is clearly isotropic in any vector space over any field. In general, this is true if the coefficients of a diagonal quadratic form $Q$ consist of $1,-1,0$ ($0$ is optional) and nothing else.","date":"2020-04-07 05:07:52","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 34, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9603016972541809, \"perplexity\": 150.50068738968935}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-16\/segments\/1585371665328.87\/warc\/CC-MAIN-20200407022841-20200407053341-00083.warc.gz\"}"} | null | null |
COURT OF APPEALS DECISION DATED AND FILED July 27, 2016 Diane M. Fremgen Clerk of Court of Appeals Appeal No. 2015AP1836-CR STATE OF WISCONSIN NOTICE This opinion is subject to further editing. If published, the official version will appear in the bound volume of the Official Reports. A party may file with the Supreme Court a petition to review an adverse decision by the Court of Appeals. See WIS. STAT. § 808.10 and RULE 809.62. Cir. Ct. No. 2014CF597 IN COURT OF APPEALS DISTRICT II STATE OF WISCONSIN, PLAINTIFF-RESPONDENT, V. ANISSA E. WEIER, DEFENDANT-APPELLANT. APPEAL from an order of the circuit court for Waukesha County: MICHAEL O. BOHREN, Judge. Affirmed. Before Neubauer, C.J., Reilly, P.J., and Hagedorn, J. ¶1 PER CURIAM. Under our criminal justice system in Wisconsin, an act that is considered a crime if committed by an adult is considered a "delinquent act" if committed by a child. The Wisconsin Legislature, however, has created No. 2015AP1836-CR narrow exceptions to this general rule. Pursuant to WIS. STAT. § 938.183(1)(am) (2013-14),1 the legislature has decreed that if a child over the age of ten has attempted or committed first-degree intentional homicide, that child will be charged in adult criminal court, absent the child's burden to prove he or she is entitled to a "reverse waiver" to juvenile court. ¶2 Anissa E. Weier appeals from a nonfinal order denying a reverse waiver to juvenile court.2 The dispositive issue is whether Weier met her burden to prove by a preponderance of the evidence that reverse waiver under WIS. STAT. § 970.032(2) is appropriate under the circumstances. The circuit court denied Weier's request after determining that she failed to do so. We affirm, as the circuit court properly exercised its discretion when it rationally considered the relevant testimony, applied the proper legal standard, and reached a conclusion that a reasonable judge could reach. BACKGROUND ¶3 Twelve-year-old Weier was charged with attempted first-degree intentional homicide3 as party to a crime, by use of a dangerous weapon, in a criminal complaint filed on June 2, 2014. As set forth in the criminal complaint, as well as testimony at the preliminary hearing, the charge stems from the events of May 31, 2014, when twelve-year-old P.L. was found by a passerby lying, 1 All references to the Wisconsin Statutes are to the 2013-14 version unless otherwise 2 This court granted leave to appeal the order. See WIS. STAT. RULE 809.50(3). noted. 3 Attempted first-degree intentional homicide is a Class B felony. § 939.32(1)(a). 2 See WIS. STAT. No. 2015AP1836-CR blood-soaked in the grass pleading for help. P.L. had been stabbed nineteen times in her chest, abdomen, arm, and legs. When asked who had done this to her, P.L. responded that it was Morgan Geyser, another defendant in this case. Officers quickly learned that a third "friend," Weier, was also involved. ¶4 Weier and Geyser were found walking together miles from the scene. Both girls admitted to conspiring to murder their friend in order to become proxies for Slenderman, a fictional figure conceived on a website devoted to horror stories. Weier explained to police that once they killed P.L. "they would become proxies of Slenderman [and] they would then move up and live with Slenderman in [his] mansion." Weier and Geyser hatched the murder plot in December 2013 or January 2014, and planned for it to coincide with Geyser's sleepover birthday party. Weier and Geyser discussed the details of the crime for months at school and on the bus, using code words so they would not be discovered. During the evening of May 30 and the morning of May 31, Weier and Geyser attempted several times to murder P.L., with each attempt being frustrated. The girls finally lured P.L. into a game of hide-and-seek in the woods, where Weier pushed P.L. to the ground and sat on her. After Weier got off P.L. and stood to the side, Geyser went "ballistic" stabbing her. After telling P.L. to lay quietly and that they would find help for her, Weier and Geyser left to find Slenderman. ¶5 After a preliminary hearing on February 16 and 17, 2015, the circuit court found probable cause to proceed. The circuit court held a two-day evidentiary hearing on May 26 and 27, 2015, on the reverse waiver, pursuant to WIS. STAT. § 970.032(2). 3 No. 2015AP1836-CR ¶6 Dr. Michael Caldwell, a psychologist at the Mendota Juvenile Treatment Center, testified that he diagnosed Weier with persistent depressive disorder, a delusional disorder, which he explained has dissipated since the time of the crime, and an underlying diagnosis of schizotypy, 4 which made Weier vulnerable to accepting a belief in Slenderman. The circuit court denied Weier's reverse waiver request, in a decision consolidated with Geyser for the purpose of disposition, noting that Weier had failed to meet her burden to prove by a preponderance of the evidence that reverse waiver under WIS. STAT. § 970.032(2) was appropriate under the circumstances. Weier appeals. DISCUSSION Standard of Review ¶7 We review a circuit court's decision to deny reverse waiver under an erroneous exercise of discretion standard. See State v. Kleser, 2010 WI 88, ¶37, 328 Wis. 2d 42, 786 N.W.2d 144. "An appellate court will affirm a discretionary decision if the circuit court examined the relevant facts, applied a proper standard of law, and using a demonstrated rational process, reached a conclusion that a reasonable judge could reach." Id. Importantly, we will not overturn a circuit court's discretionary determination if the record reflects that discretion was exercised; instead, we will seek out reasons to sustain the decision. State v. Verhagen, 198 Wis. 2d 177,191, 542 N.W.2d 189 (Ct. App. 1995). Caldwell described schizotypy as "a diminished ability to determine what is real and what is not real and a lot of people have varying degrees of this." 4 4 No. 2015AP1836-CR Reverse Waiver ¶8 The adult criminal court has exclusive, original jurisdiction over Weier by virtue of WIS. STAT. § 938.183(1)(am), which grants jurisdiction to the adult court where a juvenile over the age of ten is charged under WIS. STAT. § 940.01(1)(a) with attempted first-degree intentional homicide. The difference between a child convicted in adult court and a child adjudicated delinquent in juvenile court is significant. Stated simply, the State loses all jurisdiction and oversight over a child at the age of eighteen5 under a juvenile order, absent some other court proceeding. See WIS. STAT. § 938.355(4). In adult court, however, the state retains oversight during adulthood for the entire length of the sentence upon conviction, which in this case would not exceed sixty years. See WIS. STAT. § 939.50(3)(b). ¶9 WISCONSIN STAT. § 970.032(2) provides a mechanism by which a juvenile may obtain a reverse waiver from adult court to juvenile court. Under § 970.032(2), "[i]f the court finds probable cause to believe that the juvenile has committed the violation of which he or she is accused … the court shall determine whether to retain jurisdiction or to transfer jurisdiction [to the juvenile court]." The court must retain jurisdiction in adult court "unless the juvenile proves by a preponderance of the evidence all of the following" elements: 5 The circuit court assumed that if reverse waiver was granted and Weier was adjudicated delinquent in juvenile court she would be ordered to participate in the Serious Juvenile Offender (SJO) program under WIS. STAT. § 938.538. Under the SJO program, one exception to oversight ending at the age of eighteen is when a youth has been adjudicated delinquent for committing a Class A felony. Sec. 938.538(3)(a)1m. Under that scenario, jurisdiction and oversight could continue until the age of twenty-five. Id. All parties agree, however, that as Weier was charged with a Class B felony, the juvenile system could only maintain jurisdiction over her until the age of eighteen. 5 No. 2015AP1836-CR (a) That, if convicted, the juvenile could not receive adequate treatment in the criminal justice system. (b) That transferring jurisdiction to the court assigned to exercise jurisdiction under [WIS. STAT.] chs. 48 and 938 would not depreciate the seriousness of the offense. (c) That retaining jurisdiction is not necessary to deter the juvenile or other juveniles from committing the violation of which the juvenile is accused under the circumstances specified in [WIS. STAT. §] 938.183 (1)(a), (am), (ar), (b) or (c), whichever is applicable. Sec. 970.032(2). The weight the court affords each factor is within its discretion. See J.A.L. v. State, 162 Wis. 2d 940, 960, 471 N.W.2d 493 (1991). Importantly, if the juvenile fails to prove any one of the statutory prongs, the reverse waiver is thwarted "no matter how compelling" the evidence is on the others. See Kleser, 328 Wis. 2d 42, ¶97. WIS. STAT. § 970.032(2)(a): Adequate Treatment ¶10 The circuit court determined that regardless of whether Weier is adjudicated in adult court or in juvenile court her initial period of detention would take place at Copper Lake School for Girls. The circuit court concluded, based on a review of the testimony, that Weier would receive "essentially the same type of programming up until age 18" and the court did not "see a big difference in treatment overall at Copper Lake" under placement as either a juvenile or an adult. Conversely, the circuit court questioned whether Weier would receive adequate treatment in the juvenile system after the age of eighteen, concluding that mental health treatment/oversight would end at age eighteen under the juvenile system, but it would continue under an adult criminal disposition. ¶11 Laurie McAllister, the corrections unit supervisor at Copper Lake, testified that any youth placed at Copper Lake receives the exact same programming and the exact same treatment, regardless of whether they are placed 6 No. 2015AP1836-CR there under a juvenile order or an adult court sentence. She explained that the only difference in going to Copper Lake as an adult or a juvenile was in the process, not specifically the treatment. When a youth initially arrives at Copper Lake, regardless of being sentenced as a juvenile or as an adult, there is a twenty-one day reception period where needs, such as education or mental health, are assessed. For a juvenile offender, after those assessments are completed, Copper Lake holds a planning conference, which includes the youth, the parents, the social worker, the county representative or state agent, and a reviewer from the Office of Juvenile Offender Review (OJOR). The goal is to work on transitioning back into the community. A planning conference is held every ninety days. If, however, a juvenile is placed at Copper Lake under an adult court sentence, she will not have the same planning conference procedure. Instead, the juvenile's status is reviewed by the Bureau of Classification and Management. ¶12 Shelley Hagan, director of the OJOR, clarified the planning conference procedure, noting that while a juvenile under an adult sentence would "have the same treatment team. We treat all our kids alike, whichever door they come in," she would not have a ninety-day review and her and her family would not be included in the planning process. Hagan confirmed the difference for a youth serving an adult sentence: [T]he program review committee representative from [Taycheedah Correctional Institution] is going to be talking with a team at [Copper Lake] that consists of a social worker, a teacher, unit manager, youth counselor from the living unit. So, it's more of an institution to institution type of conversation. We don't have the parental involvement that we do with the juvenile orders, the youth isn't necessarily going to be part of that process and there's no community supervision representative at that point. ¶13 Testimony also revealed that if Weier were placed at Copper Lake under a juvenile order, she would likely enter the Serious Juvenile Offender (SJO) 7 No. 2015AP1836-CR program. Under the SJO program, pursuant to WIS. STAT. § 938.538(3)(a)1., Weier would receive a court order for a five-year maximum sentence—three years' confinement at Copper Lake and two years' supervision in the community. Hagan explained, however, that a juvenile may be released early from the threeyear confinement, serving as little as one year to eighteen months of their original sentence. When an offender completes the SJO program at Copper Lake (both the institutional and community release programs), that individual is no longer monitored or treated by the State. See § 938.538(5). This could happen on her eighteenth birthday or before. See id. Significantly, the circuit court judge would have no control over the length of time Weier would stay confined at Copper Lake receiving treatment. ¶14 Weier argues that parental involvement in the planning process is paramount to her treatment needs, and the circuit court erred as her parents will not be involved in her care if reverse waiver does not occur. The circuit court considered the relevant testimony regarding the procedural differences under a juvenile order or an adult sentence and determined that the differences in the process would not affect the adequacy of the treatment Weier would receive. The court found it imperative, given the crime and Weier's treatment needs, that adult supervision was warranted beyond Weier's eighteenth birthday. We conclude that the circuit court properly exercised its discretion given the facts presented and made a decision a reasonable judge could make. As WIS. STAT. § 970.032(2) requires that Weier prove all of the statutory prongs in order to obtain a reverse waiver, we could stop our analysis here; however, for completeness we will address the remaining elements considered by the circuit court. 8 No. 2015AP1836-CR WIS. STAT. § 970.032(2)(b): Depreciate the Seriousness of the Offense ¶15 The circuit court concluded that Weier failed to meet her burden to prove by a preponderance of the evidence that transferring her case to juvenile court would not depreciate the seriousness of the offense: The offense involved in this case was violent, was premeditated. There was a conscious decision at the time of the offense to let the victim die. This was charged as attempted murder, but you have to keep in mind for both defendants that this was in fact not a happenstance that just didn't work out, they would have killed P.L. had they had more time had they thought about it…. This was premeditated murder and an attempt to do so. According to the court, "[t]he nature of this offense, the youthfulness of the defendants, their mental development, the mental continued development of each of the defendants satisfies this Court … that to place the defendants in the juvenile setting unduly depreciates the nature of the offense, the seriousness of the offense." ¶16 Like the circuit court, other Wisconsin courts that have applied WIS. STAT. § 970.032(2) have analyzed para. (b) by considering whether the crime was premeditated. E.g., State v. Dominic E.W., 218 Wis. 2d 52, 57-58, 579 N.W.2d 282 (Ct. App. 1998) (noting that the crime was impulsive, not premeditated, in addressing para. (b)). The circuit court highlighted the specific facts of this case revealed at the preliminary hearing, noting the premeditated nature of the crime. The plot to murder P.L. was conceived months in advance, and Weier and Geyser had multiple opportunities to realize the magnitude of their choice and back out of the plan. Weier and Geyser made multiple changes to their plan before finally succeeding. The circuit court also found it significant that the girls gave false information to P.L.—telling her to remain still so she would lose less blood and telling her they would get help when in fact they were leaving her to die and 9 No. 2015AP1836-CR wanted her to be quiet—to support the court's belief in the serious nature of the offense. ¶17 The circuit court was clear in its conclusion that this was not an accidental or impulsive crime; it was "violent," "premeditated," and "[t]here was a conscious decision at the time of the offense to let the victim die." The circuit court reasonably related the serious nature of the alleged offense to the nature and duration of Weier's potential punishment, finding that a reverse waiver to juvenile court would unduly depreciate the seriousness of the offense. The circuit court did not err in this discretionary decision. WIS. STAT. § 970.032(2)(c): Deterrence ¶18 Although the circuit court touched briefly on general deterrence, noting that a message must be sent to the public "that a serious offense is dealt with on a serious basis that offers protections to everyone," the court focused its consideration predominantly on specific deterrence. The circuit court acknowledged that "Weier is diagnosed with a schizotypy disorder, it's delusional, it may have some impact with [Geyser] in that subordinate situation. [Weier] has backed off from Slenderman, acknowledges the nonexistence, she has been more subject to expressing remorse and showing some shame for what has occurred." Nevertheless, the court explained, "I'm satisfied that longer term control is necessary for the reasons that I've stated. I'm satisfied as to each of the defendants then that on the issue of deterrence, to return to the juvenile system does not offer deterrence." According to the court, in the juvenile system Weier would be released into the community: "No restraints, no supervision, no overview to see what happens, to see what happens to the person who was 12 10 No. 2015AP1836-CR when they committed this offense to what they're like at age 16, 17, or 18 to be sure they're safe in the community." ¶19 Dr. Antoinette Kavanaugh, a board certified forensic psychologist, testified that Weier has expressed remorse and regret for her part in the crime. Kavanaugh explained, however, that Weier does not understand how her mental illness played a role in the attempted murder of P.L., and she will need help understanding the role it played "so that doesn't happen again." Kavanaugh acknowledged that deterrence is difficult to get a handle on, but her analysis placed Weier as a moderate risk, which she did to err on the side of protecting the public. Caldwell, testified that he assessed Weier at a more liberal low risk compared to other juveniles subject to adult criminal prosecution, but he agreed with Kavanaugh that Weier has a high likelihood of treatability. The circuit court's determination that deterrence would be best accomplished in the adult criminal court system where Weier would receive continued treatment was not an erroneous exercise of discretion. CONCLUSION ¶20 The circuit court properly "examined the relevant facts, applied a proper standard of law, and [used] a demonstrated rational process" to reach a reasonable discretionary decision to retain adult jurisdiction of Weier. See Kleser, 328 Wis. 2d 42, ¶37. By the Court.—Order affirmed. This opinion will not RULE 809.23(1)(b)5. 11 be published. See WIS. STAT. | {
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This action, in which plaintiff is proceeding pro se, was referred to the undersigned by Eastern District of California Local Rule 302(c)(21), pursuant to 28 U.S.C. § 636(b)(1). On October 15, 2008, the undersigned issued an order dismissing plaintiff's complaint and granting plaintiff twenty days to file an amended complaint. Dckt. No. 3. Plaintiff failed to file an amended complaint or otherwise respond to the October 15, 2008 order; therefore, on January 27, 2009, the undersigned issued findings and recommendations which recommended that the action be dismissed for failure to prosecute. Dckt. No. 4. On March 19, 2009, the assigned district judge adopted that recommendation, dismissed the action, closed the case, and entered judgment accordingly. Dckt. Nos. 6, 7.
The court notes that the January 27, 2009 findings and recommendations, and the March 19, 2009 order and judgment, were returned to the court as undeliverable. However, plaintiff was properly served with those filings. It is the plaintiff's responsibility to keep the court apprised of her current address at all times. Pursuant to Local Rule 182(f), service of documents at the record address of the party is fully effective.
Notwithstanding that judgment, on April 14, 2010, plaintiff filed a "declaration" with the court. Dckt. No. 8. Plaintiff's recent filing does not appear to be one contemplated by the Federal Rules of Civil or Appellate Procedure. Therefore, this document will be disregarded. Plaintiff is advised that the court will disregard and issue no response to any future filings in this closed case.
2. The Clerk of the Court is directed to serve a copy of this order; the January 27, 2009 findings and recommendations, Dckt. No. 4; the March 19, 2009 order, Dckt. No. 6; and the March 19, 2009 judgment, Dckt. No. 7, on plaintiff at P.O. Box 1862, Elk Grove, California 95759. | {
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Home News Refurbishment at The Square helps secure commitment from prestigious brands Jack Wills...
Refurbishment at The Square helps secure commitment from prestigious brands Jack Wills and Clarks to Camberley
The second phase of the multimillion pound upgrade of The Square shopping centre in Camberley continues apace and is set to launch in time for the busy Christmas shopping period.
The long-awaited refurbishment is delivering substantial improvements to the shopping centre, including new flooring, facades and lighting – ultimately creating a fresh contemporary space.
One of Britain's quintessential fashion brands, Jack Wills, is set to open a new store in Camberley within the next two months. This follows hot on the heels of a new five year commitment from shoe retailer Clarks and the recent openings of Foneworld, Luggage Solution and new lunch favourite in December last year, Muffin Break.
Jack Wills will occupy approximately 2,300 sq ft in a prime position in The Square. As well as bringing a new fashion and lifestyle offer to Camberley, Jack Wills will be recruiting for its new store and the details will be available on The Square and Jack Wills' websites soon.
Karen Whelan, CEO, Surrey Heath Borough Council said: "We are delighted to welcome Jack Wills to The Square. It is testament to the extensive refurbishment programme currently underway in The Square and our great management team that we are able to attract prestigious brands like Jack Wills to Camberley. Having met with the Directors of the brand, we know they share our values for high quality, exceptional service and a truly unique retail experience.
We hope to bring you many more popular retailers and brands as Camberley progresses through its redevelopment driven by SHBC. Our vision for Camberley is to create a thriving town centre with a dynamic retail heart, stimulating leisure and cultural facilities and an outstanding experience for our residents and visitors.
"Neil Beaman, Property Director, Jack Wills said: "Given the commitment from Camberley and their local stakeholders to refurbish The Square, it's a great time for Jack Wills to be part of the development, and we look forward to opening in the near future."
The opening will coincide with the completion of the latest phase of The Square's refurbishment and Camberley's fantastic programme of Christmas events.
More information about the exciting refurbishment plans can be found at www.thesqcamberley.co.uk
Find out more about Camberley town centre's extensive regeneration programme at www.surreyheath.gov.uk
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{"url":"https:\/\/en.academic.ru\/dic.nsf\/enwiki\/1098986","text":"# Dollar sign\n\n\ufeff\nDollar sign\n$Dollar sign Punctuation Word dividers General typography Currency Uncommon typography apostrophe ( \u2019 ' ) brackets ( [ ], ( ), { }, \u27e8 \u27e9 ) colon ( : ) comma ( , ) dash ( \u2012, \u2013, \u2014, \u2015 ) ellipsis ( \u2026, ..., . . . ) exclamation mark ( ! ) full stop\/period ( . ) guillemets ( \u00ab \u00bb ) hyphen ( \u2010 ) hyphen-minus ( - ) question mark ( ? ) quotation marks ( \u2018 \u2019, \u201c \u201d, ' ', \" \" ) semicolon ( ; ) slash\/stroke ( \/ ) solidus ( \u2044 ) space ( ) ( ) ( ) (\u2420) (\u2422) (\u2423) interpunct ( \u00b7 ) ampersand ( & ) at sign ( @ ) asterisk ( * ) backslash ( \\ ) bullet ( \u2022 ) caret ( ^ ) copyright symbol ( \u00a9 ) dagger ( \u2020, \u2021 ) degree ( \u00b0 ) ditto mark ( \u3003 ) inverted exclamation mark ( \u00a1 ) inverted question mark ( \u00bf ) number sign\/pound\/hash ( # ) numero sign ( \u2116 ) obelus ( \u00f7 ) ordinal indicator ( \u00ba, \u00aa ) percent etc. ( %, \u2030, \u2031 ) pilcrow ( \u00b6 ) prime ( \u2032, \u2033, \u2034 ) registered trademark ( \u00ae ) section sign ( \u00a7 ) service mark ( \u2120 ) sound recording copyright ( \u2117 ) tilde ( ~ ) trademark ( \u2122 ) underscore\/understrike ( _ ) vertical\/broken bar, pipe ( \u00a6, | ) currency (generic) ( \u00a4 ) currency (specific) ( ) asterism ( \u2042 ) tee ( \u22a4 ) up tack ( \u22a5 ) index\/fist ( \u261e ) therefore sign ( \u2234 ) because sign ( \u2235 ) interrobang ( \u203d ) irony & sarcasm punctuation ( \u2e2e ) lozenge ( \u25ca ) reference mark ( \u203b ) tie ( \u2040 ) Diacritical marks Whitespace characters non-English quotation style ( \u00ab \u00bb, \u201e \u201d ) The dollar or peso sign ($) is a symbol primarily used to indicate the various peso and dollar units of currency around the world.\n\n## Origin\n\nThe sign is first attested in British, American, Canadian, Mexican and other Spanish American business correspondence in the 1770s, referring to the Spanish American peso,[1][2] also known as \"Spanish dollar\" or \"piece of eight\" in British North America, which provided the model for the currency that the United States later adopted in 1785 and the larger coins of the new Spanish American republics, such as the Mexican peso and the Peruvian eight-real and Bolivian eight-sol coins.\n\nThe best documented explanation reveals that the sign evolved out of the Spanish and Spanish American scribal abbreviation \"ps\" for pesos. A study of late eighteenth- and early nineteenth-century manuscripts shows that the s gradually came to be written over the p developing a close equivalent to the \"$\" mark.\"[3][4][5][6][7] ## Alternative hypotheses There are a number of other theories about the origin of the symbol, some with a measure of academic acceptance, others the symbolic equivalent of folk etymologies.[8] ### Drawn with one vertical line ($)\n\n#### Slash 8\n\nOne theory is that the dollar sign is derived from a slash through the numeral eight, denoting pieces of eight. The Oxford English Dictionary before 1963 held that this was the most probable explanation, though later editions have placed it in doubt.\n\n#### Spanish pieces of eight\n\nImage of 1768 Spanish Colonial Real silver coin, showing PTSI mint mark in lower right and left quadrants and the Pillars of Hercules surrounding a picture of the world.\n\nAnother theory is that the dollar sign was derived from or inspired by the mint mark on the Spanish pieces of eight that were minted in Potos\u00ed (in present day Bolivia). The mint mark, composed of the letters \"PTSI\" superimposed, bears a strong resemblance to the single-stroke dollar sign (see photo). The mark, which appeared on silver coins minted from 1573 to 1825 in Potos\u00ed, the largest mint during the colonial period, would have been widely recognized throughout the North American colonies.[citation needed]\n\n#### Greek mythology\n\nAnother theory is that the dollar sign may have also originated from Hermes, the Greek god of bankers, thieves, messengers, and tricksters: Besides the crane, one of his symbols was the caduceus, a staff from which ribbons or snakes dangled in a sinuous curve.\n\n#### Alchemic sigil for cinnabar\n\nA symbol virtually identical to dollar sign has been used as an alchemic sigil for cinnabar dating at least as far back as the early eighteenth century, although this has not been proposed as an origin of the dollar sign. [9]\n\n### Drawn with two vertical lines\n\n#### Spanish coat of arms\n\nThe Pillars of Hercules with a small \"S\" shaped ribbon around in the City of Seville, Spain (16th Century).\n\nA common theory holds that it derives from the Spanish coat of arms engraved on the colonial silver coins, the reals, (among them the Spanish dollar) that were in circulation in Spain's colonies in America and Asia. Reals and Spanish dollars were also legal tender in the English colonies in North America, which later became part of the United States and Canada.\n\nIn 1492, Ferdinand II of Aragon adopted the symbol of the Pillars of Hercules and added the Latin phrase Non plus ultra meaning \"nothing further beyond\", indicating \"this is the end of the (known) world.\" But when Christopher Columbus came to America, the legend was changed to Plus ultra: \"further beyond.\"\n\nSpain's coat of arms\n\nThe symbol was adopted by Charles V and was part of his coat of arms representing Spain's American possessions. The symbol was later stamped on coins minted in gold and silver. These coins, depicting the Pillars of Hercules over two hemispheres and a small \"S\"-shaped ribbon around each, were spread throughout America, Europe and Asia. For the sake of simplicity, traders wrote signs that, instead of saying dollar or peso, had this symbol made by hand, and this in turn evolved into a simple S with two vertical bars.\n\n#### From \"US\"\n\nA dollar sign with two vertical lines is a monogram of U.S., used on money bags issued by the United States Mint. The letters U and S superimposed resemble the historical double stroke dollar sign $\\mathrm{S}\\!\\!\\!\\Vert$: the bottom of the 'U' disappears into the bottom curve of the 'S', leaving two vertical lines. This theory does not consider the fact that the symbol was already in use before the formation of the United States.[10]\n\nThe book Atlas Shrugged by Ayn Rand includes a section where the main characters philosophize about the United States being the only nation to ever use its own monogram for its currency symbol. They suggest it means that the country had always been primarily concerned with the creation of wealth.\n\n#### \"Unit of silver\"\n\nAnother theory is that it derives from \"unit of silver\", each unit being one \"bit\" of the \"pieces of eight\". Before the American Revolution, prices were often quoted in units of the Spanish dollar. According to this theory, when a price was quoted the capital 'S' was used to indicate silver with a capital 'U' written on top to indicate units. Eventually the capital 'U' was replaced by double vertical hash marks.[citation needed]\n\n#### German Thaler\n\nAnother hypothesis is that it derives from the symbol used on a German Thaler. According to Ovason (2004), on one type of thaler one side showed the crucified Christ while the other showed a serpent hanging from a cross, the letters NU near the serpent's head, and on the other side of the cross the number 21. This refers to the Bible, Numbers, Chapter 21 (see Nehushtan).[citation needed]\n\n#### Roman sestertius\n\nThere is a theory that the dollar sign goes back to the most important Roman coin, the sestertius, which had the letters 'HS' as its currency sign. When superimposed these letters form a dollar sign with two vertical strokes (the horizontal line of the 'H' merging into the 'S').\n\n## Later history\n\nRobert Morris was the first to use that symbol in official documents and in official communications with Oliver Pollock. The US Dollar was directly based on the Spanish Milled Dollar when, in the Coinage Act of 1792, the first Mint Act, its value was \"fixed\" (per the U.S. Constitution, Article I, Section 8, clause 1 power of the United States Congress \"To coin Money, regulate the Value thereof, and of foreign Coin, and fix the Standard of Weights and Measures\") as being \"of the value of a Spanish milled dollar as the same is now current, and to contain three hundred and seventy-one grains and four sixteenth parts of a grain of pure, or four hundred and sixteen grains of standard silver.\"\n\nAccording to a plaque in St Andrews, Scotland, the dollar sign was first cast into type at a foundry in Philadelphia, United States in 1797 by the Scottish immigrant John Baine.\n\nThe plaque in St. Andrews.\n\nThe dollar sign did not appear on U.S. coinage until February 2007,[citation needed] when it was used on the reverse of a $1 coin authorized by the Presidential$1 Coin Act of 2005.[11]\n\nThe dollar sign appears as early as 1847 on the $100 Mexican War notes and the reverse of the 1869$1000 United States note.[12] The dollar sign also appears on the reverse of the 1934 $100,000 note as well as the reverse of the 1917$1 note.[citation needed]\n\n## Use in computer software\n\nThe symbol \"$\" has Unicode code point U+0024 (inherited from Latin-1). As the dollar sign is one of the few symbols that is, on one hand, almost universally present in computer character sets, but, on the other hand, rarely needed in their literal meaning within computer software, the$ character has been used on computers for many purposes unrelated to money.[13] Its uses in programming languages have often influenced or provoked its uses in operating systems, and applications.\n\n### Programming languages\n\n\u2022 $was used for defining string variables in older versions of the BASIC language (\"$\" was often pronounced \"string\" instead of \"dollar\" in this use).[13]\n\u2022 $is used for defining hexadecimal constants in Pascal-like languages such as Delphi, and in some variants of assembly language.[13] \u2022$ is used at the starts of names to define variables in the PHP language and the AutoIt automation script language, scalar variables in the Perl language (see sigil (computer programming)), and global variables in the Ruby language.[13]\n\u2022 In most shell scripting languages, $is used for interpolating environment variables, special variables, arithmetic computations and special characters, and for performing translation of localised strings.[13] \u2022$ is used in the ALGOL 68 language to delimit transput format regions.\n\u2022 $is used in the TeX typesetting language to delimit mathematical regions.[13] \u2022 Formulas in spreadsheets (e.g., Microsoft Excel) use$ to denote an absolute cell reference.[13]\n\u2022 In many versions of FORTRAN 66, $could be used as an alternative to a quotation mark for delimiting strings.[13] \u2022 In PL\/M,$ can be used to put a visible separation between syllables of identifiers. For example, 'Some$Name' refers to the same thing as 'SomeName'.[13] \u2022 In Haskell,$ is used as a function application operator.[13]\n\u2022 In several JavaScript frameworks starting with Prototype.js and also popular in jQuery, $is a common utility class. \u2022 In ASP.NET the dollar sign indicates an expression will follow it, when used in a tag in the web page. The expression that follows is .net language-agnostic, as it will work with c#, vb.net, or any CLR supported language. ### Operating systems \u2022 In CP\/M and subsequently in all versions of DOS (86-DOS, MS-DOS, PC-DOS, more) and derivatives,$ is used as a string terminator (Int 21h with AH=09h).[13]\n$is used by the prompt command to insert special sequences into the DOS command prompt string.[13] \u2022 In Microsoft Windows,$ is used at the end of the share name to hide a shared folder. For example, \\\\server\\share is accessible and visible through browsing, while \\\\server\\share$is accessible only by explicit reference.[13] \u2022 In Unix-like systems the$ is often part of the command prompt, depending on the user's shell and environment settings. For example, the default environment settings for the bash shell specify $as part of the command prompt. The using history expansion !$ (same as !!1$ and !-1$) means the last argument of the previous command in bash, !-2$ expands to the last argument of the penultimate command, !5$ expands into the last argument of the fifth command and so on. For example:\n> touch my_first_file\n> echo \"This is my file.\" > !$ where !$ expands into my_first_file.\n\u2022 In the LDAP directory access protocol, $is used as a line separator in various standard entry attributes such as postalAddress.[13] ### Applications ## Currencies that use the dollar or peso sign In addition to those countries of the world that use dollars or pesos, a number of other countries use the$ symbol to denote their currencies, including:\n\nAn exception is the Philippine peso, whose sign is written as .\n\nThe dollar sign is also still sometimes used to represent the Malaysian ringgit (which replaced the local dollar), though its official use to represent the currency has been discontinued .\n\nSome currencies use the cifr\u00e3o $(\\mathrm{S}\\!\\!\\!\\Vert )$, similar to the dollar sign, but always with two strokes:\n\nThe cifr\u00e3o is also used to account for over 130,000,000 domestic standard U.S. Mint (1986+) bullion U.S. silver dollars as one dollar per one troy ounce fine (99.9%), thereby avoiding confusion with debased U.S. trade dollar-denominated tokens and Federal Reserve notes.[citation needed]\n\nIn Mexico and another peso-using countries, the cifr\u00e3o is used as a dollar sign when a document uses pesos and dollars at the same time, to avoid confusions, but, when it used alone, usually is represented as US $(United States dollars). Example: US$5 (five US dollars).[citation needed]\n\nIn the United States, Mexico, Australia, New Zealand, Hong Kong, Pacific Island nations, and English-speaking Canada, the dollar or peso symbol precedes the number, unlike most currency symbols. Five dollars or pesos is written and printed as $5, whereas five cents is written as 5\u00a2. In French-speaking Canada, the dollar symbol usually appears after the number, although it sometimes appears in front of it, or instead may even be totally absent. ## Other Uses The dollar sign is also used in library cataloging to represent subsections. Also, it is used derisively to indicate greed or excess money such as in \"Micro$oft\", \"George W. Bu$h\", \"Lar$ Ulrich\", and \"Ke$ha\". ## See also ## References 1. ^ Lawrence Kinnaird (July 1976). \"The Western Fringe of Revolution,\" The Western Historical Quarterly 7(3), 259. 2. ^ 3. ^ Florian Cajori ([1929]1993). A History of Mathematical Notations (Vol. 2), 15-29. 4. ^ Arthur S. Aiton and Benjamin W. Wheeler (May 1931). \"The First American Mint\", The Hispanic American Historical Review 11(2), 198 and note 2 on 198. 5. ^ Nussbaum, Arthur (1957). A History of the Dollar. New York: Columbia University Press. p. 56. \"The foreign coins remained in circulation [in the United States], and the more important among them, especially the Spanish (including the Mexican) dollars, were declared by Congress on February 9, 1793, to be legal tender. The dollar sign,$, is connected with the peso, contrary to popular belief, which considers it to be an abbreviation of 'U.S.' The two parallel lines represented one of the many abbreviations of 'P,' and the 'S' indicated the plural. The abbreviation '$.' was also used for the peso, and is still used in Argentina.\" 6. ^ Riesco Terrero, \u00c1ngel (1983). Diccionario de abreviaturas hispanas de los siglos XIII al XVIII: Con un apendice de expresiones y formulas juridico-diplomaticas de uso corriente. Salamanca: Imprenta Varona, 350. ISBN 84-300-9090-8 7. ^ Bureau of Engraving and Printing. \"'What is the origin of the$ sign?' in FAQ Library\". Retrieved December 14, 2010.\n8. ^ F. Cajori discusses the origins of the slash-8, the Potosi mint mark, the Pillars of Hercules, the \"U.S.\", the Roman sestertius, and the Boaz and Jachin theories and discounts them in A History of Mathematical Notations (Vol. 2), 15-20.\n9. ^ Gettings, Fred (1981). The Dictionary of Occult, Hermetic, and Alchemical Sigils and Symbols. London: Routledge & Kegan Paul Ltd. p.\u00a086. ISBN\u00a00-7100-0095-2.\n10. ^ James, James Alton (1970) [1937]. Oliver Pollock: The Life and Times of an Unknown Patriot. Freeport: Books for Libraries Press. p.\u00a0356. ISBN\u00a09780836955279.\n11. ^ Pub. L. No. 109-145, 119 Stat. 2664 (Dec. 22, 2005).\n12. ^ Cuhaj, p. 100, 321-22\n13. ^ a b c d e f g h i j k l m n o p \"Dollar Sign ($)\" (PDF). Retrieved 2010-03-28. (Note: this paper essentially reproduces an older version of this Wikipedia article.) \u2022 Cajori, Florian (1993). A History of Mathematical Notations. New York: Dover (reprint). ISBN 0-486-67766-4. - contains section on the history of the dollar sign, with much documentary evidence supporting the \"pesos\" theory. \u2022 Cuhaj, George (2009). Standard Catalog of United States Paper Money. Krause Publications, 28th Ed.. ISBN 0-89689-939-X. \u2022 Ovason, David (2004-11-30). The Secret Symbols of the Dollar Bill. Harper Paperbacks (reprint). ISBN 0-06-053045-6. Wikimedia Foundation. 2010. ### Look at other dictionaries: \u2022 dollar sign \u2014 (also dollar mark) \u25ba NOUN \u25aa the sign$, representing a dollar \u2026 \u00a0 English terms dictionary\n\n\u2022 dollar sign \u2014 dollar ,sign noun count the symbol $, used to show that an amount is in dollars see dollar signs AMERICAN INFORMAL to think only about how much money something or someone is worth \u2026 Usage of the words and phrases in modern English \u2022 dollar sign \u2014 \u2606 dollar sign n. a symbol ($) for dollar or dollars \u2026 \u00a0 English World dictionary\n\n\u2022 dollar sign \u2014 UK \/ US noun [countable] Word forms dollar sign : singular dollar sign plural dollar signs the symbol $, used to show that an amount is in dollars \u2022 see dollar signs \u2026 English dictionary \u2022 dollar sign \u2014 noun 1. a symbol of commercialism or greed (Freq. 1) he worships the almighty dollar the dollar sign means little to him \u2022 Syn: \u2191dollar, \u2191dollar mark \u2022 Hypernyms: \u2191symbol 2 \u2026 Useful english dictionary \u2022 dollar sign \u2014 (also dollar mark) noun the sign$, representing a dollar \u2026 \u00a0 English new terms dictionary\n\n\u2022 dollar sign \u2014 noun Date: 1881 a mark $placed before a number to indicate that it stands for dollars called also dollar mark \u2026 New Collegiate Dictionary \u2022 dollar sign \u2014 n. symbol used to signify currencies that are based on the unit of a dollar,$ \u2026 \u00a0 English contemporary dictionary\n\n\u2022 dollar sign \u2014 An abbreviation ($) for a dollar or dollars. 1 Am J2d Abbr \u00a7 9 \u2026 Ballentine's law dictionary \u2022 dollar sign \u2014 dol\u2032lar sign n. num the symbol$ before a number indicating that the number represents dollars \u2022 Etymology: 1855\u201360, amer \u2026 \u00a0 From formal English to slang","date":"2019-10-19 16:52:03","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 2, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.47122442722320557, \"perplexity\": 5083.3785096959145}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-43\/segments\/1570986697439.41\/warc\/CC-MAIN-20191019164943-20191019192443-00011.warc.gz\"}"} | null | null |
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array('parent_category, name', 'required'),
array('parent_category', 'numerical', 'integerOnly'=>true),
array('name', 'length', 'max'=>64),
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array('id, parent_category, name', 'safe', 'on'=>'search'),
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return array(
'id' => 'ID',
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* Retrieves a list of models based on the current search/filter conditions.
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* Typical usecase:
* - Initialize the model fields with values from filter form.
* - Execute this method to get CActiveDataProvider instance which will filter
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* - Pass data provider to CGridView, CListView or any similar widget.
*
* @return CActiveDataProvider the data provider that can return the models
* based on the search/filter conditions.
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$criteria=new CDbCriteria;
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$criteria->compare('parent_category',$this->parent_category);
$criteria->compare('name',$this->name,true);
return new CActiveDataProvider($this, array(
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/**
* Returns the static model of the specified AR class.
* Please note that you should have this exact method in all your CActiveRecord descendants!
* @param string $className active record class name.
* @return Subcategory the static model class
*/
public static function model($className=__CLASS__)
{
return parent::model($className);
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Wilhelm Raabe, né le à Eschershausen (duché de Brunswick) et mort le à Brunswick (duché de Brunswick), est un écrivain allemand.
Biographie
Wilhelm Raabe est le fils du fonctionnaire de justice Gustav Karl Maximilian Raabe (1800-1845) et de Johanne Auguste Frederike Jeep (1807-1874). Il nait dans la petite ville de Eschershausen, dans le Weserbergland (Basse-Saxe) et passe son enfance à Holzminden et à Stadtoldendorf. À la mort de son père, sa famille s'installe à Wolfenbüttel.
Après avoir quitté prématurément l'école et abandonné en 1853 les études de libraire qu'il avait commencées à Magdeburg, Wilhelm Raabe tente en vain de passer son baccalauréat à Wolfenbüttel. Son statut de fils de notable l'autorise cependant à suivre des cours de philologie à l'université Frédéric-Guillaume de Berlin (actuellement université Humboldt). Il écrit et publie à cette époque, sous le pseudonyme de Jacob Corvinus, son premier roman La Chronique de la Rue des moineaux (Die Chronik der Sperlingsgasse). « Corvinus » est un jeu de mots sur la traduction latine de son nom, « Rabe » signifiant « corbeau » en allemand. Selon l'avis général, et de son propre aveu, ce roman reste son plus grand succès littéraire et son plus gros succès financier.
Le , il épouse Berta Emilie Wilhelmine Leiste (petite-fille du pédagogue, mathématicien et géographe Christian Leiste). Le couple donne naissance à quatre filles : Margarethe (née en 1863), Elisabeth (née en 1868), Klara (née en 1872) et Gertrud (née en 1876).
En une cinquantaine d'années, Wilhelm Raabe a publié 68 romans, récits et nouvelles, ainsi qu'un petit nombre de poèmes. Cette intense productivité est due en grande partie au fait qu'il vivait uniquement de sa plume. Son œuvre couvre un large spectre, allant du grand roman réaliste au nouvelles finement ciselées, en passant par une simple littérature de divertissement. Même si aucun de ses livres n'a atteint la popularité de son premier roman, il s'était constitué un public nombreux et fidèle.
Il est ainsi également l'auteur de Die Leute aus dem Walde (Les Gens de la forêt, 1863), Der Hungerpastor (Le Pasteur famélique, 1864), Abu Telfan (1867), Deutscher Mondschein (Clair de lune allemand, 1873) et Stopfkuchen (Gros Gourmand, 1891). Son style combine un réalisme pessimiste avec un humour à la Dickens. Il fut également peintre.
Le , grâce au soutien de l'historien et archiviste Ludwig Hänselmann, Wilhelm Raabe devient membre de la fameuse stammtisch "Die ehrlichen Kleiderseller zu Braunschweig" (les "Honnêtes Tailleurs de Braunschweig") . En 1883, il devient membre d'une autre stammtisch, appelée "Feuchter Pinsel" (la "Brosse humide"), réunissant divers artistes et amateurs d'art de la ville.
Œuvres
Die Chronik der Sperlingsgasse, 1856
Ein Frühling, Der Weg zum Lachen, 1857
Die alte Universität, Der Student von Wittenberg, Weihnachtsgeister, Lorenz Scheibenhart, Einer aus der Menge, 1858
Die Kinder von Finkenrode, Der Junker von Denow, Wer kann es wenden?, 1859
Aus dem Lebensbuch des Schulmeisterleins Michel Haas, Ein Geheimnis, 1860
Auf dunkelm Grunde, Die schwarze Galeere, Der heilige Born, Nach dem großen Kriege, 1861
Unseres Herrgotts Kanzlei, Das letzte Recht, 1862
Eine Grabrede aus dem Jahre 1609, Die Leute aus dem Walde, Holunderblüte, Die Hämelschen Kinder, 1863
Der Hungerpastor, Keltische Knochen, 1864
Else von der Tanne, Drei Federn, 1865
Die Gänse von Bützow, Sankt Thomas, Gedelöcke, 1866
Abu Telfan; oder Heimkehr aus dem Mondgebirge, 1867
Theklas Erbschaft, 1868
Im Siegeskranze, 1869
Der Schüdderump, Der Marsch nach Hause, Des Reiches Krone, 1870
Der Dräumling, 1872
Deutscher Mondschein, Christoph Pechlin, 1873
Meister Autor oder Die Geschichten vom versunkenen Garten, Höxter und Corvey, 1874
Frau Salome, Vom alten Proteus, Eulenpfingsten, 1875
Die Innerste, Der gute Tag, Horacker, 1876
Auf dem Altenteil, 1878
Alte Nester, Wunnigel, 1879
Deutscher Adel, 1880
Das Horn von Wanza, 1881
Fabian und Sebastian, 1882
Prinzessin Fisch, 1883
Villa Schönow, Pfisters Mühle, Zum wilden Mann, Ein Besuch, 1884
Unruhige Gäste, 1885
Im alten Eisen, 1887
Das Odfeld, 1888
Der Lar, 1889
Stopfkuchen, 1891
Gutmanns Reisen, 1892
Kloster Lugau, 1894
Die Akten des Vogelsangs, 1896
Hastenbeck, 1899
Altershausen (Fragment), 1902 (publication 1911)
Bibliographie
: Wilhelm Raabe. "Krähenfelder Geschichten". Lang, Bern u. a. 1990. (= Narratio; 3) ISBN 3-261-04204-4.
: Neues über Wilhelm Raabe. 10 Annäherungsversuche an einen verkannten Schriftsteller. Niemeyer, Tübingen 1988. (= Untersuchungen zur deutschen Literaturgeschichte; 46) ISBN 3-484-32046-X.
Søren R. Fauth, und Eberhard Rohse (Hrsg.): "Die besten Bissen vom Kuchen." Wilhelm Raabes Erzählwerk. Kontexte, Subtexte, Anschlüsse. Wallstein, Göttingen 2009, ISBN 978-3-8353-0544-1.
: Wilhelm Raabe. Sein Leben und seine Werke. Vieweg-Verlag, Braunschweig, 1937.
: Wilhelm Raabe. Eine Biographie. (Ungekürzte Ausgabe.) Deutscher Taschenbuch-Verlag, München 2006, 382 S., ISBN 3-423-34324-9.
: Wilhelm Raabe – Meistererzählungen. ISBN 3-7175-1924-7.
: Mit Dinte, Feder und Papier. Dichteralltag in Braunschweig. Wilhelm Raabes Zeit in Braunschweig 1870 bis 1910 nach Tagebuchaufzeichnungen und Briefen. Wolfenbüttel: Heckner 1999. ISBN 3-449-00909-5.
: Raabe und Tieck. Essen: Verl. Die Blaue Eule 1985. (= Wilhelm Raabe-Studien; 1) ISBN 3-924368-30-9.
Eberhard Rohse: Wie Raabe den Tod gebildet. Zur Ikonographie von Zeitlichkeit und Tod in späten Texten und Zeichnungen Wilhelm Raabes. In: (Hrsg.): Von Wilhelm Raabe und anderen. Vorträge aus dem Braunschweiger Raabe-Haus. Bielefeld: Verlag für Regionalgeschichte 2001 (= Braunschweiger Beiträge zur deutschen Sprache und Literatur; 5), S. 191–239. ISBN 3-89534-354-4.
Eberhard Rohse: "wie Joach. Heinr. Campe sagt" – zur Campe-Rezeption in Werken des Erzählers und Zeichners Wilhelm Raabe. In: Cord-Friedrich Berghahn u. Imke Lang-Groth (Hrsg.): Joachim Heinrich Campe. Dichtung, Sprache, Pädagogik und Politik zwischen Aufklärung, Revolution und Restauration. Universitätsverlag Winter, Heidelberg 2021 (= Germanisch-Romanische Monatsschrift, Beiheft 102), S. 339–368. ISBN 978-3-8253-4814-4.
Liens externes
Écrivain allemand du XIXe siècle
Écrivain allemand du XXe siècle
Écrivain du courant réaliste
Romancier allemand
Docteur honoris causa de l'université Humboldt de Berlin
Citoyen d'honneur de Brunswick
Naissance en septembre 1831
Naissance dans le duché de Brunswick
Décès en novembre 1910
Décès à Brunswick (Basse-Saxe)
Décès dans le duché de Brunswick
Décès à 79 ans | {
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// $scope.versionopt = [{label:"v1", value:1},{label:"v2", value:2}];
// $scope.version = $scope.versionopt[1].value;
$scope.targetlocationopt = [ { name:"Standard", value:'default'}, //100% kein margin
{ name:"zdfsport.de Startseite", value:'zdfsportstart'}, //feste größe kein margin
{ name:"zdf.de SB Raster", value:'zdfsbraster'}, //100% mit margin -8px
{ name:"zdf.de Faktenbox", value:'faktenbox'} ]; //über html-src
$scope.targetlocation = $scope.targetlocationopt[0].value;
$scope.usemobileurl = false;
$scope.mobileurl = "http://m.zdf.de";
$scope.slug = "unbenannt_" + (new Date()).getMilliseconds();
var self = this;
//geht nicht richtig resettet sich nicht nach rückkehr von maint nicht als service implementieren
$scope.$watch('activeTab', function () {
return $scope.$parent.activeTab;
//return wrtyuitabService.get();
},
function(newVal, oldVal) {
$scope.activeTab = newVal;
});
socket.on("progress", function(data){
if (data.msg == "start"){
console.log("start",data.max); // mal 3 plus start und ende event
$scope.progressSetup(data.max*2+2);
$scope.progressProgress();
} else if (data.msg == "speichern") {
console.log("speichern",data.name);
$scope.progressProgress();
} else if (data.msg == "gepspeichert") {
console.log("gepspeichert",data.name);
$scope.progressProgress();
} else if (data.msg == "finished") {
console.log("finished");
//progress 100%
$scope.progressSetup(10);
$scope.progressFinish();
}
})
socket.on("applogic.error", function(err){
console.log("Error",err);
alert("Starten sie einen neuen Versuch.");
})
socket.on('applogic.CodeComplete', function (id) {
console.log("Generation complete");
//todo auf event umschreiben
$scope.pickerData = id;
});
$scope.renderCode = function renderCode(){
//absenden
socket.emit('socket.renderImageRequest', {
code: $scope.code,
overwrite: $scope.overwrite,
screensize: $scope.screensize,
version: "v2", //$scope.version.value", //hidden
targetlocation: $scope.targetlocation,
autorefresh: $scope.autorefresh,
bgimageurl: $scope.bgimageurl,
mobileurl: $scope.mobileurl,
slug: $scope.slug
});
};
}); | {
"redpajama_set_name": "RedPajamaGithub"
} | 1,339 |
Excellent Quality!—Thrilled with my purchase! Very well made and perfect for my students! I work with K-5 students and provide math intervention. I am amazed at how helpful the Rekenreks are. I debated about making my own. I've seen ways to make them with pipe cleaners and beads. I also saw other versions for sale on Amazon. But this came highly recommended by Build Math Minds, a math learning community to which I belong. When I received my set of 7 Rekenreks, I was impressed with how well made they are. I'm considering buying the large one for teachers or ones with more rows for my older students. Well worth the investment for this Rekenrek version. Oh, and did I mention there was even a little baggie of Hershey kisses inside the box when my package was delivered? What a sweet gesture (pun intended) from this company! | {
"redpajama_set_name": "RedPajamaC4"
} | 3,281 |
{"url":"http:\/\/dataspace.princeton.edu\/jspui\/handle\/88435\/dsp01794080550","text":"Please use this identifier to cite or link to this item: http:\/\/arks.princeton.edu\/ark:\/88435\/dsp01794080550\n Title: The Localist Tradition in America Authors: Latimer, Trevor Patrick Advisors: Lane, Melissa S Contributors: Politics Department Keywords: American political thoughtlocal controllocal governmentlocalismsubsidiarity Subjects: Political scienceHistory Issue Date: 2015 Publisher: Princeton, NJ : Princeton University Abstract: The American political tradition is steeped in localism. Arguments on behalf of the local and local government are ubiquitous in American history. Here, I provide an analysis, description, and critique of the \u201ctradition of localism\u201d in American political culture with an analytical introduction, three case studies, and a normative conclusion. The existing literature on localism is mired in conceptual confusion. Therefore, I first clarify the concept of localism. Localism is actually an umbrella concept covering three sub-concepts: localism as attachment (social), localism as activity (political), and localism as theory (ideological). Two insights from political geography further clarify localism as activity: (1) \u201cthe local\u201d is relative and (2) conceptualizations of space are political. Localism as activity is defined as attempts to alter the hierarchy of governmental scale by transferring political authority from higher to lower-level governments. In chapter 2, I show that the American Anti-Federalists\u2019 localism is held together by two spatial theses: (1) attachment to government is negatively correlated with geographical distance, and (2) diversity is positively correlated with territorial size. My interpretation improves on the existing literature by providing a unified account of the Anti-Federalists\u2019 spatio-political commitments. In chapter 3, I show how popular sovereignty in the antebellum era, as advanced by Stephen A. Douglas, is best understood as an example of localism as activity rather than an offshoot of the ideal of popular sovereignty in the western political tradition. I also show that the debate over slavery in the territories is usefully understood as a conflict in the politics of space over how to define \u201cthe people.\u201d In chapter 4, I show how the ideology of local control, as a form of localism as theory, played a causal role in the demise of school desegregation beginning in the 1970s. The Supreme Court and the American public treated the benefits of local control and neighborhood schools as considerations to be weighed against desegregation. I conclude by critiquing the principle of subsidiarity\u2014a principle that captures the implicit normative claims of the localist tradition in the United States. URI: http:\/\/arks.princeton.edu\/ark:\/88435\/dsp01794080550 Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: http:\/\/catalog.princeton.edu\/ Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Politics\n\nFiles in This Item:\nThis content is embargoed until 2017-09-30. For more information contact the Mudd Manuscript Library.","date":"2017-01-22 22:30:21","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.23251669108867645, \"perplexity\": 6693.886164686859}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-04\/segments\/1484560281649.59\/warc\/CC-MAIN-20170116095121-00156-ip-10-171-10-70.ec2.internal.warc.gz\"}"} | null | null |
Q: Move SVN changes to git In the company where I work, we are currently in the process of migrating from SVN to git and also updating frameworks and languages version in the process. as a result i currently have 2 repositories, one in svn and another one git which both have received many commits after the initial migration.
Our git repository is GitHub and I used the GitHub migration tool to create the initial commit bringing all the history from svn to the Github repo.
My problem is that I need now to update the GitHub repository with the most recent bug fixes that have been applied to svn. is there any way to sync these 2 repos without doing it manually?
Any help would be appreciated since I'm applying commit by commit manually to the GitHub branch but there are so many changes that this is going to take forever.
My expectation is to be able to merge automatically the svn repo commits (history not needed) to the GitHub branch.
A: Use git-svn to create a git "mirror" of your Subversion repository. Then cherry-pick or merge changes as needed to your branch in GitHub.
Since git-svn operates bi-directionally, you can use the same setup for pushing changes from GitHub into the Subversion repository.
A: You can try svn2git, I is a tiny utility for migrating projects from Subversion to Git while keeping the trunk, branches and tags where they should be.
Here is the link https://github.com/iteman/svn2git/tree/master
Or you can have a look in this script (It is one way sync from svn to git)
https://gist.github.com/stefanfoulis/909746
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,543 |
\section{Introduction}
\label{introduction}
Quantum chromodynamics (QCD) predicts a phase transition from a hadron gas (HG) phase to a quark gluon plasma (QGP) phase with variations of thermodynamic parameters such as temperature ($T$) and/or baryon density ($\mu_{B}$)~\cite{Fodor:2004nz}.
Lattice QCD calculations indicate that the chiral and de-confinement phase transitions are a smooth crossover along the temperature axis, i.e. with $\mu_{B}$ = 0, while various other models predict that the phase transition becomes first order at high baryon density~\cite{Halasz:1998qr}. The existence of the QCD critical point is thus expected as the first order phase transition line should end somewhere at finite $\mu_{B}$ and $T$.
In order to study the properties of QGP in these experiments, it is important to choose an observable which is sensitive enough to the medium property in the early stage.
It has been proposed that the shapes of the event-by-event net-charge distributions are sensitive to
the presence of the critical point, as they are related to the conserved number susceptibilities of the system and hence to the correlation length~\cite{Gavai:2010zn}. Additionally, the shape of the emission source function can also provide signals for a second-order phase transition or proximity to the QCD critical point~\cite{Csorgo:2005it}. Two-pion correlation measurements provide important information about the space-time evolution of the particle emitting source in the collision. An emitting system which undergoes a strong first order phase transition is expected to demonstrate a much larger space-time extent than would be expected if the system had remained in the hadronic phase throughout the collision process.
The PHENIX detector at RHIC has explored the above possibilities in the recent Beam Energy Scan (BES) program of RHIC. During 2010 and 2011, RHIC provided \mbox{Au$+$Au}\xspace collisions to PHENIX at \mbox{$\sqrt{s_{_{NN}}}$}\xspace = 200 GeV, 62.4 GeV, 39 GeV, 27 GeV, 19.6 GeV, and 7.7 GeV. PHENIX recorded Cu+Cu collisions at \mbox{$\sqrt{s_{_{NN}}}$}\xspace = 200 GeV during 2005.
Results from PHENIX covering net-charge fluctuations and two-pion interferometry measurements, are discussed here.
\section{Net-charge Fluctuations}
PHENIX has measured the distributions of net-charge multiplicity (N = $N^{+}$ - $N^{-}$) and their various moments (mean ($\mu$) =${<N>}$, variance ($\sigma^2$) = ${<(N-\mu)^2>}$, skewness (S) = $\frac{<(N-\mu)^3>}{\sigma^3}$ and kurtosis ($\kappa$) =$\frac{<(N-\mu)^4>}{\sigma^4} -3$ ) at several beam energies~\cite{Adare:2015aqk}. The charged hadrons selected for this analysis cover transverse momentum (\mbox{$p_T$}\xspace) between 0.3 and 2.0 GeV/$c$ and pseudorapidity range spanning $|\eta|\leq 0.35$.
Figure~\ref{fig1} shows the efficiency corrected $\mu/\sigma^2$, $S\sigma$, $\kappa\sigma^2$, and $S\sigma^3/\mu$ as a function of \mbox{$\sqrt{s_{_{NN}}}$}\xspace for the most central (0-5\%) \mbox{Au$+$Au}\xspace collisions.
\begin{figure}[ht!]
\begin{center}
\includegraphics[scale=0.30]{Fig1.eps}
\caption{(Color online) The ratios of cumulants of net-charge distributions (a) $\mu/\sigma^{2}$ (b) S$\sigma$ (c) $\kappa\sigma^{2}$, and (d) S$\sigma^{3}/\mu$, after efficiency corrections for most central (0-5\%) \mbox{Au$+$Au}\xspace collisions. The statistical and systematic errors are shown by bars and caps, respectively. Triangles represent the efficiency corrected cumulant ratios extracted from NBD fits to positively and negatively charged particles distributions~\cite{Adare:2015aqk}.}
\label{fig1}
\end{center}
\end{figure}
In Fig.~\ref{fig1}, triangles represent the efficiency corrected cumulants ratios extracted from NBD fits to positively and negatively charged particles distributions. The $\kappa\sigma^{2}$ values are positive and constant at all the collision energies within the statistical and systematic uncertainties as is shown in Fig.~\ref{fig1}.
Comparing these measurements with the lattice calculations, freeze-out temperature ($T_{f}$) and baryon chemical potentials ($\mu_{B}$) are also extracted at freeze-out. Figure~\ref{fig2} shows the variation of $\mu_{B}$ as a function of \mbox{$\sqrt{s_{_{NN}}}$}\xspace. The extracted $\mu_{B}$ values are found comparable to the $\mu_{B}$ values extracted from particle ratio analysis given in Ref.~\cite{Cleymans:2005xv}.
\begin{figure}[ht!]
\begin{center}
\includegraphics[scale=0.27]{Fig2.eps}
\caption{(Color online) Chemical freeze-out parameter ($\mu_{B}$), extracted from PHENIX higher-moments analysis, as a function of center of mass energy (\mbox{$\sqrt{s_{_{NN}}}$}\xspace) are shown in red solid points~\cite{Adare:2015aqk}. The dashed line shows the parametrization given in Ref.~~\cite{Cleymans:2005xv} and the other experimental data are from Ref.~\cite{Cleymans:2005xv} and references therein.}
\label{fig2}
\end{center}
\end{figure}
\section{Two-pion interferometry}
PHENIX has performed measurements of two-pion correlations in Cu+Cu collisions at \mbox{$\sqrt{s_{_{NN}}}$}\xspace = 200 GeV and Au+Au collisions at \mbox{$\sqrt{s_{_{NN}}}$}\xspace = 39, 62.4 and 200 GeV~\cite{Adare:2014qvs}.
Figure~\ref{fig3} shows the two-pion correlation functions as a function of the components of the momentum difference ($\bf{q}$) between particles in the pair for several \mbox{$\sqrt{s_{_{NN}}}$}\xspace. These correlation functions are fitted with a function which incorporates Bose-Einstein enhancement and the Coulomb interaction between the pairs, to extract the HBT radii ($R_{side}$, $R_{out}$ and $R_{long}$ ). The quantities, $R^{2}_{out} - R^{2}_{side}$ and $(R_{side} - \sqrt{2}\bar{R})/R_{long}$ (see reference~\cite{Bhalerao:2005mm} for $\bar{R}$), which are related to emission duration and medium expansion velocity, respectively, are shown (Fig.~\ref{fig4}) for pair transverse mass $m_{T}$ = 0.26 GeV/$c^{2}$ to reduce the effect of position momentum correlation. Also, the PHENIX results are compared with STAR results for \mbox{$\sqrt{s_{_{NN}}}$}\xspace = 7-200 GeV and ALICE results at LHC for \mbox{$\sqrt{s_{_{NN}}}$}\xspace = 2.76 TeV. A maximum is observed as a function of \mbox{$\sqrt{s_{_{NN}}}$}\xspace in $R^{2}_{out} - R^{2}_{side}$~(Fig.~\ref{fig4}(a)) with complimentary minimum in $(R_{side} - \sqrt{2}\bar{R})/R_{long} ($Fig.~\ref{fig4} (b)). Non-monotonic behavior over a small range in \mbox{$\sqrt{s_{_{NN}}}$}\xspace may point to a softening of equation of state that may coincide with the QCD critical point.
\begin{figure}[ht!]
\begin{center}
\includegraphics[scale=0.32]{Fig3.eps}
\caption{(Color online) Correlation functions of two-pion pairs ($\pi^{+}\pi^{+}$ and $\pi^{-}\pi^{-}$) for 0-10\% central \mbox{Au$+$Au}\xspace (left) and Cu+Cu (right) collisions for pion pair transverse momenta ($\langle{k_T}\rangle$) = 0.53 GeV/c and for several \mbox{$\sqrt{s_{_{NN}}}$}\xspace. The curves represent fits to the correlation function~\cite{Adare:2014qvs}.
}
\label{fig3}
\end{center}
\end{figure}
\begin{figure}[ht!]
\begin{center}
\includegraphics[scale=0.40]{Fig4.eps}
\caption{(Color online)
The $\mbox{$\sqrt{s_{_{NN}}}$}\xspace$ dependence of (a) ($R^{2}_{out} - R^{2}_{side}$), (b) [({$R_{side}$ -$\sqrt{2}\bar{R})/R_{long}$}]. The PHENIX and STAR data points represent the results from fits to the $m_{T}$ dependence of the combined data sets~\cite{Adare:2014qvs}.
}
\label{fig4}
\end{center}
\end{figure}
\section{Summary}
PHENIX results for net-charge fluctuations and two-pion interferometry as a function of beam energy are presented. The net-charge fluctuation measurements do not give a clear indication of the presence of the QCD critical point, though the $\mu_{B}$ extracted with lattice calculations and PHENIX data are found to be consistent with previously extracted baryon chemical potentials.
A non-monotonic behavior in the quantities related to emission duration and medium expansion velocity is observed, which hints the softening of equation of state. Further, more detailed studies are required for a clear picture of QCD phase diagram.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,111 |
\section{Finite products}
We will use the following notion to ensure the CLP-compactness of finite products.
\begin{definition}
Fix $n\in\omega$. A product $X=\prod_{i\in n}X_i$ is \emph{CLP-rectangular} if for every clopen set $U\subseteq X$ and every $x\in U$ there exists a clopen rectangle $R\subseteq X$ such that $x\in R\subseteq U$.
\end{definition}
For the proof of the following proposition, see Proposition 2.4 and Proposition 2.5 in \cite{steprans}; see also Theorem 3.4 in \cite{dikranjan}.
\begin{proposition}[Stepr\={a}ns and \v{S}ostak]\label{clprectangular} Fix $n\in\omega$. Assume that $X_i$ is CLP-compact for every $i\in n$. Then $\prod_{i\in n}X_i$ is CLP-compact if and only if it is CLP-rectangular.
\end{proposition}
From now on, we will always assume that $\mathcal{F}_i$ is a collection of non-empty pairwise disjoint closed subsets of $\mathbb{N}^\ast$ for every $i\in\omega$. Given $p\in {}^{<\omega}\omega$, we will denote by $n(p)\in\omega$ the domain of $p$. We will use the notation
$$
X_p=\prod_{i\in n(p)}X(\mathcal{F}_{p(i)})
$$
for finite products, where repetitions of factors are allowed. Also, if $i\in n(p)$, we will denote by $X_{p-i}$ the subproduct $\prod_{j\in n(p)\setminus\{i\}}X(\mathcal{F}_{p(j)})$.
The following definitions isolate the multidimensional versions of `finiteness' and `cofiniteness' that we need. For every $p\in {}^{<\omega}\omega$ and $N\in\omega$, we will denote the union of the `initial stripes of height $N$' as
$$
S^N_p=\bigcup_{i\in n(p)}\{x\in X_p: x_i\in N\}\subseteq X_p.
$$
Also define
$$
T^N_p=X_p\setminus S^N_p=\prod_{i\in n(p)}(X(\mathcal{F}_{p(i)})\setminus N).
$$
\begin{proposition}\label{fincofimplies}
Assume that for every $p\in {}^{<\omega}\omega$ and every clopen set $U\subseteq X_p$, either $U\subseteq S^N_p$ or $T^N_p\subseteq U$ for some $N\in\omega$. Then $X_p$ is CLP-compact for every $p\in {}^{<\omega}\omega$.
\end{proposition}
\begin{proof}
We will use induction on $n(p)$. The case $n(p)=1$ is obvious. So assume that $X_p$ is CLP-compact for every $p\in {}^{n}\omega$ and let $p\in {}^{n+1}\omega$. By Proposition $\ref{clprectangular}$, it is enough to prove that $X_p$ is CLP-rectangular. So let $U\subseteq X_p$ be a clopen set and fix $N\in\omega$ such that $U\subseteq S^N_p$ or $T^N_p\subseteq U$. We will show that for every $x\in U$ there exists a clopen rectangle $R\subseteq X_p$ such that $x\in R\subseteq U$.
First we will assume that $x\in U$ has at least one coordinate in $N$, say coordinate $i\in n(p)$. It is easy to check that the cross-section
$$
V=\{y\in X_{p-i}:y\cup\{(i,x_i)\}\in U\}
$$
is clopen in $X_{p-i}$. Observe that $X_{p-i}$ is homeomorphic to $X_{p'}$ for some $p'\in {}^{n}\omega$. Therefore, by the inductive hypothesis and Proposition $\ref{clprectangular}$, there exists a clopen rectangle $Q\subseteq X_{p-i}$ such that $\pi_{p-i}(x)\in Q\subseteq V$, where $\pi_{p-i}:X_p\longrightarrow X_{p-i}$ is the natural projection. It is clear that the desired clopen rectangle is $R=\{y\in X_p :\pi_{p-i}(y)\in Q\textrm{ and }y_i=x_i\}$.
On the other hand, if $x\in U$ has no coordinate in $N$ then the case $U\subseteq S^N_p$ is impossible. Therefore $T^N_p\subseteq U$, so that the desired clopen rectangle is $R=T^N_p$ itself.
\end{proof}
We will also need the following definitions. Let
$$
\mathbb{S}^N_p=S^N_p\cap (\mathbb{N}^{n(p)})=\bigcup_{i\in n(p)}\{x\in \mathbb{N}^{n(p)}: x_i\in N\},
$$
$$
\mathbb{T}^N_p=T^N_p\cap (\mathbb{N}^{n(p)})=\mathbb{N}^{n(p)}\setminus\mathbb{S}^N_p=(\mathbb{N}\setminus N)^{n(p)}.
$$
The next two lemmas show that, in order to achieve what is required by Proposition $\ref{fincofimplies}$, we can just look at the trace of clopen sets on $\mathbb{N}^{n(p)}$.
\begin{lemma}\label{finimpliesfin}
Fix $p\in {}^{<\omega}\omega$. Assume that $U\subseteq X_p$ is a clopen set such that $U\cap (\mathbb{N}^{n(p)})\subseteq \mathbb{S}^N_p$. Then $U\subseteq S^N_p$.
\end{lemma}
\begin{proof}
Assume, in order to get a contradiction, that $x\in U\setminus S^N_p$. For all $i\in n(p)$ such that $x_i\in\mathbb{N}$, let $N_i=\{x_i\}\subseteq\mathbb{N}\setminus N$. For all $i\in n(p)$ such that $x_i\in \mathcal{F}_{p(i)}$, let $N_i=\{x_i\}\cup A_i$ be a neighborhood of $x_i$ in $X(\mathcal{F}_{p(i)})$ such that $A_i\subseteq\mathbb{N}\setminus N$. Since $U$ is open, by shrinking each $N_i$ if necessary, we can make sure that $\prod_{i\in n(p)}N_i\subseteq U$. This is a contradiction, because $\varnothing\neq (\prod_{i\in n(p)}N_i)\cap (\mathbb{N}^{n(p)})\subseteq \mathbb{T}^N_p$.
\end{proof}
\noindent Similarly, one can prove the following.
\begin{lemma}\label{cofimpliescof}
Fix $p\in {}^{<\omega}\omega$. Assume that $U\subseteq X_p$ is a clopen set such that $\mathbb{T}^N_p\subseteq U\cap (\mathbb{N}^{n(p)})$. Then $T^N_p\subseteq U$.
\end{lemma}
Fix $p\in {}^{<\omega}\omega$. We will say that a subset $D$ of $\mathbb{N}^{n(p)}$ is \emph{diagonal} if $D\nsubseteq \mathbb{S}^N_p$ and $\mathbb{T}^N_p\nsubseteq D$ for all $N\in\omega$ and the restriction $\pi_i\upharpoonright D$ of the natural projection $\pi_i:\mathbb{N}^{n(p)}\longrightarrow \mathbb{N}$ is injective for every $i\in n(p)$.
Given $p\in {}^{<\omega}\omega$, we will say that a pair $(D,E)$ is \emph{$p$-diagonal} if $D$ and $E$ are both diagonal subsets of $\mathbb{N}^{n(p)}$. A pair $(D,E)$ is \emph{diagonal} if it is $p$-diagonal for some $p$ as above. If $(D,E)$ is such a pair, consider the following statement.
\begin{enumerate}
\item[$\textrm{\Coffeecup}(D,E)$] There exist $K_0,\ldots,K_{n(p)-1}$, with $K_i\in \mathcal{F}_{p(i)}$ for every $i\in n(p)$, such that $D\cap (A_{0}\times\cdots \times A_{n(p)-1})$ and $E\cap (A_{0}\times\cdots \times A_{n(p)-1})$ are both non-empty whenever $A_{0},\ldots ,A_{n(p)-1}\subseteq \mathbb{N}$ satisfy $K_i\subseteq A_i^\ast$ for every $i\in n(p)$.
\end{enumerate}
\begin{proposition}\label{coffeeimplies} Fix $p\in {}^{<\omega}\omega$. Assume that the family $\{\mathcal{F}_i:i\in \omega\}$ is such that condition $\textrm{\Coffeecup}(D,E)$ holds for every $p$-diagonal pair $(D,E)$. If $U\subseteq X_p$ is a clopen set, then there exists $N\in\omega$ such that either $U\cap (\mathbb{N}^{n(p)})\subseteq \mathbb{S}^N_p$ or $\mathbb{T}^N_p\subseteq U\cap (\mathbb{N}^{n(p)})$.
\end{proposition}
\begin{proof}
Assume, in order to get a contradiction, that $U\cap (\mathbb{N}^{n(p)})\nsubseteq \mathbb{S}^N_p$ and $\mathbb{T}^N_p\nsubseteq U\cap (\mathbb{N}^{n(p)})$ for every $N\in\omega$. Then it is possible to construct (in $\omega$ steps) diagonal subsets $D$ and $E$ of $\mathbb{N}^{n(p)}$ such that $D\subseteq U$ and $E\subseteq X_p\setminus U$.
Now let $K_{0},\ldots ,K_{n(p)-1}$ be as given by condition $\textrm{\Coffeecup}(D,E)$. Define $x\in X_p$ by setting $x_i=K_i$ for every $i\in n(p)$. It is easy to see that $x\in\overline{U}\cap (\overline{X_p\setminus U})$, which contradicts the fact that $U$ is clopen.
\end{proof}
\begin{theorem}\label{finitesubproducts}
Assume that the family $\{\mathcal{F}_i:i\in \omega\}$ is such that condition $\textrm{\Coffeecup}(D,E)$ holds for every diagonal pair $(D,E)$.
Then $X_p$ is CLP-compact for every $p\in {}^{<\omega}\omega$.
\end{theorem}
\begin{proof}
We will show that the hypothesis of Proposition $\ref{fincofimplies}$ holds. This follows from Proposition $\ref{coffeeimplies}$, Lemma $\ref{finimpliesfin}$ and Lemma $\ref{cofimpliescof}$.
\end{proof}
\section{The full product}
In this section we will show how to ensure that $P=\prod_{i\in\omega}X(\mathcal{F}_i)$ is non-CLP-compact. Consider the following condition. Recall that a family $\mathcal{L}$ is \emph{linked} if $K\cap L\neq\varnothing$ whenever $K,L\in\mathcal{L}$.
\begin{enumerate}
\item[$\textrm{\Bicycle}$] For every $I\in [\omega]^\omega$, the family $\mathcal{L}=\{x_i:i\in I\}$ is not linked for any $x\in\prod_{i\in I}\mathcal{F}_i$.
\end{enumerate}
\begin{theorem}\label{fullproduct}
Assume that the family $\{\mathcal{F}_i:i\in\omega\}$ is such that condition $\textrm{\Bicycle}$ holds. Then $P=\prod_{i\in\omega}X(\mathcal{F}_i)$ can be written as the disjoint union of infinitely many of its non-empty clopen subsets.
\end{theorem}
\begin{proof}
For each $n\in\omega$, define
$$
U_n=\{x\in P:x_i=n\textrm{ whenever }0\leq i\leq n\}.
$$
It is easy to check that each $U_n$ is open (actually, clopen), non-empty, and that $U_i\cap U_j=\varnothing$ whenever $i\neq j$. Therefore we just need to show that $V=P\setminus\bigcup_{n\in\omega}U_n$ is open.
So fix $x\in V$ and consider $I=\{i\in\omega: x_i\notin\mathbb{N}\}$. First assume that $I$ is finite. If there exist $i,j\notin I$, say with $i<j$, such that $x_i\neq x_j$ then $\{y\in P:y_i=x_i\textrm{ and }y_j=x_j\}\setminus\bigcup_{n\in j}U_n$ is an open neighborhood of $x$ which is contained in $V$. So assume that $x_i=x_j$ whenever $i,j\notin I$. Since $x\in V$, we must have $I\neq\varnothing$. So fix $i\in I$ and $j\notin I$, say with $i<j$ (the other case is similar). Let $N_i=\{x_i\}\cup A_i$ be a neighborhood of $x_i$ such that $x_j\notin A_i$. Then $\{y\in P:y_i\in N_i\textrm{ and }y_j=x_j\}\setminus\bigcup_{n\in j}U_n$ is an open neighborhood of $x$ which is contained in $V$.
Finally, assume that $I$ is infinite. An application of condition $\textrm{\Bicycle}$ yields $i,j\in I$, say with $i<j$, such that $x_i\cap x_j=\varnothing$. But disjoint closed sets in $\mathbb{N}^\ast$ can be separated by a clopen set, therefore we can find disjoint clopen neighborhoods $N_i$ and $N_j$ of $x_i$ and $x_j$ respectively. Then $\{y\in P:y_i\in N_i\textrm{ and }y_j\in N_j\}\setminus\bigcup_{n\in j}U_n$ is an open neighborhood of $x$ which is contained in $V$.
\end{proof}
\section{The construction}
The next theorem guarantees the existence of our example: finite products will be CLP-compact by Theorem $\ref{finitesubproducts}$, while the full product will be non-CLP-compact by Theorem $\ref{fullproduct}$.
\begin{theorem}\label{construction}
There exists a family $\{\mathcal{F}_i:i\in \omega\}$ satisfying the following requirements.
\begin{itemize}
\item Each $\mathcal{F}_i$ consists of pairwise disjoint subsets of $\mathbb{N}^\ast$ of finite size.
\item The condition $\textrm{\Coffeecup}(D,E)$ holds for every diagonal pair $(D,E)$.
\item The condition $\textrm{\Bicycle}$ holds.
\end{itemize}
\end{theorem}
\begin{proof}
Enumerate as $\{(D_\eta,E_\eta):\eta\in\mathfrak{c}\}$ all diagonal pairs, where $D_\eta$ and $E_\eta$ are both diagonal subsets of $\mathbb{N}^{n(p)}$ for some $p=p(\eta)\in {}^{<\omega}\omega$ with domain $n(p)=n(\eta)\in\omega$.
We will construct $\{\mathcal{F}_i:i\in \omega\}$ by transfinite recursion in $\mathfrak{c}$ steps: in the end we will set $\mathcal{F}_i=\bigcup_{\xi\in\mathfrak{c}} \mathcal{F}_i^\xi$ for every $i\in\omega$. Start with $\mathcal{F}_i^0=\varnothing$ for each~$i$. By induction, we will make sure that the following requirements are satisfied.
\begin{enumerate}
\item $\mathcal{F}_i^\eta\subseteq\mathcal{F}_i^\mu$ whenever $\eta\leq\mu\in\mathfrak{c}$.
\item\label{small} $|\bigcup_{i\in\omega}\bigcup\mathcal{F}^\eta_i|<2^{\mathfrak{c}}$ for every $\eta\in\mathfrak{c}$.
\item\label{killbound} The condition $\textrm{\Coffeecup}(D_\eta,E_\eta)$, where $(D_\eta,E_\eta)$ is a $p$-diagonal pair, is satisfied at stage $\xi=\eta+1$: that is, the witness $K_i$ is already in $\mathcal{F}_{p(i)}^{\eta+1}$ for each $i\in n(p)$.
\end{enumerate}
At a limit stage $\xi$, just let $\mathcal{F}_i^\xi=\bigcup_{\eta\in\xi}\mathcal{F}_i^\eta$ for every $i\in\omega$.
At a successor stage $\xi=\eta+1$, assume that $\mathcal{F}_i^\eta$ is given for each $i$. Let $p=p(\eta)$. First, define $W=\bigcup_{i\in \omega}\bigcup\mathcal{F}^\eta_i$ and observe that $|W|<2^\mathfrak{c}$ by $(\ref{small})$. Set $\tau_i=\pi_i\upharpoonright D_\eta$ for every $i\in n(p)$. Since each $\tau_i$ is injective, it makes sense to consider the induced function $\tau_i^\ast : D_\eta^\ast\longrightarrow \mathbb{N}^\ast$. Recall that the explicit definition is given by
$$
\tau_i^\ast(\mathcal{U})=\{S\subseteq\mathbb{N}: \tau_i^{-1}[S]\in\mathcal{U}\}.
$$
It is easy to check that each $\tau_i^\ast$ is injective. Therefore, since $|D_\eta^\ast|=2^\mathfrak{c}$, it is possible to choose
$$
\mathcal{U}^\eta\in D_\eta^\ast\setminus ((\tau_{0}^\ast)^{-1}[W]\cup\cdots\cup(\tau_{n(p)-1}^\ast)^{-1}[W]).
$$
Let $\mathcal{U}^\eta_i=\tau_i^\ast(\mathcal{U}^\eta)$ for every $i\in n(p)$.
\noindent Now, define $Z=W\cup\{\mathcal{U}^\eta_i:i\in n(p)\}$. Set $\sigma_i=\pi_i\upharpoonright E_\eta$ for every $i\in n(p)$. As above, it is possible to choose
$$
\mathcal{V}^\eta\in E_\eta^\ast\setminus ((\sigma_{0}^\ast)^{-1}[Z]\cup\cdots\cup (\sigma_{n(p)-1}^\ast)^{-1}[Z]).
$$
Let $\mathcal{V}^\eta_i=\sigma_i^\ast(\mathcal{V}^\eta)$ for every $i\in n(p)$.
\noindent We conclude the successor stage by setting
$$
\mathcal{F}_k^{\eta+1}=\mathcal{F}_k^\eta\cup\{\{\mathcal{U}^\eta_i:i\in p^{-1}(k)\}\cup\{\mathcal{V}^\eta_i:i\in p^{-1}(k)\}\}
$$
for every $k\in\textrm{ran} (p)$ and $\mathcal{F}_{k}^{\eta+1}=\mathcal{F}_{k}^\eta$ for every $k\in\omega\setminus\textrm{ran} (p)$.
Next, we will verify that condition $\textrm{\Bicycle}$ holds. Assume, in order to get a contradiction, that $I\in [\omega]^\omega$ and $x\in\prod_{i\in I}\mathcal{F}_i$ are such that $\mathcal{L}=\{x_i:i\in I\}$ is linked. Observe that the only possible equalities among points of $\mathbb{N}^\ast$ produced in our construction are those in the form $\mathcal{U}^\eta_i=\mathcal{U}^\eta_j$ or $\mathcal{V}^\eta_i=\mathcal{V}^\eta_j$ for some $i,j\in n(\eta)$. Therefore each element of $\mathcal{L}$ must have been added to some $\mathcal{F}_k$ at the same stage $\xi=\eta+1$. Since $I$ is infinite, we can pick $k\in I\setminus\textrm{ran} (p(\eta))$. It is clear from the construction that $x_k\in\mathcal{L}$ cannot have been added to $\mathcal{F}_k$ at stage $\xi=\eta+1$.
Finally, we will verify that $(\ref{killbound})$ holds. For every $i\in n(p)$, set
$$
K_i=\{\mathcal{U}^\eta_j:j\in p^{-1}(p(i))\}\cup\{\mathcal{V}^\eta_j:j\in p^{-1}(p(i))\}\in\mathcal{F}_{p(i)}^{\eta+1}.
$$
Suppose $A_{0},\ldots,A_{n(p)-1}\subseteq\mathbb{N}$ are such that $K_i\subseteq A_i^\ast$ for every $i\in n(p)$. In particular $A_i\in\mathcal{U}^\eta_i$ for every $i\in n(p)$. By the definition of the induced functions, we have $\tau_{i}^{-1}[A_i]\in \mathcal{U}^\eta$ for every $i\in n(p)$. Therefore
$$
D_\eta\cap (A_{0}\times\cdots \times A_{n(p)-1})=D_\eta\cap\tau_{0}^{-1}[A_{0}]\cap \cdots\cap \tau_{n(p)-1}^{-1}[A_{n(p)-1}]
$$
is non-empty. By the same argument, using $\mathcal{V}^\eta$, one can show that $E_\eta\cap (A_{0}\times\cdots \times A_{n(p)-1})$ is non-empty.
\end{proof}
\section{Arbitrarily large products}
The main idea behind the next theorem is due to Frol\'{\i}k (see the `Proof of $\textrm{B}$ (using $\textrm{B}'$)' in \cite{frolik}). To show that $X^\omega$ can be written as the disjoint union of infinitely many of its non-empty clopen subsets, we will proceed as in the proof of Theorem 9.10 in \cite{comfort2}.
\begin{theorem}\label{singlespace}
There exists a Hausdorff space $X$ such that $X^n$ is CLP-compact for every $n\in\omega$, while $X^\omega$ can be written as the disjoint union of infinitely many of its non-empty clopen subsets.
\end{theorem}
\begin{proof}
Let $\{\mathcal{F}_i:i\in\omega\}$ be the family given by Theorem $\ref{construction}$ and set $X_i=X(\mathcal{F}_i)$ for every $i\in\omega$. It follows from Theorem $\ref{finitesubproducts}$ and Theorem $\ref{fullproduct}$ that $\{X_i:i\in\omega\}$ is a collection of Hausdorff spaces such that $X_p=\prod_{i\in n(p)}X_{p(i)}$ is CLP-compact for every $p\in {}^{<\omega}\omega$, while $\prod_{i\in\omega}X_i$ can be written as the disjoint union of infinitely many of its non-empty clopen subsets.
Define $X$ as the topological space with underlying set the disjoint union $\{0\}\oplus X_0\oplus X_1\oplus\cdots$ and with the coarsest topology satisfying the following requirements.
\begin{itemize}
\item Whenever $U$ is an open subset of $X_i$ for some $i\in\omega$, the set $U$ is also open in $X$.
\item The tail $\{0\}\cup\bigcup_{i\leq j<\omega}X_j$ is open in $X$ for every $i\in\omega$.
\end{itemize}
It is easy to check that $X$ is Hausdorff.
We will prove that $X^n$ is CLP-compact by induction on $n$. The case $n=1$ is obvious. So assume that $X^n$ is CLP-compact and consider a cover $\mathcal{C}$ of $X^{n+1}$ consisting of clopen sets. Since
$$
S=\bigcup_{i\in n+1}\{x\in X^{n+1}:x_i=0\}
$$
is a finite union of subspaces of $X^{n+1}$ that are homeomorphic to $X^n$, there exist $\mathcal{D}\in[\mathcal{C}]^{<\omega}$ such that $S\subseteq \bigcup\mathcal{D}$. It follows that there exists $N\in\omega$ such that $X^{n+1}\setminus (X_0\oplus\cdots\oplus X_{N-1})^{n+1}\subseteq\bigcup\mathcal{D}$. But
$$
T=(X_0\oplus\cdots\oplus X_{N-1})^{n+1}
$$
is homeomorphic to a finite union of spaces of the form $X_p$ for some $p\in {}^{n+1}\omega$, hence it is CLP-compact. Therefore there exists $\mathcal{E}\in[\mathcal{C}]^{<\omega}$ such that $T\subseteq\bigcup\mathcal{E}$. Hence $\mathcal{D}\cup\mathcal{E}$ is the desired finite subcover of $\mathcal{C}$.
Finally, we will show that $X^\omega$ can be written as the disjoint union of infinitely many of its non-empty clopen subsets by constructing a continuous surjection $f:X^\omega\longrightarrow\prod_{i\in\omega}X_i$. Since every $X_i$ is clopen in $X$, we can get a continuous surjection $f_i:X\longrightarrow X_i$ by letting $f_i$ be the identity on $X_i$ and constant on $X\setminus X_i$. Now simply let $f=\prod_{i\in\omega}f_i$ (that is, for every $x\in X^\omega$, define $y=f(x)$ by setting $y_i=f_i(x_i)$ for every $i\in\omega$).
\end{proof}
\begin{corollary}\label{secondhalf}
For every infinite cardinal $\kappa$, there exists a collection $\{X_\xi:\xi\in\kappa\}$ of Hausdorff spaces such that $\prod_{\xi\in F}X_\xi$ is CLP-compact for every $F\in [\kappa]^{<\omega}$, while $\prod_{\xi\in\kappa}X_\xi$ is non-CLP-compact.
\end{corollary}
\begin{proof}
Let $X_\xi=X$ for every $\xi\in\kappa$, where $X$ is the space given by Theorem $\ref{singlespace}$.
\end{proof}
\noindent\textbf{Acknowledgement.} The author thanks Wistar Comfort for valuable bibliographical informations.
| {
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Q: Accessing data from Singleton, clarification needed I have a singleton class Deck
Deck contains a bunch of Cards
Each Card knows, about amongst other things, an image assigned to it.
When the class responsible for displaying the card's image tries to access it .. well it stops here.
Why can't i access the faceImage?
A: If you type out [c faceImage]; and build, do you get (if using ARC) an error like "Receiver type 'Card' for instance message is a forward declaration", or (if not using ARC) a warning like "Instance method '-faceImage' not found (return type defaults to 'id')"?
Did you forward-declare @class Card in Deck.h?
You probably just need to #import "Card.h" in the file where you're trying to access faceImage.
| {
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{"url":"https:\/\/projecteuclid.org\/euclid.nmj\/1114632069","text":"## Nagoya Mathematical Journal\n\n### Solutions in Morrey spaces of some semilinear heat equations with time-dependent external forces\n\nXiaofang Zhou\n\n#### Abstract\n\nIn this paper, we consider the Cauchy problem for some semilinear heat equations with time-dependent external forces. Both the external force and the initial data are assumed to be small in some Morrey spaces. We first prove the unique existence of a small time-global solution. We next show the stability of that solution by proving the time-global sovability of perturbation problems.\n\n#### Article information\n\nSource\nNagoya Math. J., Volume 174 (2004), 127-163.\n\nDates\nFirst available in Project Euclid: 27 April 2005\n\nhttps:\/\/projecteuclid.org\/euclid.nmj\/1114632069\n\nMathematical Reviews number (MathSciNet)\nMR2066106\n\nZentralblatt MATH identifier\n1053.35062\n\n#### Citation\n\nZhou, Xiaofang. Solutions in Morrey spaces of some semilinear heat equations with time-dependent external forces. Nagoya Math. J. 174 (2004), 127--163. https:\/\/projecteuclid.org\/euclid.nmj\/1114632069\n\n#### References\n\n\u2022 P. Baras, M. Pierre, Probl\u00e8mes paraboliques semi-lin\u00e9aires avec donn\u00e9es measures , Applicable Anal., 18 (1984), 111\u2013149.\n\u2022 H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions , J. Math. Pure. Appl. (9), 62 (1983), 73\u201397.\n\u2022 H. Fujita, On the blowing up of solutions of the Cauchy problem for $u_t = \\Delta u + u^1 + \\alpha$ , J. Fac. Sci. Univ. Tokyo, I, 13 (1966), 109\u2013124.\n\u2022 A. Haraux and F.B. Weissler, Non-uniqueness for a semilinear initial value problem , Indiana Univ. Math. J., 31(1982), 167-189.\n\u2022 K. Hayakawa, On nonexistence of global solutions of some semilinear parabolic equations , Proc. Japan Acad. A, 49(1973), 503\u2013505.\n\u2022 K. Kobayashi, T. Sirao and H. Tanaka, On the growing up problem for semilinear heat equations , J. Math. Soc. Japan, 29(1977), 407\u2013424.\n\u2022 H. Kozono,and M. Yamazaki, Semilinear heat equations and the Navier-Stokes equation with distributions as initial data , C. R. Acad. Sci. Paris, S\u00e9r. I, 317(1993), 1127\u20131132.\n\u2022 \u2013\u2013\u2013\u2013, Semilinear heat equations and the Navier-Stokes equation with distributions in new function spaces as initial data , Comm. in P.D.E., 19(1994), 959\u20131014.\n\u2022 \u2013\u2013\u2013\u2013, The stability of small stationary solutions in Morrey spaces of the Navier-Stokes equation , Indiana Univ. Math. J., 44, No.3 (1995), 1307\u20131336.\n\u2022 \u2013\u2013\u2013\u2013, Small stable stationary solutions in Morrey spaces of the Navier-Stokes equation , Proc. Japan Acad. Ser.A, 71(1995), 199\u2013201.\n\u2022 T.-Y. Lee, Some limit theorems for super-Brownian motion and semilinear differential equations , Annals of Probability, 21 (1993), 979\u2013995.\n\u2022 Y. Niwa, Semilinear heat equations with measures as initial data , Thesis, Univ. of Tokyo, 1986.\n\u2022 C.V. Pao, Periodic solutions of systems of parabolic equations in unbounded domains , Nonlinear Analysis, 40 (2000), 523\u2013535.\n\u2022 J. Peetre, On convolution operators leaving $L^p, \\lambda$ spaces invariant , Ann. Mat. Pura Appl., 72 (1966), 295\u2013304.\n\u2022 M.E. Taylor, Analysis on Morrey spaces and applications to Navier-Stokes and other evolution equations , Comm. in P.D.E., 17 (1992), 1407\u20131456.\n\u2022 F.B. Weissler, Existence and non-existence of global solutions for a semilinear heat equation , Israel J. Math., 38(1981), 29\u201340.\n\u2022 J. Wu, Well-posedness of a semilinear heat equation with weak initial data , J. Fourier Anal. Appl., 4(1998), 629\u2013642.\n\u2022 M. Yamazaki, Solutions in the Morrey spaces of the Navier-Stokes equation with time-dependent external force , Funkcial. Ekvac., 43 (2000), No.3, 419\u2013460.\n\u2022 X.F. Zhou, The stability of small stationary solutions in Morrey spaces of the semilinear heat equations , J. Math. Sci. Univ. Tokyo, 6 (1999), 793\u2013822.","date":"2019-10-22 23:36:34","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6220057010650635, \"perplexity\": 2405.3262270831633}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-43\/segments\/1570987826436.88\/warc\/CC-MAIN-20191022232751-20191023020251-00275.warc.gz\"}"} | null | null |
153 Kennedy Trail - Get ready to move your whole family in to this spacious lake house that is set on a prime deep wooded lot with 100 feet of private beach frontage. This one of a kind home is located on Kennedy Shores, on the east shore of Higgins Lake. This open concept great room and kitchen affords a spectacular sunset view through the large wall of windows. There is plenty of room here for your family and all of your friends with the a unique master en suite , 2 sets of jack and jill bedrooms, 2 half baths, a bar room complete with a full bar and beer coolers, a gourmet kitchen, a bonus room above the 5 car garage. Not only can this home accommodate all of your family and friends, the generous size garage can house all of your lake life toys. | {
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Michelbuch (gemeentevrij gebied)
Michelbuch (Achern) - wijk in Achern, Baden-Württemberg
Michelbuch (Vichten) - wijk in Vichten, Luxemburg | {
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Definition - What does Certified Safety & Health Professional (CSHP) mean?
The certified safety professional (CSP) is a certification that can be obtained through the Board of Certified Safety Professionals (BCSP), a government organization in the United States. A CSP is a qualified person who is trained and competent in the detection and appraisal of hazardous materials, procedures and the activities of workers in their company, along with outside work environments and materials. The CSP is a person who has been educated and trained to handle safety in the work environment.
The certified safety professional (CSP) program bases it's procedures on safety practices that are standard in the USA. The CSP will have earned a bachelor's degree in a four year study program, as well as have three more years of experience in the safety field, as well as knowledge of the practices that should be in place. This includes an examination that must be passed, such as the Certified Safety Professional and Associate Safety Professional examinations. The examination for CSP examination emphasizes principles and practices of the profession of safety, while the ASP examination highlights the safety subjects as a core. Both exams will contain questions that will cover the knowledge and skills that are necessary for the CSP professional. These skills include environmental assessment, health, safety, engineering, management, communications and information. | {
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\section{Introduction}
\label{sec:intro}
The recent discovery of the Higgs boson \cite{Aad:2012tfa, Chatrchyan:2012xdj} and the ongoing measurements of its properties \cite{Khachatryan:2016vau} are in good agreement with the hypothesis that this particle is a remnant of the Brout-Englert-Higgs mechanism, i.e. the spontaneous breaking of $\mathrm{SU}(2)_L \times \mathrm{U}(1)_Y \to \mathrm{U}(1)_\mathrm{QED}$.
While the precise determination of the Higgs and gauge boson masses, as well as the interactions of the Higgs boson with elementary particles, including itself, will continue to improve our understanding of the scalar potential's local structure in the vicinity of the vacuum, its global structure, which can possibly explain the nature of electroweak symmetry breaking, is very difficult to probe experimentally.
For example, the nature of the Higgs, whether elementary or composite, is still an open question. Even if the Higgs is assumed to be elementary, the shape of its potential remains unknown. It could be of mexican-hat shape as in
the Standard Model (SM), or it could be deformed by strong quantum corrections due to virtual effects of additional fields. Were the Higgs boson to be a composite pseudo-Nambu-Goldstone boson of a strongly-coupled sector, one would expect
a periodic potential involving trigonometric functions. In all cases, the Higgs mass is fixed by the curvature of the potential at its minimum, and so in the vicinity of the latter the shape of the potential will be similar in all possible models. Nevertheless, deviations are allowed away from the minimum. For example, one could have a barrier at zero temperature between the vacuum and the origin of field-space. Moreover, in
composite Higgs models the relation between the Higgs field's vacuum expectation value (VEV) and the gauge boson masses differs from its SM counterpart, and thus the location of the minimum in field-space may vary.
Discriminating between the different possibilities is of fundamental importance for our understanding of nature and, hence, the embedding of the effective Standard Model in an underlying UV theory. This motivates to consider possible observables which could be sensitive to the Higgs potential beyond its minimum. A possible candidate is the energy scale of baryon-number-violating processes. If baryon number is only violated by the anomaly under the weak interactions, then it follows that processes that violate baryon-number are associated with transitions between vacua classified by their weak topological charge. The minimum energy barrier between these vacua thus sets the expected scale of baryon-violating processes, which is an observable that could potentially be probed by experiments, either at colliders \cite{Aoyama:1986ej,Ringwald:1989ee,Espinosa:1989qn,Farrar:1990vb,Ringwald:1990qz,Gibbs:1994cw} or cosmic ray and neutrino detectors \cite{Morris:1991bb,Morris:1993wg,Han:2003ru,Ahlers:2005zy,Anchordoqui:2005ey,Fodor:2003bn}. Getting accurate predictions for the rates of baryon-number-violating interactions is a difficult problem, due to a possible breakdown of
the semiclassical expansion used to compute vacuum transitions. There have been extensive discussions in the literature (see for example \cite{McLerran:1989ab,Cornwall:1990hh,Arnold:1990va,Khlebnikov:1990ue,Porrati:1990rk,Khoze:1990bm,Khoze:1991mx,Rubakov:1992ec,Bezrukov:2003er,Ringwald:2003ns,Tye:2015tva}), which has not led to a definite consensus. Recent estimates point towards rates that could be probed by future experiments \cite{Ringwald:2003ns,Tye:2015tva}. However, these estimates use different methods than previous calculations giving more negative results, and a detailed understanding of the reasons for the discrepancies is still lacking. For recent analyses of measurement prospects at colliders, cosmic ray and neutrino detectors, see for example \cite{Ellis:2016ast,Brooijmans:2016lfv,Ellis:2016dgb}.
Aside from determining the rate of observable baryon-violation effects, it should be noted that the energy barrier between topological vacua can also play a crucial role in potential explanations of the baryon asymmetry of the Universe. In the early Universe, finite temperature effects become important and affect the height of the barrier. At temperatures at which the electroweak symmetry is restored, the barrier effectively disappears and vacuum transitions are unsuppressed \cite{Arnold:1987mh,Khlebnikov:1988sr,Dine:1989kt}, while below the electroweak phase transition the tunneling rate becomes Boltzmann suppressed. In scenarios of
electroweak baryogenesis \cite{Kuzmin:1985mm} (for reviews, see \cite{Trodden:1998ym,Morrissey:2012db}), the baryon asymmetry is created during the nucleation of bubbles of the broken electroweak phase in a first order transition, in such a way that unsuppressed vacuum transitions in the unbroken phase convert a chiral asymmetry into net baryon number. The latter can then survive in the broken phase only if the corresponding vacuum transitions are strongly suppressed, which enforces a bound on the relative size of the energy barrier with respect to the temperature at the onset of bubble nucleation. On the other hand, in mechanisms of leptogenesis \cite{Fukugita:1986hr} (see \cite{Buchmuller:2004nz,Davidson:2008bu} for reviews), out-of equilibrium decays or oscillations of heavy neutrinos generate a net lepton asymmetry, which is then partly reprocessed into baryon number by vacuum transitions. A viable mechanism then requires the lepton asymmetry to be generated while vacuum transitions are still active.
The existence of a minimum energy barrier between vacua can be inferred from topological arguments \cite{Manton:1983nd}, and indeed one can calculate the field configurations at the top of the barrier. These are the so called sphalerons,
which correspond to saddle-points of a bosonic energy functional. This functional depends on the spatial derivatives of the gauge and scalar fields, as well as the scalar potential. The resulting sphaleron configurations
involve a nontrivial profile for the scalar fields, which probe field values beyond the minimum of the scalar potential. Thus the resulting sphaleron energy is potentially sensitive to the details of the potential away from the Higgs vacuum. On the other hand, non-standard derivative interactions can also affect the energy functional and the sphaleron barrier.
The previous considerations motivate us to calculate the sphaleron barrier in nonstandard realizations of the Higgs vacuum, in order to look for possible deviations with respect to the SM value coming from
a modified potential and/or derivative terms. Sphaleron configurations have been calculated not only for the Standard Model \cite{Dashen:1974ck,Klinkhamer:1984di} (with a resulting energy barrier of the order of 9 TeV for the observed value of the Higgs mass), but also in a number of extensions of the Standard Model
involving an elementary Higgs and other scalars \cite{Kastening:1991nw,Enqvist:1992kd,Bachas:1996ap,Moreno:1996zm,Kleihaus:1998bh,Grant:1998ci,Grant:2001at,Funakubo:2005bu,Ahriche:2007jp,Ahriche:2009yy,Ahriche:2014jna}. In many of these models, the deviations from the SM behaviour arise mainly due to the existence of additional scalars with electroweak charges, all of them acquiring nontrivial profiles in the sphaleron configuration. Still, the sphaleron barrier was never found to deviate substantially from its SM value. In this work, we restrict to models with a single electroweak scalar, and focus on possible
large deformations of the SM case, either through sizable interactions that change the shape of the potential for an elementary Higgs, or by considering composite Higgs models, in which not only the potential is modified, but there are also new derivative interactions.
In the first case, a good example of a potential which is very different from that of the SM is one
in which the Higgs vacuum is separated from the origin by a potential energy barrier at zero temperature. Such type of scenarios was introduced in reference \cite{Grojean:2004xa}, using higher-dimensional operators, and motivated by electroweak baryogenesis. A UV completion involving extra scalars with strong couplings to the Higgs was found in \cite{Espinosa:2007qk,Espinosa:2008kw}, and the large couplings were shown not to spoil perturbation theory in \cite{Tamarit:2014dua}.
Hence, we will here adopt a general parametrization of the potential, capturing its features without worrying about the concrete realization in terms of additional scalars. We assume additional scalars to be stabilized at the origin, without inducing tadpoles in a given Higgs background, and thus playing no role in the calculation of sphaleron configurations.
Composite Higgs scenarios, well motivated by naturalness considerations, realise the Higgs boson as a pseudo-Goldstone boson with a potential that remains protected from large quantum corrections due to
an approximate global symmetry. We will center our attention on the minimal composite scenarios of reference \cite{Agashe:2004rs}, in which the pattern of global symmetry breaking is SO(5)$\rightarrow$SO(4).
The organization of the paper is as follows. In section \ref{sec:csn} we summarize the link between B+L violating processes and the sphaleron barrier. The calculation of the sphaleron configuration in
the SM is reviewed in section \ref{sec:sphalsm}, while \ref{sec:sphaldef} focuses on the case of a deformed potential. Section \ref{sec:sphalcomp} focuses on the sphaleron energy in minimal composite Higgs models and in Section~\ref{sec:summary} we offer a summary.
\section{Overview of sphalerons and B+L violation}
\label{sec:csn}
In a nonabelian gauge theory, vacua are associated with pure gauge configurations: since the Hamiltonian is gauge invariant, such configurations have the same energy as the one with zero gauge fields. Fore more general field configurations, the requirement of finite action demands them to tend to such vacuum configurations at infinity. ``Infinity'' can be understood as a 3-sphere $S_3$ of infinite radius within $\mathbb{R}^4$, and thus finite action configurations are associated with mappings from $S_3$ to the gauge group. If the group is compact, such as the electroweak SU(2)$_L$, which itself
has the topology of a sphere, the mappings are classified by an integer
winding number or topological charge, counting the number of times that the compact group can be wrapped around $S_3$.
This topological charge $q$ can be written in terms of the nonabelian field-strength as
\begin{equation}
q=\frac{1}{16\pi^2}\int d^4x\, {\rm tr} \,\tilde F_{\mu\nu}F^{\mu\nu},
\end{equation}
where $\tilde F^{\mu\nu}\equiv\frac{1}{2} \epsilon^{\mu\nu\rho\sigma}F_{\rho\sigma}$.
The integrand above is a total derivative, and thus only picks a contribution from the boundary at infinity, as expected from the fact that $q$ is associated with mappings of the sphere at infinity into the gauge group. One can always choose a so-called topological gauge in which $A_0=0$ and all the gauge field components go to zero at spatial infinity. Then the only nonzero contributions to $q$ at the boundary of $\mathbb{R}^4$ are localized at the two space slices at $t=\pm\infty$. It can then be seen that one may write
\begin{align}
\label{eq:qNS}
q=N_{CS}(t=\infty)-N_{CS}(t=-\infty),
\end{align}
where $N_{CS}(t)$, known as the Chern-Simons number, is given in the topological gauge by the following integral over a spatial slice with fixed $t$:
\begin{align}
\label{eq:NCS}
N_{CS}(t)=\frac{1}{16\pi^2}\int_{t}\!d^3x\,\epsilon_{ijk}\left(A^a_i \partial_j A^a_k+\frac{1}{3}\epsilon^{abc} A^a_i A^b_j A^c_k\right).
\end{align}
Although the topological charge $q$ is an integer, $N_{CS}$ is not necessarily so. The Chern-Simons number becomes an integer only when evaluated over pure gauge configurations. Note that, since arbitrary gauge configurations of finite action tend to a pure gauge transformation at infinity, the topological charge given by \eqref{eq:qNS} is indeed an integer.
We conclude that vacua can be characterized by integer values of the Chern-Simons number. This implies that there can be an
energy barrier between configurations with integer $N_{CS}$. One can then consider paths in field space between vacuum configurations along which the height of the barrier is minimized. The field configurations at the top of this minimal
barriers are known as sphalerons, and the height of the barrier is the sphaleron energy.
In order to be more precise about the aforementioned energy of the gauge field configurations, it can be defined, in analogy with a zero-dimensional quantum mechanics problem, from the contributions to the Hamiltonian that do not involve time derivatives. This gives a functional $V_{\rm bos}$ which in the topological gauge adopts the form
\begin{equation}
\label{eq:Vbos}
V_{\rm bos}[A_\mu^a,\phi_i]\equiv\int\!d^3x\,\left\{\frac{1}{4g^2}F^a_{ij}F^{a}_{ij}+{\cal L}_{\rm kin,sp}^{\rm matter}[A_\mu^a,\phi_i]+V^{\rm matter}[\phi_i]\right\},
\end{equation}
where $\phi_i$ represents generic scalar fields, ${\cal L}_{\rm kin,sp}^{\rm matter}$ stands for the contributions of spatial derivatives to their kinetic terms, while $V^{\rm matter}$ denotes their potential energy density. Sphalerons correspond
to saddle points of $V_{\rm bos}$, as is intuitively clear from their role as configurations with maximal energy along minimal-barrier paths between vacua. Being extremal points of $V_{\rm bos}$, sphalerons are static solutions of the Euclidean equations of motion of the theory, i.e. satisfying
\begin{align}
\partial_\nu\frac{\delta V_{\rm bos}}{\delta \partial_\nu A^a_\mu}-\frac{\delta V_{\rm bos}}{\delta A^a_\mu}=0,\quad \partial_\nu\frac{\delta V_{\rm bos}}{\delta\partial_\nu \phi_i}-\frac{\delta V_{\rm bos}}{\delta\phi_i}=0.
\end{align}
As emphasized in Sec.~\ref{sec:intro}, because $V_{\rm bos}$ is sensitive to the potential energy density of the scalars and contributions involving their spatial derivatives, the sphaleron energy can vary if either of them is modified.
Aside from the sphaleron configurations, which are extrema of $V_{\rm bos}$, one can also define constrained extrema of $V_{\rm bos}$ by demanding a fixed value of $N_{CS}$. This gives a function $V^{\rm saddle}_{\rm bos}[N_{CS}]$. Sphalerons correspond to local maxima of $V^{\rm saddle}_{\rm bos}[N_{CS}]$. As $V_{\rm bos}$ is invariant under gauge transformations, and because gauge transformations
with nontrivial topological charge change $N_{CS}$ by integer quantities, $V^{\rm saddle}_{\rm bos}[N_{CS}]$ is a periodic function of $N_{CS}$. Further, $V_{\rm bos}$ is also invariant under parity transformations of the fields, under which $N_{CS}$ changes sign. It then follows that the graph of the function $V^{\rm saddle}_{\rm bos}[N_{CS}]$ is invariant under reflections around lines with constant half-integer and integer values of $N_{CS}$, as illustrated in Fig.~\ref{fig:VbosNCS}. It is known that $V^{\rm saddle}_{\rm bos}[N_{CS}]$ can be multivalued away from integer values of $N_{CS}$, implying the existence of multiple families of extrema. In the SM, for $m_h< 12~m_W$, there is a single branch, with $V^{\rm saddle}_{\rm bos}[N_{CS}]$ having negative second derivatives in between the vacua, as in the left plot of Fig.~\ref{fig:VbosNCS}. The reflection symmetry implies then that the maximum of the curve $V^{\rm saddle}_{\rm bos}[N_{CS}]$ in between integer values of $N_{CS}$ lies at half-integer values of $N_{CS}$. Or, in other words, sphaleron configurations are invariant under parity transformations for $m_h = 125$ GeV. For $m_h\geq 12~m_W$, a new branch of sphalerons appears \cite{Kunz:1988sx,Yaffe:1989ms}, which come in pairs related by parity transformations; these are known as bisphalerons. In this case the extremal path in field-space defining $V^{\rm saddle}_{\rm bos}[N_{CS}]$ becomes multivalued, and $V^{\rm saddle}_{\rm bos}[N_{CS}]$ develops cusps.
Nevertheless one can define deformed paths for which sphaleron configurations do indeed sit atop an energy barrier \cite{Kunz:1994ah}. The situation is schematically depicted in the right plot in Fig.~\ref{fig:VbosNCS}.
\begin{figure}[h]
\begin{center}
\includegraphics[width=0.49\textwidth]{pot1.pdf}
\includegraphics[width=0.49\textwidth]{pot2.pdf}
\caption{\label{fig:VbosNCS} Left: Schematic representation of $V^{\rm saddle}_{\rm bos}[N_{CS}]$ in the presence of a single-valued branch of extremal solutions. Note the translation and reflection symmetries of the graph. Right: Illustration of $V_{\rm bos}[N_{CS}]$ evaluated at non-extremal paths between vacua when bisphalerons are present (right).}
\end{center}
\end{figure}
The former definition of bosonic potential energy, inspired by quantum mechanics, might seem ad-hoc, so that the physical meaning of $E_{\rm sph}$ needs some further clarification. In fact, it is not obvious to see how $E_{\rm sph}$ may play a role in tunneling processes between the topological vacua. The reason is that tunneling rates are computed from solutions to the full Euclidean equations of motion, known as instantons \cite{Belavin:1975fg,'tHooft:1976fv}. These differ from sphalerons
because the latter are static solutions, while instantons depend as well on time. Despite this, the sphaleron energy can play a role when considering not just spontaneous vacuum transitions, but scattering processes at a fixed energy. The existence of multiple topological vacua affects the wave function of the true vacuum, and this effect can be incorporated in a path integral formalism by including sums over field configurations
around instanton backgrounds. This gives rise to new effective instanton vertices that can be incorporated in diagrammatic expansions, which encode the nontrivial effects of the vacuum transitions. In principle, these vertices are suppressed by exponential factors involving the Euclidean action of the instantons, $\exp(-S^E_{\rm inst})$, which as said before also determine the tunneling rates. Actual calculations show that when the external
particles have energies of the order of $E_{\rm sph}$, the exponential suppression of the instanton effects can be lifted \cite{ McLerran:1989ab,Cornwall:1990hh,Arnold:1990va,Khlebnikov:1990ue,Porrati:1990rk,Khoze:1990bm,Khoze:1991mx,Rubakov:1992ec,Bezrukov:2003er,Ringwald:2003ns,Tye:2015tva}. Thus, $E_{\rm sph}$ can indeed be interpreted as a physical energy barrier between topological vacua, because the effect of vacuum transitions becomes unsuppressed when one prepares states with $E>E_{\rm sph}$.
A more direct connection between sphalerons and energy barriers can be established at finite temperature. Thermal fluctuations allow states with energies above the barrier, which can then induce classical
vacuum transitions. The thermal transition rate is determined from static solutions to the Euclidean equations of motion -- i.e. sphalerons -- and the rate scales as $\exp(-S^{E,3D}_{\rm sph}/T)=\exp(-E_{\rm sph}/T)$, where $S^{E,3D}_{\rm sph}$ is the thermal Euclidean action, defined as the spatial integral of the Euclidean Lagrangian evaluated on time-independent configurations. Thermal fluctuations induce
excitations with average energy of the order of $T$, and when $T\gtrsim E_{\rm sph}$ the rate becomes unsuppressed. Again, $E_{\rm sph}$ can be interpreted as an energy barrier between the topological vacua.
We can conclude this section by reviewing the link between sphalerons and B+L violation. In the SM, B-L is conserved while B+L is an anomalous symmetry. Denoting the SU(2)$_L$ field strength as $W_{\mu\nu}$, the B+L
current satisfies the following anomalous conservation equation,
\begin{align}
\label{eq:anomeq}
\partial_\mu J^\mu_{B+L}=\frac{3}{8\pi^2}\,{\rm tr}\, \tilde W_{\mu\nu}W^{\mu\nu}.
\end{align}
This means that a given gauge field background with topological charge $q$ induces the following change of B+L between $t=-\infty$ and $t=\infty$:
\begin{align}
\label{eq:anomaly}
\Delta(B+L)=\int d^3x \left[J^0_{B+L}(t=\infty)-J^0_{B+L}(t=-\infty)\right]=\int d^4 x \,\partial_0 J^0_{B+L}= \frac{3}{8\pi^2}\int d^4x\,{\rm tr}\, \tilde W_{\mu\nu}W^{\mu\nu}=6 q,
\end{align}
where we used Eq.~\eqref{eq:anomeq} with the assumption that the current vanishes at spatial infinity. Tunneling between topological vacua is associated with instanton configurations
which tend towards pure gauge configurations with different integer values of $N_{CS}$ at $t=\pm \infty$. Thus the instanton configurations have a nonzero topological charge $q=N_{CS}(\infty)-N_{CS}(-\infty)$, which implies that vacuum transitions are immediately associated with violations of B+L. In this way, the sphaleron energy sets the scale of baryon-number-violating processes. Equation \eqref{eq:anomaly} implies that in a vacuum transition with $\Delta N_{CS}=1$, there is a change of B+L by six units. Thus, sphaleron-related processes involve the production of large numbers of particles. The allowed processes can be identified by using the
effective instanton vertices mentioned earlier. For an instanton background with topological charge $q$, the vertices involve a number of fermion fields related to the number of fermionic zero modes of the background; the resulting interaction violates B+L by $6q$ units. For example, a one-instanton vertex inducing a transition with $\Delta N_{CS}=1$, generates an interaction with twelve fermion fields, of the form $\Pi_i (u_L d_L d_L \nu_L)_i,$ with $i=1,\dots 3$ labelling the generations \cite{Harvey:1990qw}. This can for example give rise to the creation of three baryons and three neutrinos from the vacuum, or can induce $2\rightarrow 10$ processes with quarks and leptons. As mentioned before, the production cross sections are up for debate.
In the following, we will calculate the sphaleron energy in elementary Higgs boson scenarios with a modified potential, and in composite Higgs boson scenarios. In the first case, the modified Higgs potential can be understood
as arising from the virtual effects of heavier fields. In the second case, the sphaleron energy can be calculated in an effective
theory arising after integrating out modes of the strongly coupled sector. We have argued before that sphaleron effects become relevant at processes with energies of the order of the sphaleron energy. Then if $E_{\rm sph}$ is larger than the mass of the heavy fields or the compositeness scale, the question might arise of whether at those energies one can still trust the original calculation of the minimum energy barrier. This is the case because the effective theory in which the heavy fields are integrated out describes the dynamics when those fields lie at their energy minima, and so minimal energy configurations of the full theory can be reliably calculated in the effective description. In the composite case, it should be noted that the Higgs, being a pseudo-Goldstone boson, is protected by the global symmetry of the composite sector. Interactions inside the latter cannot generate contributions to the Higgs potential, which arises from interactions that break the global symmetry and are already taken into account in the effective theory. The situation is then similar to the case of an elementary Higgs with an effective potential induced by heavy fields, and the previous conclusion applies.
\section{Sphaleron energy in the Standard Model}
\label{sec:sphalsm}
In this section we review the calculation of the SM sphaleron configuration, mostly following the treatment in \cite{Schaldach}. As we are considering the minimum barrier between vacua with different weak topological charge, we can simply restrict to field
trajectories connecting the vacua without exciting degrees of freedom that do not couple to the weak bosons -- doing otherwise would just give higher energy configurations. This allows to ignore gluons, and forces
to consider the Higgs field. As in a nonzero Higgs background the weak bosons mix with the hypercharge boson, in principle one should take it into account it as well, but because the mixing is small, the effect is subleading (less than $1\%$, \cite{Kleihaus:1991ks,Ahriche:2014jna}) and will
be ignored. Thus one has to consider the functional
\begin{equation}
\label{eq:VbosSM}
V^{\rm SM}_{\rm bos}[A_\mu^a,H]=\int\!d^3x\,\left\{\frac{1}{4g^2}W^a_{ij}W^{a}_{ij}+D_i H^\dagger D_i H+V(H)\right\},
\end{equation}
where $D_i H=\partial_i H-i\sigma^a A^a_i H$, with $\sigma^a$ being the usual Pauli matrices. $V(H)$ is the Higgs potential normalized to be zero at the Higgs vacuum, so that $V^{\rm SM}_{\rm bos}$ evaluated at the sphaleron configuration can be directly interpreted as the energy barrier between topological vacua.\footnote{This is because with this choice of normalization, the bosonic energy of the vacuum configuration with zero gauge fields and the Higgs at its VEV becomes zero.} At tree level $V(H)$ is given in terms of the Higgs mass squared $m^2_h$ and the Higgs VEV $v$ by
\begin{align}
V(H)=-\frac{m^2_h}{2v^2}\left(H^\dagger H-\frac{v^2}{2}\right)^2.
\end{align}
It is useful to work in dimensional units, and to do so we rescale the fields and coordinates in units of the $W$ mass, which in the limit of zero Weinberg angle is $m^2_W=g^2 v^2/4$:
\begin{align}
\label{eq:rescaling}
x^\mu&\rightarrow\frac{1}{m_W} y^\mu,& A^a_\mu&\rightarrow m_W \tilde A^a_\mu, & H&\rightarrow\frac{m_W}{\sqrt{2}g} \tilde H.
\end{align}
Then one can find the sphaleron configuration by extremising the dimensionless functional
\begin{align}
\label{eq:rescaledVbosSM}
\tilde V^{\rm SM}_{\rm bos}=\frac{1}{g^2}\int\!d^3y\,\left\{\frac{1}{4g^2}\tilde W^a_{ij}\tilde W^{a}_{ij}+\frac{1}{2}D_i \tilde H^\dagger D_i \tilde H+\tilde V(\tilde H)\right\},
\end{align}
where $ \tilde V(\tilde H)\equiv\frac{\kappa^2}{32}(\tilde H^\dagger \tilde H-4)^2$ and $\kappa^2\equiv\frac{m^2_h}{m^2_W}$. The equations of motion of the sphaleron configuration are
\begin{eqnarray}\begin{aligned}
\label{eq:eomSM}
&({\cal D}_j \tilde W_{ij})^a+\frac{i}{4}\left(\tilde H^\dagger \sigma^a D_i \tilde H-D_i \tilde H^\dagger \sigma^a D_i\tilde H\right)=0,\\
&\left[D^2_i-2\frac{\partial}{\partial ( \tilde H^\dagger \tilde H)}\tilde V(\tilde H)\right]\tilde H=0.
\end{aligned}\end{eqnarray}
To solve the former equations, we impose a rotationally symmetric ansatz\footnote{This ansatz is often called hedgehog solution.} \cite{Dashen:1974ck,Manton:1983nd,Klinkhamer:1984di,Akiba:1988ay}. Defining $r\equiv \sqrt{\sum y^2_i}$ and $n_i\equiv y_i/r$, the ansatz is given by
\begin{equation}
\label{eq:ansatz}
\begin{aligned}
&\tilde A_i^a=\epsilon_{aij}n_j\frac{1-A(r)}{r}+(\delta_{ai}-n_an_i)\frac{B(r)}{r}+n_an_i\frac{C(r)}{r},\\
&\tilde H(r)=2\left(F(r)\,\mathbb{I}+i G(r)\,\vec{n}\cdot\vec{\sigma}\right)\left[
\begin{array}{c}
0\\
1
\end{array}\right].
\end{aligned}
\end{equation}
One can consider SU(2)$_L$ transformations preserving the $A_0=0$ gauge condition. Taking a group element of the form
\begin{equation}
U(r)=\exp[{\vec{n}\cdot\vec{\sigma}} P(r)]=\cos P(r)+i{\vec{n}\cdot\vec{\sigma}}\sin P(r),
\end{equation}
the functions in the ansatz of \eqref{eq:ansatz} transform as
\begin{equation}
\label{eq:gaugetr}
\begin{aligned}
A\rightarrow &\, A\cos 2P-B \sin 2P,& B\rightarrow& B\cos 2 P+ A\sin 2P, &C\rightarrow& C+ 2r P',\\
F\rightarrow &\, F \cos P - G\sin P, & G\rightarrow& G\cos P+F \sin P.
\end{aligned}
\end{equation}
We can use this freedom to set $C(r)=0$, although the price to pay is that one will lose the topological gauge condition $A_i\rightarrow0$ for $r\rightarrow\infty$.\footnote{In the topological gauge, given the ansatz \eqref{eq:ansatz}, $A_i\rightarrow0$ implies for example $A(r)\rightarrow1$, which is not respected by the gauges transformations of equation \eqref{eq:gaugetr}.} Inserting the ansatz \eqref{eq:ansatz} with $C(r)=0$ into the first of the equations in \eqref{eq:eomSM}, one gets an equation of the form
\begin{equation}
\label{eq:eqgauge}
\begin{aligned}
E_1 \frac{2n_an_i}{r^2}+E_2\frac{n_an_i-\delta_{ai}}{r}+E_3\,\epsilon_{aij}\frac{n_j}{r}=0.
\end{aligned}
\end{equation}
The orthogonality of the 2-index objects with indices $a,i$ of Eq.~(\ref{eq:eqgauge}) means that its
solutions must satisfy $E_1=E_2=E_3=0$, which yields
\begin{equation}
\label{eq:Es}
\begin{aligned}
&\,B A'-AB'+r^2 (GF'-FG')=0,\\
&\,B''-\frac{B}{r^2}\left(A^2+B^2-1\right)+2GF-B(G^2+F^2)=0,\\
&\,A''-\frac{A}{r^2}\left(A^2+B^2-1\right)-A(G^2+F^2)-G^2+F^2=0.
\end{aligned}
\end{equation}
The second equation in \eqref{eq:eomSM}, after substitution of the ansatz, adopts the form
\begin{align}
E_4\,\mathbb{I}+E_5\,{\vec{n}\,\vec{\sigma}}=0.
\end{align}
This implies $E_4=E_5=0$, which gives
\begin{eqnarray}\label{eq:E4E5SM}\begin{aligned}
&\frac{2}{r^2}(r^2G')'-\frac{G}{r^2}\left((A+1)^2+B^2\right)+\frac{2BF}{r^2}-\kappa^2G(F^2+G^2-1)=0,\\
&\frac{2}{r^2}(r^2F')'-\frac{F}{r^2}\left((A-1)^2+B^2\right)+\frac{2BG}{r^2}-\kappa^2F(F^2+G^2-1)=0.
\end{aligned}
\end{eqnarray}
By calculating the derivative with respect to $r$, one can show that the first equation of Eqs.~\eqref{eq:Es} is not independent of the others, leaving four equations with four unknown functions.
Solving them requires to impose boundary conditions for the unknown functions and their derivatives.
At large $r$, finiteness of $V_{\rm bos}$ evaluated with the sphaleron solution implies that gauge fields must approach a pure gauge configuration, while the scalar fields must tend to a minimum of their potential. The choice of boundary conditions can be simplified by obtaining asymptotic solutions with the desired properties,
which will depend on fewer parameters. For the SM, the asymptotic solutions for large and small $r$ at the chosen accuracy level depend each on 3 parameters, and are given in appendix \ref{app:asympt}.
A regular sphaleron solution can be found by applying an iterative numerical procedure such that, at each step, one obtains two solutions to the sphaleron equations by imposing boundary conditions at large and small r, respectively, while the steps are repeated with varying boundary conditions until the two solutions match smoothly at an intermediate value of $r$.
Before illustrating the solutions, it should be noted that one can reduce the equations further by redefining the unknown functions. Given
the gauge transformation properties \eqref{eq:gaugetr}, one may define gauge-invariant quantities $R^2\equiv A^2+B^2$, $S^2\equiv H^2+G^2$. Then one has
\begin{equation}
\label{eq:RS}
\begin{aligned}
A=&R \cos\theta, & B=& R \sin\theta,\\
F= &\,S \cos \phi, & G=& S\sin\phi.
\end{aligned}
\end{equation}
The above mapping does not uniquely define the variables $R,S,\theta,\phi$, since $A,B,F,G$ are invariant under two discrete transformations, i.e.
\begin{eqnarray}\begin{aligned}
\label{eq:jumps1}
R\rightarrow R,\quad \theta=\theta+2m\pi, \\
S\rightarrow S,\quad \phi\rightarrow\phi+2n\pi,
\end{aligned}\end{eqnarray}
and
\begin{eqnarray}\begin{aligned}
\label{eq:jumps2}
R\rightarrow-R,\quad \theta=\theta+(2m+1)\pi, \\
S\rightarrow-S,\quad \phi\rightarrow\phi+(2n+1)\pi,
\end{aligned}\end{eqnarray}
with $m,n,\in\mathbb{Z}$.
When looking for smooth sphaleron profiles, it should be noted that the former discrete changes in $R,S,\theta,\phi$ can still be admitted, since they don't affect
the functions $A,B,F,G$. In terms of the new variables the four independent equations become
\begin{eqnarray}
\label{eq:RSSM}
\begin{aligned}
&r^2R''+r^2S^2 \cos [2 \phi -\theta ]+R-R \left(R^2+r^2(\theta '^2+S^2\right))=0,\\
&2 r^2 S''-2r^2 S \phi'^2+4r S'-S \left(\kappa^2 r^2 \left(S^2-1\right)-2 R \cos [2 \phi -\theta ]+R^2+1\right)=0,\\
&R \theta ''+2 \theta ' R'+S^2 \sin [2 \phi -\theta ]=0,\\
&r^2 S \phi''+2 r\phi' \left(r S'+S\right)-R S \sin [2 \phi -\theta ]=0.
\end{aligned}\end{eqnarray}
The last two equations can be solved by
\begin{align}
\label{eq:thetas}
\theta'=\phi'=0~~\mathrm{and}~~\phi=\frac{\theta}{2}+\omega\frac{\pi}{2},\,~~\mathrm{with}~~\omega\in \mathbb{Z},
\end{align}
which finally yields
\begin{equation}
\label{eq:eqsRsimpleSM}
\begin{aligned}
&r^2 R''-{R^3}+ R \left(1-r^2 S^2\right)\pm r^2 S^2=0,\\
&2r^2 S''+4 r S'-S \left((R\mp1)^2+\kappa^2 r^2(S^2-1)\right)=0.
\end{aligned}
\end{equation}
The upper and lower signs are associated with even and odd $\omega$ in \eqref{eq:thetas}, and the corresponding equations can be related by the transformation $R\rightarrow-R$. However, if the sign of $R$ is fixed at large values of $r$ with a suitable boundary condition, both types of equations could give rise to different branches of sphalerons. For $m_h=125$ GeV and $R>0$ at large values of $r$, only the upper-sign branch has solutions. Equations \eqref{eq:thetas}, \eqref{eq:eqsRsimpleSM} do not allow to fix the constant values of $\theta,\phi$, which, given the identities in Eq.~\eqref{eq:RS}, prevents to reconstruct the values of the four unknown functions $A,B,H,G$ in the ansatz \eqref{eq:ansatz} in the gauge $C=0$. Nevertheless, $\theta$ can be determined from the generic properties of the functional $V^{\rm saddle}_{\rm bos}[N_{CS}]$ introduced in section \ref{sec:csn}, up to the ambiguity of Eqs.~\eqref{eq:jumps1} and \eqref{eq:jumps2}. As mentioned before, for the observed value of the Higgs mass there is a single branch of parity-invariant sphaleron solutions, and the symmetries
of $V^{\rm saddle}_{\rm bos}[N_{CS}]$ then imply that sphalerons have $N_{CS}=1/2+n,\,\, n\in \mathbb{Z}$. In order to get the expression of $N_{CS}$ in the $R,S,\theta,\phi$
field coordinates, one has to be careful because the relation of Eq.~\eqref{eq:NCS} for $N_{CS}$ is only valid in a topological gauge with $A_i\rightarrow0$ for $r\rightarrow\infty$. However, in order to eliminate
the function $C(r)$ from the ansatz \eqref{eq:ansatz} we performed a further gauge transformation which can violate the previous gauge condition. Nevertheless, one can use the properties of gauge transformations in Eq.~\eqref{eq:gaugetr} to map the fields in the $C=0$ gauge into fields in the topological gauge, where Eq.~\eqref{eq:NCS} holds. Expressing the result in terms of functions in the $C=0$ gauge one finally obtains:
\begin{equation}
\label{eq:NCSC0}
N_{CS}=\frac{1}{2\pi}\int dr (A'B-B'A)+\frac{1}{2\pi}\arctan\frac{B_\infty}{A_\infty}=\frac{\theta_\infty+ n\pi}{2\pi}-\frac{1}{2\pi}\int dr R^2\theta', \,\,n\in\mathbb{Z}.
\end{equation}
$B_\infty, A_\infty,\theta_\infty$ denote the values of the corresponding functions at infinity. In the $C=0$ gauge it no longer holds that the gauge fields vanish at $r\rightarrow\infty$. The ambiguity in $\theta_\infty$ up to multiples of $\pi$ is due to the discrete redundancy of Eqs.~\eqref{eq:jumps1} and \eqref{eq:jumps2}. From Eq.~\eqref{eq:NCSC0}, when imposing Eq.~\eqref{eq:thetas} one can see that the sphaleron solutions with $N_{CS}=1/2$ have constant $\arctan B_\infty/A_\infty=\theta_\infty+ n\pi=\pi$. This, together with Eq.~\eqref{eq:thetas}, allows to fix the ansatz \eqref{eq:ansatz} in the $C=0$ gauge by simply solving the two differential equations in \eqref{eq:eqsRsimpleSM}.
The boundary conditions for the two functions $R$ and $S$ can be obtained from the asymptotic solutions for the functions $A,B,G,F$ in appendix \ref{app:asympt}, imposing Eq.~$\eqref{eq:thetas}$ and $\theta=\pi+n\pi$.
At the chosen level of accuracy, this reduces the free parameters of the asymptotic solutions from six to four.
For $N_{CS}=1/2$ and $R>0$ at large values of $r$, only the upper sign choice in Eq.~\eqref{eq:eqsRsimpleSM} gives a solution, and one can choose $\theta=\pi$. The upper sign choice corresponds to even $\omega$ in Eq.~\eqref{eq:thetas}, i.e. $\phi=\theta/2+n \pi,$ with $n\in\mathbb{Z}$. As is clear from Eq.~\eqref{eq:RS}, this implies that the sphaleron has $F=B=0$ for all $r$. As mentioned earlier, for $r\rightarrow\infty$ the scalar field must lie in a minimum of its potential energy in order for the sphaleron to have finite energy. This is satisfied for $F^2+G^2=S^2=1$, as can be seen from the ansatz \eqref{eq:ansatz} and the rescaled potential term in $\tilde V_{\rm bos}^{\rm SM}$ in Eq.~\eqref{eq:rescaledVbosSM}. On the other hand, regularity at $r=0$ forces $G(0) = 0$, which, together with the condition
$F(r)=0\,\forall\, r$, means that the scalar field must be zero at $r=0$. Thus, the sphaleron probes the Higgs potential between the origin ($F=G=0$) and the vacuum configuration ($F^2+G^2=1$).
The sphaleron energy can be obtained from $m_W \tilde V_{\rm bos}$ evaluated in the sphaleron configuration; in terms of the $R,S,\theta,\phi$ variables, $\tilde V_{\rm bos}$ is equal to
\begin{eqnarray}\begin{aligned}
\label{eq:tildeVbosSM}
\tilde V_{\rm bos}=\frac{2\pi }{g^2}\int \frac{dr}{r^2}\,&\left\{2 r^2 \left[{R'}^2+R^2 {\theta '}^2+2 r^2 \left(S^2 {\phi '}^2+{S'}^2\right)\right]+\kappa ^2 r^4 \left(S^2-1\right)^2+2 R^2 \left(r^2 S^2-1\right)\right.\\
&\left.-4 r^2 R S^2 \cos [\theta -2 \phi ]+2 r^2 S^2+R^4+1\right\}.
\end{aligned}\end{eqnarray}
Solving the different systems of equations -- either \eqref{eq:Es} and \eqref{eq:E4E5SM}, or the system \eqref{eq:RSSM}, or the reduced system \eqref{eq:eqsRsimpleSM} -- with the iterative procedure described above, fixing $m_h=125.09$ GeV and $m_W=80.398$ GeV \cite{Olive:2016xmw} we recover in all cases the known value of the SM sphaleron barrier,
\begin{align}
E^{SM}_{\rm sph}=9.11\, {\rm TeV}.
\end{align}
Fig. \ref{fig:profiles_SM} illustrates the profiles for $R$ and $S$ in the sphaleron solution, as well as the contributions to the dimensionless bosonic energy density -- defined as the integrand in equation \eqref{eq:tildeVbosSM} -- from the derivatives of the gauge fields, those of the scalars, and the scalar potential. The contribution from the potential is substantially lower than that of the derivatives. This hints towards a limited sensitivity of $E_{\rm sphal}$ to the details of the scalar potential, and greater sensitivity to modified derivative interactions. This will be confirmed in the following section dedicated to nonstandard Higgs scenarios.
\begin{figure}[h!]
\begin{center}
\begin{minipage}{0.5\textwidth}
\includegraphics[width=.95\textwidth]{SM_2.pdf}
\end{minipage}%
\begin{minipage}{0.5\textwidth}
\hfil\hskip0.8cm\includegraphics[width=.95\textwidth]{VbosSM.pdf}
\end{minipage}
\caption{Left: Profiles for $R,S$, in units of $m_W$, in the SM sphaleron configuration obtained by solving the reduced system of 2 differential equations. The vertical line marks the scale at which the low $r$ solution (red) was matched with the high $r$ solution (blue). Right: Contributions to the dimensionless integrand in $\tilde V_{\rm bos}^{SM}$, evaluated on the sphaleron solution, due to the gauge fields (solid blue), derivatives of the scalar field (dashed orange) and the potential
energy density of the Higgs (dotted green).}
\label{fig:profiles_SM}
\end{center}
\end{figure}
\section{Sphaleron energy for an elementary Higgs in a deformed potential}
\label{sec:sphaldef}
As an illustration of the effect of a modified potential away from the Higgs vacuum, in this section we consider a theory with an elementary Higgs, yet with a nonstandard potential. The experience with the SM shows that the sphaleron configuration for an elementary Higgs is sensitive to field values between the origin and the vacuum configuration, as follows from the
boundary conditions at $r\rightarrow\infty$ and $r\rightarrow0$. Thus we may consider potentials which deviate from the SM in this
region, while having a minimum whose VEV and curvature reproduce the correct Higgs and gauge boson masses. A potential which is very different from the SM can be achieved for example if the Higgs vacuum at zero
temperature is
separated from the origin of field space by a potential energy barrier. Such type of scenarios was introduced in reference \cite{Grojean:2004xa}, using higher-dimensional operators. A UV completion involving
extra scalars with strong couplings to the Higgs boson was found in \cite{Espinosa:2007qk,Espinosa:2008kw}, and the large couplings were shown not to spoil perturbation theory in \cite{Tamarit:2014dua}. Here we will adopt a practical
approach and simply model the Higgs potential with strong logarithmic corrections, i.e.
\begin{align}
\label{eq:VHdef}
V(H)=V_0+m_H^2H^\dagger H+(H^\dagger H)^2\left(-\lambda+\beta\log\left[\gamma+\frac{2H^\dagger H}{\phi^2_0}\right]\right).
\end{align}
In the equation above, $\beta$ represents an effective quartic coupling arising from loop corrections, and $\gamma$ -- which would be associated with the field-independent contributions to the masses of the
particles running in the loop corrections -- guarantees that the potential is analytic at $H=0$. $\phi_0$ can be chosen at will to be the Higgs VEV $v$ (the difference can be compensated by a redefinition
of the other couplings), and $V_0$ is fixed by requiring as before that the potential is zero at the minimum. Imposing that the correct Higgs and $W$ masses are generated at tree-level, one can eliminate the couplings $m^2_H$ and $\lambda$, and end up with a potential
\begin{align}
\label{eq:VHdef2}
V^{\rm log}(H)=H^\dagger H\left(-\frac{m^2_h}{2}+\frac{(2+3\gamma)\beta v^2}{2(1+\gamma)^2}\right)+(H^\dagger H)^2\left(\frac{m^2_h}{2v^2}-\frac{\beta(3+4\gamma)}{2(1+\gamma)^2}+
\beta\log\left[\frac{\gamma v^2+2H^\dagger H}{v^2(1+\gamma)}\right]\right),
\end{align}
with only $\beta$, $\gamma$ as free parameters.
The parameter $\beta$ controls the size of the barrier with respect to the origin and the energy of the Higgs vacuum. A barrier appears for $\beta>0$, yet increasing $\beta$ too much ($\gtrsim 0.26$ for the measured values of $m_h$ and $m_W$) raises the Higgs vacuum above the origin, so that the symmetric phase becomes preferred. A negative value of $\beta$ causes an instability at values of the field beyond the Higgs vacuum,
which captures the situation in the SM for the measured value of the Higgs and top masses. The allowed window of values of $\beta$ can be obtained by requiring that the electroweak vacuum is sufficiently long-lived with
respect to tunneling towards large values of the fields (for $\beta<0$) or towards the origin ($\beta>0$). The tunneling rate can be calculated from the exponential of the Euclidean action of the scalar field evaluated at a bounce solution \cite{Coleman:1977py}. We have computed the latter numerically for $\beta>0$, while for $\beta<0$, in the presence of a runaway as in the SM, we used the analytic approximation of \cite{Isidori:2001bm}. Doing so we obtain the following window of allowed parameters:
\begin{align}
\label{eq:stabwind}
-0.005\lesssim\beta\lesssim0.5.
\end{align}
The shape
of the potential is illustrated in figure \ref{fig:potentialdef} for different values of $\beta$, including the extrema of the above interval.
\begin{figure}[h!]
\begin{center}
\begin{minipage}{0.5\textwidth}
\includegraphics[width=0.95\textwidth]{Vdef.pdf}
\end{minipage}%
\begin{minipage}{0.5\textwidth}
\includegraphics[width=0.95\textwidth]{Vdef2.pdf}
\end{minipage}
\caption{Deformed Higgs potential for $\gamma=0.1$ and varying values of $\beta$. The dots represent the Higgs minimum, with VEV and curvature fixed by the $W$ and Higgs masses. On the left hand, the values of $\beta$ ensure absolute stability of the Higgs vacuum. The right
hand plot shows the extremal values of $\beta$ for which the metastable Higgs vacuum is still sufficiently long lived at zero temperature. The shaded areas reflect the region of the potential probed by sphaleron configurations.}
\label{fig:potentialdef}
\end{center}
\end{figure}
If the extra scalar fields that originate the logarithmic corrections are stabilized at the origin and do not receive induced tadpoles in a given Higgs background (as can be ensured
with appropriate discrete or global symmetries), they will not play a role in the calculation
of the sphaleron barrier and can be set to zero. Thus the sphaleron configuration can be obtained, as in the SM case, by extremising the bosonic energy functional involving the spatial
derivatives of the gauge fields and the Higgs, and the modified Higgs potential of equation \eqref{eq:VHdef2}. Performing the same rescalings as in Eq.~\eqref{eq:rescaling}, the rescaled bosonic energy looks as Eq.~\eqref{eq:rescaledVbosSM}, but with $\tilde V(\tilde H)$ substituted by
\begin{align}
\tilde V(\tilde H)=\frac
{\kappa^2}{32}(\tilde H^\dagger \tilde H-4)^2-\frac{2\hat\beta(1+2\gamma)}{(1+\gamma)^2}+\frac{\hat\beta(2+3\gamma)}{(1+\gamma)^2}\tilde H^\dagger \tilde H+\frac{\hat\beta(\tilde H^\dagger\tilde H)^2}{4}\left\{\log\left[\frac{4\gamma+\tilde H^\dagger \tilde H}{4(1+\gamma)}\right]-\frac{(3+4\gamma)}{2(1+\gamma)^2}\right\},
\end{align}
where we defined $\hat\beta\equiv \beta/g^2$. The equations of the sphaleron are formally the same as in Eq.~\eqref{eq:eomSM}, but with the above potential. Introducing again the ansatz
\eqref{eq:ansatz} and choosing the gauge $C(r)=0$, one gets identical results as before for the first family of equations in \eqref{eq:eomSM}, i.e. Eqs \eqref{eq:Es}, as they are not sensitive to the potential, while the second family of equations is modified. Once more, there are only four independent equations, which are:
\begin{equation}
\label{eq:Esdef}
\begin{aligned}
&\,B''-\frac{B}{r^2}\left(A^2+B^2-1\right)+2GF-B(G^2+F^2)=0,\\
&\,A''-\frac{A}{r^2}\left(A^2+B^2-1\right)-A(G^2+F^2)-G^2+F^2=0,\\
&\frac{2}{r^2}(r^2G')'-\frac{G}{r^2}\left((A+1)^2+B^2\right)+\frac{2BF}{r^2}-\kappa^2G(F^2+G^2-1)+G\Delta=0,\\
&\frac{2}{r^2}(r^2F')'-\frac{F}{r^2}\left((A-1)^2+B^2\right)+\frac{2BG}{r^2}-\kappa^2F(F^2+G^2-1)+F\Delta=0,
\end{aligned}
\end{equation}
where we defined
\begin{eqnarray}
\label{eq:gammadeltasdef}
\begin{aligned}
\Delta\equiv&\,\frac{4 \beta }{\gamma _0^2 \gamma _1}\Big\{2 \gamma _0^2 \gamma _1 \left(F^2+G^2\right)\log \frac{\gamma _0}{\gamma _1} -\left(F^2+G^2-1\right) \left(\gamma ^2 \left(F^2+G^2
-3\right)-2 \gamma \left(F^2+G^2+1\right)-2 \left(F^2+G^2\right)\right)\Big\},\\
\gamma_0\equiv&\,(1+\gamma),\\
\gamma_1\equiv&\,(F^2+G^2+\gamma).
\end{aligned}
\end{eqnarray}
The presence of $F, G$ in the gauge-invariant combination suggests that the equations will be simpler using the variables $R,S,\theta,\phi$ as in Eq.~\eqref{eq:RS}. We find
\begin{eqnarray}
\label{eq:eqsRdef}
\begin{aligned}
&r^2R''+r^2S^2 \cos [2 \phi -\theta ]+R-R \left(R^2+r^2(\theta '^2+S^2\right))=0,\\
&2 r^2 S''-2r^2 S \phi'^2+4r S'-S \left(\kappa^2 r^2 \left(S^2-1\right)-2 R \cos [2 \phi -\theta ]+R^2+1\right)+r^2 S\Delta_S=0,\\
&R \theta ''+2 \theta ' R'+S^2 \sin [2 \phi -\theta ]=0,\\
&r^2 S \phi''+2 r\phi' \left(r S'+S\right)-R S \sin [2 \phi -\theta ]=0,
\end{aligned}
\end{eqnarray}
where now, using $\gamma_0=1+\gamma$ and $\gamma_1=S^2+\gamma$ as in Eqs.~\eqref{eq:gammadeltasdef},
\begin{eqnarray}
\begin{aligned}
\Delta_S\equiv-\frac{4\hat\beta }{\gamma_0^2\gamma_1}\left\{\gamma _1 \left(3 \gamma -(4 \gamma +3) S^2+2\right)+\gamma _0^2 S^2 \left(2 \gamma _1 \log\frac{\gamma _1}{\gamma_0}+S^2\right)\right\}.
\end{aligned}
\end{eqnarray}
As in the SM case, the last two equations are solved by Eq.~\eqref{eq:thetas}, and one gets a simplified set of only two differential equations:
\begin{equation}
\begin{aligned}
\label{eq:eqsRsimpledef}
&r^2 R''-{R^3}+ R \left(1-r^2 S^2\right)\pm r^2 S^2=0,\\
&2r^2 S''+4 r S'-S \left((R\mp1)^2+\kappa^2 r^2(S^2-1)\right)+r^2 S\Delta_S=0.
\end{aligned}
\end{equation}
Once more, the upper and lower sign correspond to branches of solutions with either even or odd $\omega$ in Eq.~\eqref{eq:thetas}.
The asymptotic solutions and the boundary conditions for the equations are similar to those in the SM case, and discussed in appendix \ref{app:asympt}.
Using the same iterative method, we have solved the systems
\eqref{eq:Esdef}, \eqref{eq:eqsRdef} and \eqref{eq:eqsRsimpledef}, obtaining compatible results in all cases. As in the SM, for the measured Higgs and $W$ boson masses we only found a single branch
of sphaleron solutions, which for $R>0$ at large $r$ corresponds to the upper sign choice in \eqref{eq:eqsRsimpledef}, with $N_{CS}=1/2$, and with $\theta=\pi,\phi=\pi/2$, i.e. $F=B=0$.
The resulting energy barrier differs at the level of $\lesssim9\%$ from the SM one, even for the limiting cases in the stability window of equation \eqref{eq:stabwind}. For absolutely stable Higgs vacua, the deviations are below 3\%; these results are illustrated in Fig.~\ref{fig:Esph_def}. Figure \ref{fig:profiles_def} shows the profiles and the contributions to the bosonic energy density coming from
a sphaleron configuration with $\beta$ near the upper stability limit of Eq.~\eqref{eq:stabwind}. This gives the largest deviation from the SM, with the Higgs minimum above the origin (see Fig.~\ref{fig:potentialdef}). Note that with the potential normalized to zero at the former minimum, the energy density at the origin becomes negative, and the sphaleron configuration probes negative energies, as shown on the right plot in Fig.~\ref{fig:profiles_def}. This plays a role in lowering the sphaleron energy barrier, which becomes $E_{\rm sph}[\beta=0.495]=8.29$ TeV.
\begin{figure}[h!]
\begin{center}
\includegraphics[width=.5\textwidth]{Esph_def.pdf}
\caption{In red, sphaleron energy as a function of $\beta$ in models with a deformed Higgs potential, for $\beta$ in the allowed stability window. The dash-dotted gray line represents the SM result. $\gamma$ was fixed to $0.1$, and hardly influences the results. The shaded band corresponds to absolutely stable Higgs vacua, as in the left plot in figure \ref{fig:potentialdef}.}
\label{fig:Esph_def}
\end{center}
\end{figure}
\begin{figure}[h!]
\begin{center}
\begin{minipage}{0.5\textwidth}
\includegraphics[width=.95\textwidth]{def_2.pdf}
\end{minipage}%
\begin{minipage}{0.5\textwidth}
\hfil\hskip0.8cm\includegraphics[width=.95\textwidth]{Vbosdef.pdf}
\end{minipage}
\caption{Properties of sphaleron configurations with $\gamma=0.1$ and $\beta=0.495$. The left plot shows the profiles for $R,S$, in units of $m_W$, with the vertical lines marking the scale at which the low $r$ solution (red) was matched with the high $r$ solution (blue). The plot on the right shows the contributions to the dimensionless integrand in $\tilde V_{\rm bos}$, evaluated on the sphaleron solution, due to the gauge fields (solid blue), derivatives of the scalar field (dashed orange) and the potential
energy density of the Higgs (dotted green). In all plots, the gray dash-dotted lines correspond to the SM results.}
\label{fig:profiles_def}
\end{center}
\end{figure}
\section{Sphaleron energy in composite Higgs scenarios}
\label{sec:sphalcomp}
In this section we will study sphaleron configurations in minimal composite Higgs scenarios, in which the Higgs arises as a pseudo-Goldstone boson of a global SO(5) symmetry broken down to SO(4) \cite{Agashe:2004rs}.
The pattern of symmetry breaking enforces non-standard derivative interactions for the Higgs, as well as a modified relation between the Higgs VEV and the weak boson masses. Interactions that break the global symmetry generate a nonstandard Higgs potential, which still exhibits a discrete translational symmetry. Both the modified derivative interactions and potential can affect the sphaleron energy, and we expect larger deviations
than before. This is not only due to the modified derivative interactions, but also to the modified relation between the Higgs VEV and the $W$ boson mass. In models with elementary Higgses, we saw that the sphaleron probes
the potential between the origin and the minimum. With the location and curvature of the minimum fixed by the Higgs and gauge boson masses, the potential of an elementary Higgs can only be modified by changing the depth of
the minimum, or the shape of the potential in between the latter and the origin. In composite Higgs models there is in principle a further degree of freedom associated with the location of the minimum, as a result of the modified relation between the $W$ mass and the Higgs VEV.
Following \cite{Agashe:2004rs}, one can work in an effective theory involving the gauge and pseudo-Goldstone fields. The breaking of SO(5) into SO(4) leaves four Goldstones $h^m,m=1,\dots,4$, which can be included
in a multiplet $\Sigma$ carrying a nonlinear representation of the broken SO(5). The breaking is assumed to originate from a field $\Sigma_0$
in the fundamental of SO(5), which acquires a VEV involving a scale $f_\pi$: $\langle\Sigma_0\rangle^\top=[0,0,0,0,f_\pi]$. Then the field multiplet $\Sigma$ is given by
\begin{equation}
\Sigma=\exp\frac{\Pi}{f_\pi}\times\Sigma_0,
\end{equation}
with $\Pi$ given by a sum over broken global SO(5) generators $\tilde G^a$ multiplied by its corresponding Goldstone fields $\Pi=i\sqrt{2} \tilde G^a h^a$. The result is
\begin{equation}
\label{eq:Sigma}
\Sigma^\top=\frac{\sin\frac{h}{f_\pi}}{h}[h^1,h^2,h^3,h^4,h\cot\frac{h}{f_\pi}],
\end{equation}
where we defined $h\equiv(\sum_m(h^m)^2)^{1/2}$. With these conventions, and gauging an $SU(2)$ subgroup of the surviving SO(4) symmetry of the composite sector,
the effective Lagrangian of the gauge and pseudo-Goldstone fields becomes \cite{Agashe:2004rs}
\begin{equation}
\label{eq:L}
{\cal L}= \,\frac{f_\pi^2}{2}(D_\mu\Sigma)^\top D^\mu\Sigma-\frac{1}{4g^2}W^a_{\mu\nu}W^{a,\mu\nu}-\alpha\cos\frac{h}{f_\pi}+\beta\sin^2\frac{h}{f_\pi}.
\end{equation}
The last two terms represent the scalar potential for the pseudo-Goldstones, arising from explicit sources of SO(5) breaking, such as Yukawas and the gauging of $\mathrm{SU}(2)_L$. We may identify the Goldstones $h^m$ with the usual elementary Higgs multiplet as
\begin{equation}
\label{eq:Hh}
H=\left[
\begin{array}{c}
H^+\\
H^0
\end{array}
\right]=\frac{1}{\sqrt{2}}\left[
\begin{array}{c}
h^1+ih^2\\
h^3+ih^4
\end{array}
\right].
\end{equation}
In the Higgs vacuum we have respectively $\langle h\rangle=\langle h^3\rangle\neq0$, and
\begin{align}
\label{eq:vacuum}
\langle\Sigma^\top\rangle=[0,0,\epsilon,0,\sqrt{1-\epsilon^2}],\quad\epsilon=\sin\frac{\langle h\rangle}{f_\pi}.
\end{align}
The covariant derivatives in the Lagrangian of Eq.~\eqref{eq:L} include SU(2)$_L$ generators. From the identification of Eq.~\eqref{eq:Hh} we may construct the representation of SU(2)$_L$ on the Goldstone
multiplet $\Sigma$ as follows,
\begin{equation}
\label{eq:SU2gen}
\begin{aligned}
D_\mu\Sigma=&\partial_\mu\Sigma-i A_\mu^a T^a\Sigma,\\
T^1=&\frac{i}{2}\left[
\begin{array}{ccccc}
0 & 0 & 0 & 1 & 0\\
0 & 0 & -1 & 0 & 0\\
0 & 1 & 0 & 0 & 0\\
-1 & 0 & 0 & 0 & 0\\
0 & 0 & 0 & 0 & 0
\end{array} \right],
\,T^2=&\frac{i}{2}\left[
\begin{array}{ccccc}
0 & 0 & -1 & 0 & 0\\
0 & 0 & 0 & -1 & 0\\
1 & 0 & 0 & 0 & 0\\
0 & 1 & 0 & 0 & 0\\
0 & 0 & 0 & 0 & 0
\end{array} \right],
\,T^3=&\frac{i}{2}\left[
\begin{array}{ccccc}
0 & 1 & 0 & 0 & 0\\
-1 & 0 & 0 & 0 & 0\\
0 & 0 & 0 & -1 & 0\\
0 & 0 & 1 & 0 & 0\\
0 & 0 & 0 & 0 & 0
\end{array} \right].
\end{aligned}
\end{equation}
Note how the generators are a subset of the unbroken SO(4) symmetry acting on the first four components of $\Sigma$.
The mass of the gauge bosons in the vacuum is defined by
\begin{equation}
m^2_W=\frac{g^2\epsilon^2 f^2_\pi}{4}\equiv\frac{g^2v^2}{4},
\label{eq:mw}
\end{equation}
where at tree-level $v= \epsilon f_\pi = 246$ GeV. Note that $v$ here does not represent the pseudo-Goldstone VEV, but rather parameterizes the $W$ mass. For $|\alpha/(2\beta)|\leq1$ the scalar potential has a minimum at
\begin{equation}
\label{eq:vev2}
\cos\frac{\langle h\rangle}{f_\pi}=-\frac{\alpha}{2\beta},
\end{equation}
and the fluctuations of the field $h^3$ -- the pseudo-Goldstone version of the Higgs -- acquire a mass
\begin{align}
m^2_h=\frac{2\beta\epsilon^2}{f_\pi^2}.
\end{align}
Note that a positive Higgs mass requires $\beta>0$, while Eq.~\eqref{eq:vev2} will have a solution for either positive or negative $\alpha$. It appears that there are two families of solutions, but as we will
argue later they are physically equivalent. Beyond the known value of the weak gauge coupling, the bosonic low-energy Lagrangian of Eq.~\eqref{eq:L} has three parameters $f_\pi,\alpha,\beta$, and there is freedom in choosing the sign of $\alpha$. Requiring that the masses of the gauge bosons and the Higgs
reproduce their measured values leaves one free parameter, which we take as $f_\pi$. Thus we may write $\alpha,\beta$ in terms of the physical masses $m_W,m_h$ and $f_\pi$:
\begin{align}
\label{eq:abeta}
\alpha=\pm\frac{g f_\pi^4}{4}\frac{m^2_h}{m_W}\sqrt{\frac{g^2}{m^2_W}-\frac{4}{f_\pi^2}},\quad \beta=\frac{g^2 f^4_\pi}{8}\frac{m^2_h}{m^2_W}.
\end{align}
Note that consistency demands
\begin{align}
\label{eq:fmin}
f_\pi > \frac{2m_W}{g}.
\end{align}
Picking the lowest possible value of $\langle h\rangle$ yielding the correct gauge boson mass, (i.e. $\sin h/f_\pi>0$) one has
\begin{equation}
\label{eq:vev}
\begin{aligned}
&\langle h\rangle_-=v+\frac{v^3}{6f_\pi^2}+\frac{3v^5}{40f_\pi^4}+{\cal O}\left(\frac{1}{f_\pi^6}\right)~~\mathrm{for}~~\alpha<0,\\
&\langle h\rangle_+=\pi f_\pi-\langle h\rangle_-=\pi f_\pi-v-\frac{v^3}{6f_\pi^2}-\frac{3v^5}{40f_\pi^4}+{\cal O}\left(\frac{1}{f_\pi^6}\right)~~\mathrm{for}~~\alpha>0,
\end{aligned}
\end{equation}
which shows explicitly the modified relation between the Higgs VEV and the $W$ masses alluded to before. At this point, one would be tempted to argue that models in the large $f_\pi$, $\alpha>0$ branch,
with $\langle h\rangle \gg v$, should develop a larger sphaleron barrier. In previous sections we saw that the sphaleron configurations probe
the potential between the origin and the Higgs VEV, and so for large $\langle h\rangle$ the sphaleron profile would have to cover a larger amount of field-space,
implying larger kinetic contributions to the bosonic energy. Alas, this intuition is misleading. An important difference with respect to the elementary Higgs case is that the theory has a discrete selection rule.
It can be easily seen that in a unitary gauge with $h^i=0,i\neq3$, and thus $h^3=h$, the Lagrangian of Eq.~\eqref{eq:L} is invariant under the discrete transformation
\begin{align}
\label{eq:alphalaw}
\alpha\rightarrow-\alpha,\quad h\rightarrow \pi f_\pi-h.
\end{align}
This means that sphaleron solutions for one choice of sign of $\alpha$ can be related to sphaleron solutions for the other choice, with matching energies. For this reason the two choices of sign of $\alpha$ are physically equivalent. This equivalence can also be seen by expanding the Lagrangian in the unitary gauge around the vacuum configurations, $ h=\langle h\rangle+\delta h$, with $\langle h\rangle$ given in Eq.~\eqref{eq:vev}, and with $\alpha$ either positive or negative as in Eq.~\eqref{eq:abeta}. Doing a $1/f_\pi$ expansion, the resulting terms are related by an unphysical $Z_2$ transformation $\delta h\rightarrow-\delta h$. The same conclusion applies to fermionic couplings, which we did not discuss here but can be modelled again with $\sin h/f$ interactions \cite{Agashe:2004rs}. Therefore both scenarios with $\alpha>0$ and $\alpha<0$ are indistinguishable, and we will focus on the $\alpha<0$ case. We show in figure \ref{fig:Vcomp} the potential energy density of $h$ for $f=260$ GeV, showing the two equivalent realizations with different signs of $\alpha$. Note the different position of the VEVs and how the potentials are related by the transformation \eqref{eq:alphalaw}.
\begin{figure}[h!]
\begin{center}
\begin{minipage}{0.5\textwidth}
\includegraphics[width=0.95\textwidth]{Vcompneg.pdf}
\end{minipage}%
\begin{minipage}{0.5\textwidth}
\includegraphics[width=0.95\textwidth]{Vcomppos.pdf}
\end{minipage}
\caption{Composite Higgs potential for $f_\pi=260$ GeV, for the physically equivalent realizations with $\alpha<0$ (left) and $\alpha>0$ (right). Both cases yield the correct Higgs and $W$ masses at tree-level. The darker shade shows the region of the potential probed by the
sphaleron branch in common with the SM, while the lighter shade corresponds to the region probed by the new, higher-energy sphaleron branch present in composite models.}
\label{fig:Vcomp}
\end{center}
\end{figure}
Given the row of zeros in the SU(2)$_L$ generators in Eq.~\eqref{eq:SU2gen}, it is clear that $\Sigma$ involves two irreducible representations. We may write $\Sigma=\tilde\Sigma\oplus\Lambda$, with
\begin{align}
\label{eq:tildeSigma}
\tilde\Sigma^\top=\frac{\sin\frac{h}{f_\pi}}{h}[h^1,h^2,h^3,h^4],\quad
\Lambda=\cos\frac{h}{f_\pi}.
\end{align}
Then $D_\mu\tilde\Sigma=\partial_\mu\tilde\Sigma-iA^a_\mu\tilde T^a\tilde\Sigma$, with the $\tilde T^a$ given by the upper-left $4\times4$ blocks of the generators in Eq.~\eqref{eq:SU2gen}. In this way
we can rewrite Eq.~\eqref{eq:L} as
\begin{equation}
\label{eq:L2}
{\cal L}= \,\frac{f_\pi^2}{2}\partial_\mu\Lambda\partial^\mu\Lambda+\frac{f_\pi^2}{2}(D_\mu\tilde\Sigma)^\top D^\mu\tilde\Sigma-\frac{1}{4g^2}W^a_{\mu\nu}W^{a,\mu\nu}-\alpha\cos\frac{h}{f_\pi}+\beta\sin^2\frac{h}{f_\pi}.
\end{equation}
We are now ready to define the bosonic potential energy relevant for sphaleron configurations. As in the previous cases, this is just given by the Hamiltonian in the temporal $A_0=0$ gauge, with time derivatives
omitted (or equivalently, the Euclidean Lagrangian evaluated in static configurations). Performing rescalings as in Eq.~\eqref{eq:rescaling}, with $h_i\rightarrow m_W/g h_i$, the dimensionless bosonic energy functional becomes
\begin{equation}
\tilde V_{\rm bos}=\frac{1}{g^2}\int\!d^3y\,\left\{\frac{1}{4}\tilde W^a_{ij}\tilde W^{a}_{ij}+\frac{\hat f_\pi^2}{2}\partial_i\Lambda \partial_i\Lambda+\frac{\hat f_\pi^2}{2}(D_i\tilde\Sigma)^\top D_i\tilde\Sigma+\hat\alpha\cos\frac{\tilde h}{\hat f_\pi}-\hat\beta\sin^2\frac{\tilde h}{\hat f_\pi}\right\},
\end{equation}
where we defined the following modified couplings,
\begin{align}
\hat f_\pi\equiv\frac{g f_\pi}{m_W},\quad \hat \alpha\equiv\frac{\alpha g^2}{m^4_W},\quad \hat \beta\equiv\frac{\beta g^2}{m^4_W}.
\end{align}
The equations for the sphaleron configurations that extremise $\tilde V_{\rm bos}$ are:
\begin{equation}
\label{eq:eom}
\begin{aligned}
({\cal D}_j W_{ij})^a+\frac{i\hat f_\pi^2}{2}\left(\tilde\Sigma^\top T^a D_i\tilde\Sigma-(D_i\tilde\Sigma)^\top T^a \Sigma\right)=0,\quad i,a=1,\dots,3,\\
\hat f^2_\pi\left(\partial^2\Lambda\frac{\partial\Lambda}{\partial h^m}+(D^2\tilde\Sigma)^n\frac{\partial\tilde\Sigma^n}{\partial h^m}\right)+\frac{h^m}{h\hat f_\pi}\sin\frac{h}{\hat f_\pi}
\left(\hat\alpha+2\hat\beta\cos\frac{h}{\hat f_\pi}\right)=0,\quad m=1,\dots,4,
\end{aligned}
\end{equation}
with
\begin{align}
\frac{\partial\Lambda}{\partial h^m} &=-\frac{h^m}{h\hat f_\pi}\sin\frac{h}{\hat f_\pi},& \frac{\partial\tilde\Sigma^n}{\partial h^m} &=\frac{1}{h^3\hat f_\pi}\left(h \cos\frac{h}{\hat{f}_\pi}
-\hat{f}_\pi\sin\frac{h}{\hat{f}_\pi}\right)h^m h^n+\frac{\delta^{mn}}{h}\sin\frac{h}{\hat{f}_\pi}.
\end{align}
We shall proceed as before and introduce the same rotationally symmetric ansatz as in Eq.~\eqref{eq:ansatz}, with $\tilde H$ interpreted in terms of the dimensionless Goldstone fields $\tilde h^i$ as
$\tilde H=[\tilde h_1+i\tilde h_2, \tilde h_3+i\tilde h_4]^\top$.
After introducing the ansatz in the equations of motion, and going as before into the $C=0$ gauge, one gets four independent equations of motion, which can be written as:
\begin{equation}
\label{eq:Escomp}
\begin{aligned}
&\,B''-\frac{B}{r^2}\left(A^2+B^2-1\right)+{\cal F}^2_1\left[2GF-B(G^2+F^2)\right]=0,\\
&\,A''-\frac{A}{r^2}\left(A^2+B^2-1\right)-{\cal F}^2_1\left[A(G^2+F^2)+G^2-F^2\right]=0,\\
\end{aligned}
\end{equation}
\begin{equation}
\begin{aligned}
&\,{{{\cal F}_1}}\left\{\hat{f}_\pi^2 \left[{{\cal F}_2} G \left(4 F \left(2 B G+r \left(r F''+2 F'\right)\right)-G^2 \left(2 A^2+4 A+2 B^2+2\right)-F^2 \left(2 A^2-4 A+2 B^2+2\right)\right.\right.\right.\\
&\left.\left.+4 r G\left(r G''+2 G'\right)\right)+{{\cal F}_1} F \left(F \left(4 r^2 G''+8 r G'-8 A G\right)-4 G^2 B+4F^2 B-4 G r \left(r F''+2 F'\right)\right)\right]\\
&\left.+4 \hat\alpha G^3 r^2+4 \hat\alpha G F^2 r^2+8 \hat\beta {{\cal F}_2} G r^2 \left(G^2+F^2\right)\right\}\\
&+{2\hat{f}_\pi^2 \,r}\left\{{{\cal F}_1}' \left[4 {{\cal F}_2} G\left(G^2+F^2\right) +4 r G' \left({{\cal F}_1} F^2+{{\cal F}_2} G^2\right)+4 r G F ({{\cal F}_2}-{{\cal F}_1}) F'\right]+2G \left(G^2+F^2\right)( r{{\cal F}_2} {{\cal F}_1}'' \right.\\
&\left.-r {{\cal F}_1} {{\cal F}_2}'' -2 {{\cal F}_1} {{\cal F}_2}' )\right\}=0
,\\
\ \\
&\,{{{\cal F}_1}}\left\{\hat{f}_\pi^2 \left[{{\cal F}_2} F \left(4 F \left(2 B G+r(r F''+2 F')\right)-G^2 \left(2 A^2+4 A+2 B^2+2\right)-F^2 \left(2 A^2-4 A+2 B^2+2\right)\right.\right.\right.\\
&\left.\left.+4 r G \left(r G''+2 G'\right)\right)+ {{\cal F}_1} G \left(G(4r^2 F''+8 r F'+8 A F)+4 B G^2-4 B F^2-4 r F(r G''+2G')\right)\right]\\
&\left.+4 \hat\alpha G^2 F r^2+4 \hat\alpha F^3 r^2+8 \hat\beta {{\cal F}_2} F r^2 \left(G^2+F^2\right)\right\}\\
&+{2 \hat{f}_\pi^2\, r}\left[ {{\cal F}_1}' \left(4{{\cal F}_2} F\left(G^2+F^2\right) +4 r F' \left({{\cal F}_1} G^2+{{\cal F}_2} F^2\right)+4 G F r ({{\cal F}_2}-{{\cal F}_1}) G'\right)+2 F \left(G^2+F^2\right) \left(r{{\cal F}_2} {{\cal F}_1}''\right.\right.\\
&\left.\left.-r{{\cal F}_1} {{\cal F}_2}''-2 {{\cal F}_1} {{\cal F}_2}'\right)\right]=0.
\end{aligned}
\end{equation}
In the previous equations, we defined the ``form-factors''
\begin{eqnarray}\begin{aligned}
{\cal F}_1\equiv&\,\frac{\hat{f}_\pi\sin\frac{h}{\hat{f}_\pi}}{h}=\frac{\hat{f}_\pi}{2\sqrt{G^2+F^2}}\sin\left[\frac{2\sqrt{G^2+F^2}}{\hat{f}_\pi}\right],\\
{\cal F}_2\equiv&\,\cos\frac{h}{\hat{f}_\pi}=\cos\left[\frac{2\sqrt{G^2+F^2}}{\hat{f}_\pi}\right].
\end{aligned}
\end{eqnarray}
These form factors ${\cal F}_1,{\cal F}_2$ encode the nontrivial interactions of the composite Higgs. They tend to $1$ for large $\hat{f}_\pi$, for which one recovers the limiting case of the SM Higgs. This can be explicitly
checked from the above sphaleron equations, or by realizing that in this limit the bosonic Lagrangian of Eq.~\eqref{eq:L} coincides with the SM one.
The variables introduced in Eq.~\eqref{eq:RS} allow for a substantial simplification for the equations, which become
\begin{equation}
\label{eq:eqsR}
\begin{aligned}
& R''+\frac{\hat{f}_\pi^2}{4} \sin ^2\left[\frac{2 S}{\hat{f}_\pi}\right] \cos [2 \phi-\theta]+R \left(\frac{\hat{f}_\pi^2}{8} \cos \left[\frac{4 S}{\hat{f}_\pi}\right]-\frac{\hat{f}_\pi^2}{8}+\frac{1}{r^2}-\theta'^2\right)-\frac{R^3}{r^2}=0,\\
&2 r \left(r S''\!+2 S'\right)+\frac{\hat{f}_\pi}{4} \sin \left[\frac{4 S}{\hat{f}_\pi}\right] \left(2 R \cos [2 \phi-\theta]\!-\!2 r^2 \phi'^2\!-\!R^2\!-\!1\right)+\frac{r^2}{\hat{f}_\pi} \sin \left[\frac{2 S}{\hat{f}_\pi}\right] \left({\hat\alpha}+2 {\hat\beta} \cos \left[\frac{2 S}{\hat{f}_\pi}\right]\right)=0,\\
& 4 R \theta''+8 R' \theta'+\hat{f}_\pi^2 \sin ^2\left[\frac{2 S}{\hat{f}_\pi}\right] \sin [2 \phi-\theta]=0,\\
& r \left(\hat{f}_\pi r \phi''+2 \phi' \left(2 r S' \cot \left[\frac{2 S}{\hat{f}_\pi}\right]+\hat{f}_\pi\right)\right)-\hat{f}_\pi R \sin [2 \phi-\theta]=0.
\end{aligned}
\end{equation}
In these variables we may write $\tilde V_{\rm bos}$ as
\begin{equation}
\label{eq:Vbospol}
\begin{aligned}
\tilde V_{\rm bos}=&\frac{4\pi}{g^2}\int dr\left\{\frac{1}{4} \left[\hat{f}_\pi^2 \sin ^2\left[\frac{2 S}{\hat{f}_\pi}\right] \left((R-1)^2+2 R(1- \cos [2 \phi-\theta])\right)+4 R^2{ \theta'}^2+4 {R'}^2\right]\right.\\
&\left.+\frac{1}{2} \left(R^2-1\right)^2+\frac
{r^2}{4}\left[\frac{1}{\beta}\left(\hat\alpha+2 \hat\beta \cos \left[\frac{2 S}{\hat{f}_\pi}\right]\right)^2+2 \hat{f}_\pi^2 {\phi'}^2 \sin ^2\left[\frac{2 S}{\hat{f}_\pi}\right]+8 {S'}^2\right]
\right\}.
\end{aligned}
\end{equation}
As in the previous cases, the last two equations in \eqref{eq:eqsR} can be solved as in \eqref{eq:thetas}. This gives the simplified system
\begin{equation}
\label{eq:eqsRsimple}
\begin{aligned}
&R''+ R \left(\frac{1}{r^2}-\frac{1}{4} \hat{f}_\pi^2 \sin ^2\left[\frac{2 S}{\hat{f}_\pi}\right]\right)\pm\frac{1}{4} \hat{f}_\pi^2 \sin ^2\left[\frac{2 S}{\hat{f}_\pi}\right]-\frac{R^3}{r^2}=0,\\
&r^2 S''+2 r S'+\frac{1}{8\hat{f}_\pi}\left(4 \hat\alpha r^2 \sin \left[\frac{2 S}{\hat{f}_\pi}\right]-\sin \left[\frac{4 S}{\hat{f}_\pi}\right] \left(\hat{f}_\pi^2 (R\mp1)^2-4 \hat\beta r^2\right)\right)=0.
\end{aligned}
\end{equation}
The aforementioned physical equivalence between models with $\alpha>0$ and $\alpha<0$ can be understood from the bosonic energy \eqref{eq:Vbospol} and equations \eqref{eq:eqsR}, \eqref{eq:eqsRsimple} by noting that they are invariant under the discrete symmetry
\begin{align}
\hat\alpha\rightarrow-\hat\alpha,\quad S\rightarrow S+\frac{\pi}{2} \hat{f}_\pi.
\end{align}
Thus, solutions with one sign of $\hat\alpha$ can always be mapped onto solutions with the other sign. With the sign of $\hat\alpha$ fixed, another discrete symmetry of the bosonic energy and the sphaleron equations is
\begin{align}
\label{eq:discretesym}
S\rightarrow \pi \hat{f}_\pi\pm S.
\end{align}
The asymptotic solutions for Eq.~\eqref{eq:Escomp} in the limit of
large and small $r$ are given in appendix \ref{app:asympt}, and for fixed $f_\pi$ depend on the same number of parameters as in cases with an elementary Higgs. The corresponding solutions for \eqref{eq:eqsR} and \eqref{eq:eqsRsimple} can be obtained by using the definitions in \eqref{eq:RS}. Once again, reconstructing the full profile of the sphaleron from the solutions to the simplified system \eqref{eq:eqsRsimple} requires to fix the ambiguity in the solution \eqref{eq:thetas} for $\theta,\phi$. As in the SM, parity-invariant sphalerons are expected to have $N_{CS}=1/2$, which fixes $\theta=\pi+n\pi$. Fixing $R>0$ at large $r$, we have found solutions with $\theta=\pi$ in the upper branch of Eq.~\eqref{eq:eqsRsimple}, corresponding to $\phi=\pi/2$ (see \eqref{eq:thetas}).
A distinguishing feature of composite Higgs scenarios is that there are new types of asymptotic solutions at $r\rightarrow0$ that can support novel sphaleron solutions with $N_{CS}=1/2$. In the SM and in the case of a deformed potential, sphalerons ended up having $S(r=0)=0$, as can be seen in figures \ref{fig:profiles_SM} and \ref{fig:profiles_def}. The existence of new solutions with
$S(0)\neq0$ can be understood as follows. By continuity with the SM case, one expects solutions with $S(0)=0$ for both $\hat\alpha>0$ and $\hat\alpha<0$. However, as was just argued, solutions with $\hat\alpha>0$ and $S(0)=0$ can be mapped to solutions with the opposite sign of $\hat\alpha$ by doing $S\rightarrow S+\pi/2 \hat{f}_\pi$, so that one ends up with $S(0)=\pi/2\hat{f}_\pi$. For $\hat\alpha<0$ this corresponds to a local maximum of the potential.
We see that sphalerons interpolating between the minimum of the scalar potential and the origin, for a given choice of $\hat\alpha$, are equivalent to sphalerons that interpolate between the minimum and a local maximum for the opposite choice of $\hat\alpha$ (see figure \ref{fig:Vcomp}). The existence of new solutions with different behaviour near $r=0$ implies that there must be a new family of asymptotic solutions for small $r$,
which is given in appendix \ref{app:asympt}. Amusingly, as further discussed in the appendix, although the choices of opposite values $\hat\alpha$ are equivalent, regular solutions for a given sign of $\hat\alpha$ correspond to singular solutions with the opposite $\hat\alpha$, although the singularity is unphysical, as it can be removed with a gauge transformation. The existence of a new family of sphalerons with $N_{CS}=1/2$ and for the observed value of the Higgs mass is a novel effect which is not present in models with elementary Higgses. In that case, as in the SM, new branches of sphalerons typically have $N_{CS}\neq 1/2$ and only appear if the Higgs is much more massive than observed.
We have computed numerically the sphaleron energy in both families of sphalerons, using the iterative method described in previous sections. The solutions using the four differential equations \eqref{eq:eqsR} confirm the constant values of the angles, $\theta=\pi=2\phi$, derived from \eqref{eq:thetas} and the requirement for $N_{CS}=1/2$. Restricting the analysis to $\hat\alpha<0$, the family of solutions with the usual $S(0)=0$ behaviour gives a sphaleron barrier which, as expected, recovers the SM result in the limit of large $f_\pi$. The new family of $N_{CS}=1/2$ solutions
has greater energies.
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.48\textwidth]{E_vs_f_smallh.pdf}
\includegraphics[width=0.48\textwidth]{E_vs_f_largeh_2.pdf}
\caption{Energy barrier between topological vacua as a function of $f_\pi$, in the $S(0)=0$ (left) and $S(0)\neq0$ branches. The horizontal line marks the SM limit.}
\label{fig:barrier_smallh}
\end{center}
\end{figure}
As anticipated earlier, the fact that in composite models not only the potential of the Higgs but also its derivative interactions are modified allows for larger deviations from the value of $E_{\rm sph}$, even for the usual family with $S(0)=0$. In this case, $E_{\rm sph}$ reaches nearly 12 TeV for the theoretical minimum
$f_\pi=v$ (see equation \eqref{eq:fmin}), while it decreases rapidly with growing $f_\pi$. With current collider bounds demanding $f_\pi\gtrsim 0.5$ TeV \cite{Aad:2015pla, Azatov:2013hya}, the sphaleron barrier differs from the SM by less than three percent. In the $S(0)\neq0$ branch, the sphaleron barrier starts similarly at 12 TeV and grows linearly with $f_\pi$. The dependence of $E_{\rm sph}$ with the compositeness scale in the two branches is illustrated in Fig.~\ref{fig:barrier_smallh}. The energies in the $S(0)\neq0$ branch are subject to more numerical uncertainties due to the function $S$ becoming very steep at the origin, which prevents convergence of the iterative approach for large enough values of $f_\pi$. Still, our calculations show a linear growth which, when extrapolated, predicts a barrier of around 28 TeV for $f_\pi=500$ GeV and 70 TeV for $f_\pi=1.2$ TeV, respectively.
Example profiles for $R,S$ of the resulting solutions are shown in Fig.~\ref{fig:profiles}. Note the steepness of $S$ near the origin in the lower graphs corresponding to the $S(0)\neq0$ branch, which affects numerical convergence. For the same examples, Fig.~\ref{fig:Ecomp} shows the contributions to the integrand of the dimensionless bosonic energy functional $\tilde V_{\rm bos}$.
For the $S(0)\neq0$ branch and for large enough $f_\pi$, $E_{\rm sph}$ becomes dominated
by the scalar derivatives, in contrast to the cases with elementary fields (see figures \ref{fig:profiles_SM} and \ref{fig:profiles_def}). This is a consequence of the fact that, in this branch, the sphaleron profile interpolates between the electroweak vacuum and the maximum of the scalar potential at $\pi f_\pi$. The distance in field space travelled by the sphaleron increases linearly with $f_\pi$, and we observe the same for the integral yielding $E_{\rm sph}$.
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.49\textwidth]{RS_250_2_small.pdf}
\includegraphics[width=0.49\textwidth]{RS_1000_2_small.pdf}
\includegraphics[width=0.49\textwidth]{RS_250_2.pdf}
\includegraphics[width=0.49\textwidth]{RS_260_2.pdf}
\caption{Profile functions for $R,S$ in the sphaleron configurations obtained by solving the system of 2 differential equations. The vertical line marks the scale at which the low $r$ solution (red) was matched with the high $r$ solution (blue). Top: solutions in the $S(0)=0$ branch, with $f_\pi=250$ GeV (left) and $f_\pi=1$ TeV (right). Bottom: solutions in the $S(0)\neq0$ branch, with $f_\pi=250$ GeV (left) and $f_\pi=1$ TeV (right).}
\label{fig:profiles}
\end{center}
\end{figure}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.49\textwidth]{Vbosdef_comp_small.pdf}
\includegraphics[width=0.49\textwidth]{Vbosdef_comp_large.pdf}
\caption{Contributions to the integrand of the dimensionless bosonic energy functional for $\hat{f}_\pi=260$ GeV in the $S(0)=0$ branch (left) and for $S(0)\neq0$ GeV (right). The contributions in solid blue are due to the gauge fields; those coming from derivatives of the scalar fields are shown with dashed orange lines, while those coming from the scalar potential
energy density are shown with dotted green curves. }
\label{fig:Ecomp}
\end{center}
\end{figure}
\section{Summary}
\label{sec:summary}
In this paper we have investigated the size of the sphaleron energy barrier in non-standard realizations of the Higgs vacuum. The sphaleron energy, which in the Standard Model lies near 9 TeV, sets the scale of baryon number violating processes mediated by the B+L anomaly, and is sensitive to properties of the Higgs potential away from the electroweak minimum. Thus, sphaleron-induced processes -- which would manifest themselves through the production of a large number
of quarks and leptons -- could offer new perspectives on the nature of the Higgs particle, offering global information about its potential. This is in contrast to the perturbative processes usually considered at colliders, which only probe the Higgs interactions locally, i.e. at the electroweak vacuum.
The sphaleron energy can also be affected by modifications of the derivative interactions of the Higgs. In order to quantify the possible variations of $E_{\rm sph}$ in non-standard scenarios, we have calculated
$E_{\rm sph}$ in models which exhibit either a modified potential for an elementary Higgs, or both a modified potential and modified derivative terms for a composite Higgs. Such examples capture quite generic possibilities for the Higgs interactions, and can be considered as benchmarks for the possible variations of the scale of baryon number violation processes in theories beyond the Standard Model.
For an elementary Higgs with a modified potential, we considered a generic parametrization of the former involving a logarithmic term, which can introduce a barrier with respect to the origin and
modify the depth of the electroweak vacuum. For long-lived electroweak vacua we find deviations of the sphaleron barrier which are at most of the order of 10\%. Such small deviations become less surprising after realizing that already in the SM the sphaleron energy is dominated by derivative contributions, which mostly depend on the distance on field space covered by the scalar profile of the sphaleron. In models with an elementary Higgs, the sphaleron interpolates between the origin and the electroweak vacuum, whose position is fixed by the masses of the weak gauge bosons.
In composite Higgs models the situation could be in principle different, since both the derivative interactions and the relation between the weak boson masses and the Higgs VEV are modified. We centered our study in minimal composite Higgs models, in which the Higgs is a pseudo-Goldstone of a global SO(5) symmetry broken down to SO(4). We have found that,
in contrast with models with elementary Higgses, for which there are no multiple sphaleron branches for the observed values of the Higgs and gauge boson masses, composite Higgs models exhibit at least two branches of sphaleron solutions. The existence of a new branch can be understood from the discrete translation symmetries of the effective action for the pseudo-Goldstone fields. In contrast to known non-standard sphaleron branches for heavy elementary Higgses, sphalerons in this new branch still have half-integer Chern-Simons number, and an energy higher than the sphalerons in the usual branch. In the latter, although large deviations of $E_{\rm sph}$ are possible at low values of the compositeness scale, they are ruled out by collider bounds, so that the minimum sphaleron energy can only differ from the SM one by less than 3\%. On the other hand, sphalerons in the new branch have an energy that grows linearly with the compositeness scale, and would reach around 28 TeV if extrapolated to $\hat{f}_\pi=500$ GeV, and 70 TeV for $\hat{f}_\pi=1.2$ TeV. The new branch of sphaleron configurations is suggestive of a new high-energy threshold for baryon-violating processes in addition to the SM-like threshold at 9 TeV.
Concerning the theoretical precision precision of our calculations, it should be noted that we set the weak mixing angle $\theta_W$ to zero. In models with elementary Higgses, a nonzero $\theta_W$ is known to induce changes in the sphaleron energy of less than a percent \cite{Kleihaus:1991ks,Ahriche:2014jna}. Such modifications are smaller than the largest deviations of $E_{\rm sph}$ with respect to its SM value that were calculated in the models analyzed in this work. Hence, we expect our estimates to be robust with respect to the inclusion of mixing-angle effects.
\acknowledgements
We want to thank Valya Khoze and Kazuki Sakurai for very helpful discussions and comments. MS is supported in part by the European Commission through the ``HiggsTools'' Inital Training Network PITN-GA-2012-316704.
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} | 4,264 |
La rivière Doubtful (en ) est un cours d'eau de la région de Canterbury dans l'Île du Sud de la Nouvelle-Zélande.
Géographie
Elle prend naissance près du 'Mont Barron' et s'écoule vers le sud puis vers le sud-est à travers le Parc Forestier du Lac Sumner, atteignant la rivière Boyle à à l'ouest de la ville de Hanmer Springs. La chaîne de « Doubtful Range » siège au sud. La rivière Doubtless et le torrent "Devilskin Stream" sont des affluents entrant par le nord .
Le Department of Conservation maintient en état un sentier de randonnée le long des berges de la rivière avec des routes partant vers le nord et le sud. Un refuge est disponible pour les randonneurs près de la jonctions avec le torrent « Devilskin Stream » et la rivière Doubtless .
Voir aussi
la liste des cours d'eau de la Nouvelle-Zélande
Notes et références
Notes
Références
*Land Information New Zealand - Search for Place Names
Cours d'eau de la région de Canterbury en Nouvelle-Zélande | {
"redpajama_set_name": "RedPajamaWikipedia"
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Q: Unwrapping datatypes in Haskell without extraneous code Say I have
x = Just 2
Is there a way (preferrably a builtin mechanism/function) to use x in a single statement such that if it is a Just, then the 2 is automatically unwrapped and used, and if it is a Nothing, an exception is raised?
That is,
(f x) + 2 == 4 if x == Just 2, and raises an exception if x == Nothing.
A: Data.Maybe.fromJust has been mentioned by other answers already:
fromJust :: Maybe a -> a
fromJust Nothing = error "Maybe.fromJust: Nothing"
fromJust (Just x) = x
There's also maybe (found in both Prelude and Data.Maybe):
maybe :: b -> (a -> b) -> Maybe a -> b
maybe n _ Nothing = n
maybe _ f (Just x) = f x
fromJust can be written using maybe:
fromJust = maybe (error "Maybe.fromJust: Nothing") id
As you can see, maybe allows you flexibility in handling both cases without requiring pattern matching:
\x -> maybe 0 (+ 2) x -- Nothing -> 0, Just 2 -> 4
Similarly, Prelude and Data.Either have either :: (a -> c) -> (b -> c) -> Either a b -> c:
\x -> either (subtract 1) (* 2) x -- Left 5 -> 4, Right 3 -> 6
If you define a data type
data MyDataType
= TypeA { foo :: Int, bar :: String }
| TypeB { foo :: Int, baz :: () }
| TypeC { bar :: String, baz :: () }
like this, you end up with partial functions for accessors.
foo :: MyDataType -> Int
bar :: MyDataType -> String
baz :: MyDataType -> ()
They're called partial functions, as opposed to total functions, because they only return results for a subset of their inputs.
foo (TypeA { foo = 15, bar = "hello!" }) -- 15
bar (TypeB { foo = 12345679, baz = () }) -- error
A: For this particular case, fromJust. In general
let Just k = x in f k + 2 == 4
This trick works with any datatype constructor and is very commonly used with (:) for nonempty lists.
A: fromJust should do what you want.
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"redpajama_set_name": "RedPajamaStackExchange"
} | 4,304 |
Gulf Of Aden Vortex
2010 Where is this story in the international media? The combined naval might of twenty-seven countries is concentrated off the Somali coast allegedly to fight the poorly armed pirates who continue to act with apparent impunity. (Note that the sharks can walk on land and smaller sharks can eat bigger sharks. Personally, did several runs into the Persian Gulf on a number of ships. The largest dust plume can be observed in the upper left quadrant, blowing northeastward over the Red Sea, off the coast of Sudan, September 04, 2012. 16: MS-13 Suspected in Car Bombing that Injures Two Policía Nacional Civil (PNC) in Soyapango, El Salvador. The magnetic anomalies indicate that the sea floor in the Gulf is likely to have had three phases of spreading, so it has not been continuously formed. -Claramente existe un vortex en el Golfo de Aden. In this study we evaluated the spatial distribution and. ← Aaron McCollum and the Gulf of Aden Chemical Bio Expert Murdered After Arkansas Bird Catastrophe, John Wheeler Special Assistant to the Secretary of the Airforce → 1 Response to Wikileaks, the US secret bunker, the Gulf of Aden Vortex: Contact made? reports English Pravda. now what and why? Well to really fk u up, I gotta pull a bible out. An example is given from the Gulf of Aden of a total intensity magnetic anomaly which cannot be explained by a body assumed to be magnetized in the direction of the Earth's present magnetic field. It is nowhere near the Persian Gulf. Others have speculated that the portal could be the result of machinations at CERN or another particle collider, as a similar vortex was allegedly reported above Norway in 2009. Aaron McCollum is a very bright straight-shooter who is coming forward at this time to raise awareness regarding what he believes is going on in the Gulf of Aden. Under the vision of the Kirlian photograph, Walter's water has a prana field that extends from the glass of water out about eight inches. I have been looking through the Ning and ZetaTalk archives regarding the Gulf of Aden vortex. Trailing the Pacific Crest from Space. Explore Sharon Phillips's board "Gulf of Aden Vortex", followed by 160 people on Pinterest. Wikileaks, the US secret bunker, the Gulf of Aden Vortex: Contact made? 08. If you are searching for read reviews Gulf Of Aden Vortex Wikileaks price. The oceanic region comprised of the Persian Gulf (also known as the Arabian Gulf or simply the Gulf), Strait of Hormuz, and Gulf of Oman (Fig. Personally, did several runs into the Persian Gulf on a number of ships. ru Where is this story in the international media? The combined naval might of twenty-seven countries is concentrated off the Somali coast allegedly to fight the poorly armed pirates who continue to act with apparent impunity. The perplexing theory, described by some enthusiasts as the "greatest conspiracy theory of all time," claims that a "magnetic anomaly" opened up an interdimensional "stargate portal" in the Gulf Of Aden, one of the busiest waterways in the world between Yemen in the Arabian Peninsula and Somalia in the Horn of Africa. 5/11/17, Pirates in Gulf of Aden attempt to board a Turkish vessel. Density surfaces and core water we searched the National Oceanic and Atmo- approximate depths (in the eastern GOA) are indicated. [37] Several groups are presently investigating the region north of mountainous Socotra (P. Russia, the PR China and the USA joined efforts to study what it was but discovered that it defied logic and the laws of physics. The Mystery of the Gulf of Aden In 2008 a set of mysterious and long-forgotten caves was rediscovered by a British exploration team consisted of Andrew Collins, Sue Collins, and Nigel Skinner-Simpson with the help of engineer Rodney Hale. Coastal sediments in the northern Gulf of Mexico have a high potential of being contaminated by petroleum hydrocarbons, such as polycyclic aromatic hydrocarbons (PAHs), due to extensive petroleum exploration and transportation activities. It was investigated until 2008, when it started to expand, around the time the CERN SHC started to experiment. Abstract As the Red Sea overflow water (RSOW) enters the Gulf of Aden (GOA), it interacts with a sequence of nearly barotropic, mesoscale eddies originating in the Indian Ocean. View thousands of free gulf stream clip art that you can download without any purchase required. The Gulf of Aden [photo 2 nd left] is one of the most vital waterways in the world located in the Arabian Sea between Yemen, on the south coast of the Arabian Peninsula, and Somalia in the Horn of Africa that sees over 21,000 ships sailing through its waters each year. Re: Vortex, Gulf of Aden EarthsAngel on Tue Jan 25, 2011 9:55 pm I had to watch this video twice before I could really make out the face, maybe my eyes are getting bad, but there is something there, there is a face and it's really weird. According to a report allegedly prepared by Admiral Maksimov of Russia's Northern Fleet, in late 2000, a magnetic vortex was discovered in the area of the Gulf of Aden. In response to the fluid situation in the Gulf of Aden and Somali basin, industry bodies have updated the Best Management Practices document, the latest incarnation is version 4 (BMP4). Yeah, but Yemen is not a "Gulf state. The Flower of life Grid, The Gulf of Aden Stargate Vortex and more geomancy and ley lines. According to a report allegedly prepared by Admiral Maksimov of Russia's Northern Fleet, in late 2000, a magnetic vortex was discovered in the area of the Gulf of Aden. 1) is one of the most important waterways in the world. Into Somali Vortex Written by Charles Scaliger Tweet font size Given the increasing boldness of the Somali pirates' attacks on shipping in the Gulf of Aden, and the. Definitions index 108-adu for Webster's New World College Dictionary, The American Heritage Dictionary of the English Language and Ologies & Isms. I have been looking through the Ning and ZetaTalk archives regarding the Gulf of Aden vortex. Note: This page is continually updated as new transcripts become available. " Now, what does that mean, Mr. Citation: Fratantoni, D. The tanker, laden with lubricating oil and ethylene dichloride was headed for Singapore when attacked by a. Update: I just met the messenger with 52 disguise and no sociability skill. -Conclusiones: 1º. Gulf of Aden vortex may very well be a "Stargate" opening up into our world from a dimension and/or world we known nothing about. The GA is characterised with westward propagating cyclonic and anti-cyclonic eddies. Welkom bij misschien wel de grootste Hosta database en zeer uitgebreide zoekmachine! Zoek in deze database die 12260 Hosta's bevat en op dit moment 18814 foto's van 3688 verschillende Hosta's!. The English Electric (BAC) Lightning v1. GULF OF ADEN STARGATE. That a real Stargate has been found, and it's seven miles underground in the Gulf of Aden in an underground military base. The northernmost extent of the Indian Ocean is approximately 30° north in the Persian Gulf. The al Houthi movement claimed that ten drones had targeted the Shaybah oilfield near the UAE border and said that the attack was the "largest attack" in the history of the Yemen conflict. It connects the Red Sea and the Gulf of Aden, as such the link between the Mediterranean and the Indian Ocean. Shop a wide selection of products for your home at Amazon. The Gulf of Aden (GA) is a small semi-enclosed oceanic region between the Red Sea and the western Arabian Sea. A bizarre report prepared for Prime Minister Putin by Admiral Maksimov of Russia's Northern Fleet states that a 'mysterious magnetic vortex' currently centered in the Gulf of Aden has "defied" all the combined efforts of Russia, The United States and China to shut it down, or even to ascertain its exact origin or "cause for being". This is supposedly where a Stargate is burried two miles under the ocean floor. The al Houthi movement attacked an oilfield in eastern Saudi Arabia with multiple drones on August 17. The Gulf of Aden is located between the coast of Arabia and the Horn of Africa, at the opening of the Persian Gulf. com )- An accurate count of the AK47 type rifles confiscated in the Gulf of Aden on 28 August 2018, has been released. Bureau Home > Australia > Weather Maps > Latest Colour Mean Sea-Level Pressure Analysis. title = "Somali Current rings in the eastern Gulf of Aden", abstract = "New satellite-based observations reveal that westward translating anticyclonic: rings are generated as a portion of the Somali Current accelerates northward through the Socotra Passage near the mouth of the Gulf of Aden. Reptilian base under Gulf of Aden is a priority target "Both of these bases, the one south of the Saudi Arabian, UAE, Yemen, Oman peninsula, this is the one in the Gulf of Aden, and the one off of the coast of China - both are well fortified, re-enforced fortresses, if you will, deep under water bases located on the ocean floor. As you may or may not know the "vortex" phenomena also happened in this body of water, the Gulf of Aden. title = "Somali Current rings in the eastern Gulf of Aden", abstract = "New satellite-based observations reveal that westward translating anticyclonic: rings are generated as a portion of the Somali Current accelerates northward through the Socotra Passage near the mouth of the Gulf of Aden. An unbiased look at myths, articles, and anything related to global. 31, 2011 ExopoliticsTV interview, the human representative of the Andromeda Council confirmed that a 5. The Sargasso Sea is a region in the gyre in the middle of the North Atlantic Ocean. Xceleration Media is proud to present the Summer/Fall 2016 issue of OneDirt. Not about climate change, not about refugees, not about homelessness, older women adrift without a secure income, or the stinginess of Newstart. Link to abstract: Gulf of Aden Magnetic Anomaly and the Curie Temperature Isotherm. There are several groups that specialise in the minutea of WW2 and post-war RAF uniforms and they may be in a better position to say what is "correct" for any particular period, given the original wearers of such are getting fewer as time passes. Gulf of Mexico hot spot, Sunrise light tower, Panama UFO display, Military Tribunals EO, Slovak elections, Skripal UK poisoning, Hillary India slip, S Africa expropriation, Nibiru's face, Prong 3 revival, Alberto Monster Nibiru overlay, Winter Cherry mall bombing: Feb 28, 2018. 16: MS-13 Suspected in Car Bombing that Injures Two Policía Nacional Civil (PNC) in Soyapango, El Salvador. La cuestión de la utilización del mismo escapa de la lógica de la fundamentación civil, lo que sugiere intervención militar en la zona, con tecnologías que implican el conocimiento avanzado de la fundamentación aquí expuesta. Just like the smoke rings of Kelvin seemed flexible objects, the energy vortex can appear like stable and solid particles. According to an ancient tradition, with this name, a city was founded in Thessaly, in central Greece from the mythical hero Hellenas [ Έλληνας ], patriarch of the Greeks. 1st of the best of 3 series in the WGL week 2 Blops 2 Send off DE league. 31 ExopoliticsTV interview regarding the Gulf of Aden earthquake and Andromeda Council destruction of a reptilian undersea base. The Stratfor public. bizarre report prepared for Prime Minister Putin by Admiral Maksimov of Russia's Northern Fleet states that a 'mysterious magnetic vortex' currently centered in the Gulf of Aden has "defied" all the combined efforts of Russia, The United States and China to shut it down, or even to ascertain its exact origin or "cause for being". Apollyon,THE DESROYER And The bottomless pit and the Large Cern Hadron collider What I found kind of startled me. Wikileaks, the US secret bunker, the Gulf of Aden Vortex: Contact made? english. The Gulf of Aden, formerly known as the Gulf of Berbera, is a deepwater gulf amidst Yemen to the north, the Arabian Sea and Guardafui Channel to the east, So. The Gansevoort Meatpacking rests within a certain vortex of New York City's elite, steps from top-tier shopping, members-only club Soho House and plenty of smart restaurants and clubs like The Top of the Standard. The Gulf of Aden Vortex has been under scrutiny for several years now. Deep depression intensifies into cyclonic storm 'Sagar' over Gulf of Aden indiabloomsFirst cyclone of the season likely in Arabian Sea Skymet WeatherFull coverage. The Gulf of Aden [photo 2 nd left] is one of the most vital waterways in the world located in the Arabian Sea between Yemen, on the south coast of the Arabian Peninsula, and Somalia in the Horn of Africa that sees over 21,000 ships sailing through its waters each year. You will need bring your (3 pieces) Arabian clothing. A bizarre report prepared for Prime Minister Putin by Admiral Maksimov of. The table below lists "events at sea" occurring after January 1, 2009, including cruise ship accidents. Bloomberg says Bechtel Group has expressed interest in the project. 3 degrees East; about 140 km east-southeast of Aden (Yemen) and 820 km west-southwest of Socotra Islands. [A] Swashbuckling Thriller…Coonts takes us on a heck of a good ride. Magnetic vortex in the gulf of aden? 26 countries navy are gathered there because of the vortex? true or false? 1 following. ) You are operating Hungry Park England that was built next to a the coast of London. HAARP : GULF OF MEXICO / ATACAMA CHILE / EUROPA (1) HAARP CHEMTRAILS ORBS CRITTERS (1) HAARP EL HIERRO ERUPTION 2011 (1) HAARP from ISS - desde la Estacion Espacial (1) HAARP Gran Canaria 11-2011 (1) HAARP Gran Canaria 19-01-201 (1) HAARP Lenticular Clouds Nubes Lenticulares 2 (1) HAARP Lenticular cloudsNubes (1) HAARP Vortex in Tenerife Oct. —Kirkus ReviewsIn Pirate Alley, a luxurious vacation cruise to the exotic locales of the Red Sea and the Gulf of Aden turns into a nightmare for passengers and crew. Misleading Wikileaks: "Mysterious magnetic vortex" in Gulf of Aden has defied all efforts of Russia, USA and China to shut it down, or even to ascertain its exact origin or "cause for being". Office 1, Arwa street, Crater, Aden, Yemen. According to a report allegedly prepared by Admiral Maksimov of Russia's Northern Fleet, in late 2000, a magnetic vortex was discovered in the area of the Gulf of Aden. 9 / 01 jul 18 / greg goebel * During the 1950s, the British English Electric (later BAC) firm developed Britain's first (and in a sense last) operational Mach 2 fighter. There is a new subject that has come to light on the internet. 1 answer 1. I originally arrived at Jever after sailing from Harwich to the Hook of Holland, and then the long train Journey through Holland and Germany to Jever. Dossier vortex interdimensionnel dans le Golfe d'Aden, porte des étoiles, tremblements de terre, LHC du CERN à Genève. Earth Changing Extremities I cover many earth changing extremities ranging from Earthquakes, Quake Swarms, Volcanic Activity/Eruptions, CME's - Coronal Mass Ejections, Solar Flares, Geomagnetic Storms, Magnetosphere Pressure plus other solar related radiation pulses, Asteroid/Meteorite Threats, Solar System Threats, Landslides, Flooding, Sink Holes, Hurricanes, Typhoons, Storms, Tsunami's. TheMym2012 LIGHT FOR A ETERNAL LIFE. De la cuna a la tumba es una escuela, por eso lo que llamas, problemas son lecciones y la vida es dinámica por eso está en constante movimiento, por eso sólo debes estar atento al presente, por eso mi madre decía " yo me encargo del presente, el futuro es asunto de Dios " por eso Jesús decía " El mañana no interesa, él traerá nueva experiencia, a cada día le basta con su propio. It has a swirl pattern like a portal in the sky. Acts of terrorism and piracy have also affected vessels trading in regions such as the South China Sea and the Gulf of Aden off the coast of Somalia. According to the report, a magnetic vortex has formed in the bottom of the ocean in the Gulf of Aden. Free shipping and free returns on eligible items. The Hawk LIFT's cockpit has three color flat-panel MFDs, HOTAS controls, and a HUD. Collectively effecting geomagnetic's of earth as detected from satellites on. La cuestión de la utilización del mismo escapa de la lógica de la fundamentación civil, lo que sugiere intervención militar en la zona, con tecnologías que implican el conocimiento avanzado de la fundamentación aquí expuesta. Gulf of Aden vortex By Dust | Posted December 2, 2010 "A bizarre report prepared for Prime Minister Putin by Admiral Maksimov of Russia's Northern Fleet states that a 'mysterious magnetic vortex' currently centered in the Gulf of Aden has "defied" all the combined efforts of Russia, The United States and China to shut it down, or. The Flower of life Grid, The Gulf of Aden. As such, the Gulf of Oman acts as an "eddy‐guide" for their propagation (a similar situation is found in the Gulf of Aden) [Bower and Furey, 2012. Once again the Wikileaks cables come into play. HAARP : GULF OF MEXICO / ATACAMA CHILE / EUROPA (1) HAARP CHEMTRAILS ORBS CRITTERS (1) HAARP EL HIERRO ERUPTION 2011 (1) HAARP from ISS - desde la Estacion Espacial (1) HAARP Gran Canaria 11-2011 (1) HAARP Gran Canaria 19-01-201 (1) HAARP Lenticular Clouds Nubes Lenticulares 2 (1) HAARP Lenticular cloudsNubes (1) HAARP Vortex in Tenerife Oct. I find it hard to believe that some low ranking soldier can pop in a thumb drive and make off with terabytes of classified data covering every topic imaginable. Piracy May Draw U. Update: I just met the messenger with 52 disguise and no sociability skill. They may be, out of necessity, paying captains and crews a bonus for hazardous duty while transi. Misleading Wikileaks: "Mysterious magnetic vortex" in Gulf of Aden has defied all efforts of Russia, USA and China to shut it down, or even to ascertain its exact origin or "cause for being". The Gulf of Aden Vortex has been under scrutiny for several years now. Coastal sediments in the northern Gulf of Mexico have a high potential of being contaminated by petroleum hydrocarbons, such as polycyclic aromatic hydrocarbons (PAHs), due to extensive petroleum exploration and transportation activities. 2010 Where is this story in the international media? The combined naval might of twenty-seven countries is concentrated off the Somali coast allegedly to fight the poorly armed pirates who continue to act with apparent impunity. I remember that the RAF travelled in comparative luxury on the train compared to the army lads, we had plenty of room, the carriages were newer and smarter, whereas the army carriages were. And what is revealed is terrifying. Near the strait, the inflow from the Gulf of Aden forms an intense, short western boundary current. They contribute to the energy conversions between large-scale circulation and mesoscale dynamics, and regulate the bio-geo-. 2 Red Sea and Gulf of Aden The Red Sea is a long and narrow basin that only connects to the open ocean through the shallow strait of Bab el Mandeb in the south. Many world officials believe it is an attack on our planet by "interdimensional" or "extraterrestrial" forces ( wikileaks. Stargate in the Gulf of Aden There is a new subject that has come to light on the internet. 5 or greater) 0 earthquakes in the past 24 hours 0 earthquakes in the past 7 days. Map of Gulf of Aden, Gulf of Aden Location Facts, Major Bodies of Water, Asia. me free gulf stream collection now. Historians will have a "field-day" here too, visiting the white Indo-Arabic city of Mukalla, its feet bathing in the sea, or Aden, the ancient port of the Awsan Kinqdom from around the 6 th century B. Itsorientation(075 kinematics is consistent with an oblique rifting configura-E)anditskinematics (about030 Edivergence. The Gulf of Aden is a western arm of the Arabian Sea between the south coast of Yemen on the Arabian Peninsula and the northeast coast of Somalia and Djibouti in Africa. ) to have occurred in the Gulf of Aden at 1:22 am on October 31. The intrepid MI6 officer's latest challenge begins in the Gulf of Aden and soon has him searching for the link to a series of bizarre assassinations. bizarre report prepared for Prime Minister Putin by Admiral Maksimov of Russia's Northern Fleet states that a 'mysterious magnetic vortex' currently centered in the Gulf of Aden has "defied" all the combined efforts of Russia, The United States and China to shut it down, or even to ascertain its exact origin or "cause for being". A bizarre report prepared for Prime Minister Putin by Admiral Maksimov of Russia's Northern Fleet states that a 'mysterious magnetic vortex' currently centered in the Gulf of Aden has "defied" all the combined efforts of Russia, The United States and China to shut it down, or even to ascertain its exact origin or "cause for being". Bureau Home > Australia > Weather Maps > Latest Colour Mean Sea-Level Pressure Analysis. The BAE Hawk v1. Filmy, hry, hudba, softver a xxx na stiahnutie zadarmo,. The tanker, laden with lubricating oil and ethylene dichloride was headed for Singapore when attacked by a. According to a report allegedly prepared by Admiral Maksimov of Russia's Northern Fleet, in late 2000, a magnetic vortex was discovered in the area of the Gulf of Aden. Shop a wide selection of products for your home at Amazon. The Brainly community is constantly buzzing with the excitement of endless collaboration, proving that learning is more fun — and more effective — when we put our heads together. The recent upsurge in piracy off the coast of Somalia, and particularly in the Gulf of Aden, is the latest feature of the increasing disorder prevailing in that country. Surface Drifters occupied in the Gulf of Aden (GOA) in February - March [22] In an attempt to further confirm the origin of the ring 2001 [see Johns et al. The answers yes. As you may or may not know the "vortex" phenomena also happened in this body of water, the Gulf of Aden. 0 earthquake reported by the U. At the moment warships from China, Japan, England, The U. But, Gulf 1 to the side, there was usually just one carrier group in the Gulf. Science of Peace has found after 250+ scientific studies that inner peace(a feeling)=outer peace because we are all connected via the field. 26, 2011, the Andromeda Council representative stated (in part), "[The reptilian undersea base] is located in the area of the Gulf of Aden. Apollyon,THE DESROYER And The bottomless pit and the Large Cern Hadron collider What I found kind of startled me. 31, 2011 ExopoliticsTV interview, the human representative of the Andromeda Council confirmed that a 5. The tanker, laden with lubricating oil and ethylene dichloride was headed for Singapore when attacked by a. 3,245 likes · 42 talking about this. There is a new subject that has come to light on the internet. If you searching to test Vortex Cone Dust Collector Gulf Of Aden Vortex Wikileaks price. 2 Red Sea and Gulf of Aden The Red Sea is a long and narrow basin that only connects to the open ocean through the shallow strait of Bab el Mandeb in the south. Gulf of Aden Stargate Project Camelot interviews Aaron McCollum Aaron McCollum is a third generation member of Project Talent, the MKUltra program used to develop psychic warriors and supersoldiers by the secret government. Meridionally, the Indian Ocean is delimited from the Atlantic Ocean by the 20° east meridian, running south from Cape Agulhas, and from the Pacific Ocean by the meridian of 146°55'E, running south from the southernmost point of Tasmania. Mysterious 'Vortex' Warned Is Creating Global Weather Catastrophe Released on 2013-02-19 00:00 GMT. Title inspired by Science of Miracles by Gregg Braden and NESARA. Gulf of Mexico hot spot, Sunrise light tower, Panama UFO display, Military Tribunals EO, Slovak elections, Skripal UK poisoning, Hillary India slip, S Africa expropriation, Nibiru's face, Prong 3 revival, Alberto Monster Nibiru overlay, Winter Cherry mall bombing: Feb 28, 2018. What I am wondering about is is the high military presence around the vortex. It forms, along with The Bering Strait the divide between the two largest landmasses on Earth: Eurasia and The Americas. /dsdt/cwtg/egof. -Claramente existe un vortex en el Golfo de Aden. Research highlights In this study, we model the interaction between the RSOW and Gulf of Aden eddies. Tropical Depression Sagar will bring a significant threat for flooding to northwestern Somalia and neighboring Djibouti into Sunday. The modeled Red Sea overflow's pathways rely on Gulf of Aden eddies. There is a new subject that has come to light on the internet. Stargates and Wormholes. Explore more on Gulf Of Aden. 5 or greater) 0 earthquakes in the past 24 hours 1 earthquake in the past 7 days. Operation Dawn 8: Gulf of Aden. That a real Stargate has been found, and it's seven miles underground in the Gulf of Aden in an underground military base. Note: This page is continually updated as new transcripts become available. Members are strongly recommended to adhere to the guidance and recommendations contained within BMP4. Although phytoplankton can be an important food source for fish and other marine animals, in recent years we've observed more frequent toxic blooms. ← Aaron McCollum and the Gulf of Aden Chemical Bio Expert Murdered After Arkansas Bird Catastrophe, John Wheeler Special Assistant to the Secretary of the Airforce → 1 Response to Wikileaks, the US secret bunker, the Gulf of Aden Vortex: Contact made? reports English Pravda. CNN NEWSROOM. They approached us wanting to sell fish. Gulf of Aden Mysterious Vortex Ancient Eye of Ra has been awakened 2012. The English Electric (BAC) Lightning v1. After a strange cloud formation looking like a vortex appeared over The Gulf of Aden in the early 2000s, several alternative theory websites theorized that it could be the result of a Stargate. From: [email protected] Russia, the PR China and the USA joined efforts to study what it was but discovered that it defied logic and the laws of physics. I agree 100% I think it is a disinformation operation. Scale 1:35,000,000 Robinson Projection standard parallels 38°N and 38°S AUSTRALIA Independent state Bermuda Dependency or area of special sovereignty Sicily / AZORES Island / island group Major chokepoint Major port Shipping lane. After remaining 'relatively stable' since its discovery in November, 2000, this report continues, the Gulf of Aden vortex began to "expand" in late 2008 prompting the United States to issue an "extraordinary" warning to the entire world about this mysterious occurrence and which in response the following Nations rushed their Naval. features: island, dubai, peninsula, persian gulf, palm island resort, gulf, city of dubai at night, urban area Geographic Region: UNITED ARAB EMIRATES Photo #: ISS021-E-5555 Technical Info. Gulf of Aden, deepwater basin that forms a natural sea link between the Red Sea and the Arabian Sea. The waters of the Gulf of Aden flow into the Red Sea through the Bab el Mandeb ( strait ), and because it provides an outlet to the west for the Persian Gulf Oil, it's now one. Coastal sediments in the northern Gulf of Mexico have a high potential of being contaminated by petroleum hydrocarbons, such as polycyclic aromatic hydrocarbons (PAHs), due to extensive petroleum exploration and transportation activities. So dangerous WikiLeaks founder Julian Assange has become, Interpol has issued a `red notice' warrant for his immediate capture in order to prevent him from release the entire US "Gulf of Aden Vortex" file he currently has. Latest Colour Mean Sea-Level Pressure Analysis. A US Navy spokesman says two of its supply ships briefly collided in the Gulf of Aden but that no one was injured. Filmy, hry, hudba, softver a xxx na stiahnutie zadarmo,. War In Yemen; Gulf Of Aden Vortex; Norway Spiral Connected? Posted on April 13, 2015 by Linda Sky I have heard several people relate Cern to the Germanwing's crash, this video makes that link clear, as well as connecting several other dots. 2 °F) during 1901–2012. Hartmut Peters joined ESR in 2008 after time on the faculties at the University of Miami and the State University of New York at Stony Brook. Wikileaks, the US secret bunker, the Gulf of Aden Vortex: Contact made? Where is this story in the international media? The combined naval might of twenty-seven countries is concentrated off the Somali coast allegedly to fight the poorly armed pirates who continue to act with apparent impunity. Stargates and Wormholes. Gulf of Aden Stargate Project Camelot interviews Aaron McCollum Aaron McCollum is a third generation member of Project Talent, the MKUltra program used to develop psychic warriors and supersoldiers by the secret government. 2 degrees North and longitude 46. I have been looking through the Ning and ZetaTalk archives regarding the Gulf of Aden vortex. The LFGCS supplies LFG to the Perdido LFG energy facility, owned and operated by Gulf Power, a division of the Southern Company. Although phytoplankton can be an important food source for fish and other marine animals, in recent years we've observed more frequent toxic blooms. Wikileaks, the US secret bunker, the Gulf of Aden Vortex: Contact made? 08. This item is extremely nice product. Geological Survey (U. It also explains: Tarek Bin Laden shares the same father as Osama Bin Laden. There is no doubt that something is going on. Answering questions also helps you learn!. Trailing the Pacific Crest from Space. Playing next. The local time is midmorning with the Sun shining from the left. At the moment warships from China, Japan, England, The U. 3 degrees East; about 140 km east-southeast of Aden (Yemen) and 820 km west-southwest of Socotra Islands. Pirates of the Gulf of Aden: The Coalition is the Strategy, 45 TANFORD S JOURNAL OF INTERNATIONAL L AW 202-241 (2009) (with Wilson) International Security and International Law inthe Northwest Passage, 42 ANDERBILT V J OURNAL OF. Many world officials believe it is an attack on our planet by "interdimensional" or "extraterrestrial" forces ( wikileaks. Explore more on Gulf Of Aden. UN News produces daily news content in Arabic, Chinese, English, French, Kiswahili, Portuguese, Russian and Spanish, and weekly programmes in Hindi, Urdu and Bangla. Browse photos, see new properties, and research neighborhoods on HAR. The Gulf of Aden, formerly known as the Gulf of Berbera, is a deepwater gulf amidst Yemen to the north, the Arabian Sea and Guardafui Channel to the east, Somalia and Somaliland) to the south, and Djibouti to the west. Russia, the PR China and the USA joined efforts to study what it was but discovered that it defied logic and the laws of physics. Gulf of Aden. 407110 = Swarm Universe. Link to abstract: Gulf of Aden Magnetic Anomaly and the Curie Temperature Isotherm. But, Gulf 1 to the side, there was usually just one carrier group in the Gulf. com )- An accurate count of the AK47 type rifles confiscated in the Gulf of Aden on 28 August 2018, has been released. 31, 2011 ExopoliticsTV interview, the human representative of the Andromeda Council confirmed that a 5. Just like the smoke rings of Kelvin seemed flexible objects, the energy vortex can appear like stable and solid particles. the portal This blog is the official communication outlet for the Resistance Movement. The table below lists "events at sea" occurring after January 1, 2009, including cruise ship accidents. The al Houthi movement claimed that ten drones had targeted the Shaybah oilfield near the UAE border and said that the attack was the "largest attack" in the history of the Yemen conflict. CERN Stargate Portal Opening Different Dimensions? Gulf Of Aden Vortex; Norway Spiral Connected? Link to War in Yemen!! Huge News GMN Shares All!. American scientists noticed the Gulf of Aden vortex in 2000 and allegedly established a base in Djibouti on the Horn of Africa to study it. Historians will have a "field-day" here too, visiting the white Indo-Arabic city of Mukalla, its feet bathing in the sea, or Aden, the ancient port of the Awsan Kinqdom from around the 6 th century B. Date: 2011-05-25 03:13:22. From earlier last month, this report continues, the Gulf of Aden vortex began an "extraordinary" series of "expansions" that for the first time since its discovery were preceded by earthquake activity. Misleading Wikileaks: "Mysterious magnetic vortex" in Gulf of Aden has defied all efforts of Russia, USA and China to shut it down, or even to ascertain its exact origin or "cause for being". Admiral Ayyari said that there is controlled insecurity in the Gulf of Aden and they escorted 4,000 oil tankers along with cargo ships into safe regions without any need for disruption in oil and non-oil exports and imports. If I tell you, you wont believe me anyway. Several plumes of dust can be seen blowing off the coast of the African continent, over bodies of water, towards the Arabian Peninsula. Trailing the Pacific Crest from Space. In 2008 the vortex began to expand prompting the USA to issue a serious warning to world leaders. These film is an inspiration from the true story of the PASKAL operatives during their duties as United Nations in Angola in 1998 and the success of PASKAL seized MV Bunga Laurel's trade vessel in the event of the Gulf of Aden in 2011. and China to stop it, without being able to determine its exact origin or reason for being. Footage has emerged online that purportedly shows the moment a bright orb UFO flies straight into the swirling vortex of an inter-dimensional portal in the sky over the Large Hadron Collider (LHC) facility built by the European Organization for Nuclear Research (CERN) near Geneva, Switzerland. Several plumes of dust can be seen blowing off the coast of the African continent, over bodies of water, towards the Arabian Peninsula. Latest Colour Mean Sea-Level Pressure Analysis. According to an ancient tradition, with this name, a city was founded in Thessaly, in central Greece from the mythical hero Hellenas [ Έλληνας ], patriarch of the Greeks. (Gulf of Aden) forms the southern boundary of the ArabianPlate. 3 degrees East; about 140 km east-southeast of Aden (Yemen) and 820 km west-southwest of Socotra Islands. The US asked for help keeping it safe, as it started to defy laws of physics, and most of the countries of the world sent navy forces. Hartmut Peters joined ESR in 2008 after time on the faculties at the University of Miami and the State University of New York at Stony Brook. We would recommend this store to suit your needs. It is the only sea on Earth which has no coastline. A bizarre report prepared for Prime Minister Putin by Admiral Maksimov of Russia's Northern Fleet states that a 'mysterious magnetic vortex' currently centered in the Gulf of Aden has "defied" all. Cyclone Sagar: IMD warns of high-speed winds over Gulf of Aden. I will call in short term as Gulf Of Aden Vortex For those who are looking for Gulf Of Aden Vortex review. We have also been approached by high speed skiffs in the Gulf of Aden, sometimes with hooded crew. Wikileaks, the US secret bunker, the Gulf of Aden Vortex: Contact made? 08. Operation Dawn 8: Gulf of Aden (Malay: Operasi Fajar 8) was a naval operation carried out by the Royal Malaysian Navy against pirates in the Indian Ocean on 20 January 2011. That a real Stargate has been found, and it's seven miles underground in the Gulf of Aden in an underground military base. En 2008, plus de 50 000 personnes ont ainsi traversé le golfe d'Aden vers le Yémen, selon le HCR [2], contre 29 500 en 2007 [3]. Buy Online keeping the car safe transaction. For more information on these materials search ADAHCAT using this number v 35004 under a Basic Search using the option of Keyword Relevance Search. and other countries are surveilling the region. Publicado por Ana Maria Boscovich en 14:39. Department of State, Washington, August 12, 1844. /dsdt/cwtg/egof. Navy ship in the Gulf of. What I am wondering about is is the high military presence around the vortex. Science of Peace has found after 250+ scientific studies that inner peace(a feeling)=outer peace because we are all connected via the field. (Note that the sharks can walk on land and smaller sharks can eat bigger sharks. Probably a little truth mixed in with a bunch of lies. Find Gulf Of Aden Latest News, Videos & Pictures on Gulf Of Aden and see latest updates, news, information from NDTV. American scientists noticed the Gulf of Aden vortex in 2000 and allegedly established a base in Djibouti on the Horn of Africa to study it. The Red Sea and the Gulf of Aden were formed as the Arabian plate separated from Nubia, as Nubia obliquely collided with the Eurasian plate (Figure 1). Probably a little truth mixed in with a bunch of lies. According to a report allegedly prepared by Admiral Maksimov of Russia's Northern Fleet, in late 2000, a magnetic vortex was discovered in the area of the Gulf of Aden. -NATO - Allied Command Operations News (Search for news items in January, 2010) IV. Is there really a magnetic vortex in Gulf of Aden!? How long do you think it will take for the piracy to end at the Gulf of Aden now that Blackwater is involved? Will Johnny Depp's new Disney Pirate movie be titled: Pirates of the Gulf of Aden?. 3 struck the Gulf of Aden between Yemen and Somalia on Saturday, but preliminary reports from Yemen said it appeared to have caused little damage. This gulf is located in the Arabian Sea between Yemen, on the south coast of the Arabian Peninsula, and Somalia in the. 9 - 2019/01/19) - original concept by Hugo Philips - Note: this routine uses Javascripting and works best in Firefox, Chrome. 16: MS-13 Suspected in Car Bombing that Injures Two Policía Nacional Civil (PNC) in Soyapango, El Salvador. Yeah, but Yemen is not a "Gulf state. These film is an inspiration from the true story of the PASKAL operatives during their duties as United Nations in Angola in 1998 and the success of PASKAL seized MV Bunga Laurel's trade vessel in the event of the Gulf of Aden in 2011. The largest dust plume can be observed in the upper left quadrant, blowing northeastward over the Red Sea, off the coast of Sudan, September 04, 2012. We would recommend this store to suit your needs. They may be, out of necessity, paying captains and crews a bonus for hazardous duty while transi. The Disposables fight the pirates and take them out in a minute without breaking a sweat. the gulf of aden vortex On the south coast of the Arabian peninsula, between Yemen and Somalia, there is a region that has attracted international attention. If you searching to test Vortex Point Theme Song Gulf Of Aden Vortex 2018 price. It connects the Red Sea and the Gulf of Aden, as such the link between the Mediterranean and the Indian Ocean. The waters of the Gulf of Aden flow into the Red Sea through the Bab el Mandeb ( strait ), and because it provides an outlet to the west for the Persian Gulf Oil, it's now one. It is enferred that the natural remanent magnetization is much greater than the induced magnetization and computations have been made which suggest. Department of State, Washington, August 12, 1844. HAARP : GULF OF MEXICO / ATACAMA CHILE / EUROPA (1) HAARP CHEMTRAILS ORBS CRITTERS (1) HAARP EL HIERRO ERUPTION 2011 (1) HAARP from ISS - desde la Estacion Espacial (1) HAARP Gran Canaria 11-2011 (1) HAARP Gran Canaria 19-01-201 (1) HAARP Lenticular Clouds Nubes Lenticulares 2 (1) HAARP Lenticular cloudsNubes (1) HAARP Vortex in Tenerife Oct. As polar vortex lingers, parts of U. It forms, along with The Bering Strait the divide between the two largest landmasses on Earth: Eurasia and The Americas. 8 million b/d of crude and refined products transited in 2016. GOALS Acronym for the U. features: island, dubai, peninsula, persian gulf, palm island resort, gulf, city of dubai at night, urban area Geographic Region: UNITED ARAB EMIRATES Photo #: ISS021-E-5555 Technical Info. China May Build Navy Port in Gulf of Aden As the US economy collapses under Mexican invasion and outsourcing, the Chinese economy increased at 9% last. Abstract New satellite-based observations reveal that westward translating anticyclonic rings are generated as a portion of the Somali Current accelerates northward through the Socotra Passage near the mouth of the Gulf of Aden. MORE: Rock painting from 10,000 years ago. Latest Colour Mean Sea-Level Pressure Analysis. 9 / 01 jul 18 / greg goebel * During the 1950s, the British English Electric (later BAC) firm developed Britain's first (and in a sense last) operational Mach 2 fighter. A Marine Corps helicopter with 25 aboard crashed Monday in the Gulf of Aden, and all aboard were rescued, the Navy said. As you may or may not know the "vortex" phenomena also happened in this body of water, the Gulf of Aden. Personally, did several runs into the Persian Gulf on a number of ships. (Note that the sharks can walk on land and smaller sharks can eat bigger sharks. Map of the World Oceans, August 2013 August 2013 Boundary representation is not necessarily authoritative. Gulf of Aden waters flow into the Red Sea through the Bab el Mandeb (strait), and because it provides an outlet to the west for Persian. This gulf is located in the Arabian Sea between Yemen, on the south coast of the Arabian Peninsula, and Somalia in the. So dangerous WikiLeaks founder Julian Assange has become, Interpol has issued a `red notice' warrant for his immediate capture in order to prevent him from release the entire US "Gulf of Aden Vortex" file he currently has. I did some digging and apparently the expansion of the Vortex coincided with reports of the South Atlantic anomaly and the separation of land mass in Africa. In 2008 the vortex began to expand prompting the USA to issue a serious warning to world leaders. the gulf of aden vortex On the south coast of the Arabian peninsula, between Yemen and Somalia, there is a region that has attracted international attention. Find Gulf Of Aden Latest News, Videos & Pictures on Gulf Of Aden and see latest updates, news, information from NDTV. See more ideas about Ancient aliens, Universe and Cern collider. Welkom bij misschien wel de grootste Hosta database en zeer uitgebreide zoekmachine! Zoek in deze database die 12260 Hosta's bevat en op dit moment 18814 foto's van 3688 verschillende Hosta's!. Navy in Gulf of Aden Arizona -( Ammoland. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,078 |
Dear Client,
This book will teach you how to get what you want from creative people.
Sincerely,
Bonnie Siegler
for buster & oscar
It doesn't make sense to hire smart people and then tell them what to do; we hire smart people so they can tell us what to do.
—Steve Jobs
To design is much more than simply to assemble, to order, or even to edit; it is to add value and meaning, to illuminate, to simplify, to clarify, to dramatize, to persuade, and perhaps even to amuse.
—Paul Rand
There are three ways to ultimate success: The first is to be kind. The second way is to be kind. The third way is to be kind.
—Mr. Rogers
INTRODUCTION
No. 1 THE THING ABOUT CREATIVES
No. 2 BE HONEST
No. 3 KNOW THYSELF
No. 4 MAKE ME ICONIC
No. 5 HAVE CLARITY OF PURPOSE
No. 6 WHO IS YOUR AUDIENCE?
No. 7 CARE ABOUT EVERY AUDIENCE
No. 8 DECIDE WHO WILL DECIDE
No. 9 DO NOT SEND OUT AN RFP
No. 10 A BRIEF CASE FOR WRITING A BRIEF
No. 11 TELL ME THE PROBLEM, NOT THE SOLUTION
No. 12 GET BUY-IN
No.13 EXPERIENCE ISN'T EVERYTHING
No. 14 THOSE AWKWARD FIRST PHONE CALLS
No. 15 THE IMPORTANCE OF MEETING IN PERSON
No. 16 GET A PROPOSAL
No. 17 CALL REFERENCES, FOR GOD'S SAKE
No. 18 INTRODUCE EVERYONE AT THE MEETING
No. 19 DON'T SCHEDULE MEETINGS ONE RIGHT AFTER THE OTHER SO THAT WE'RE BOUND TO RUN INTO EACH OTHER IN THE LOBBY
No. 20 BE UP FRONT ABOUT MONEY
No. 21 THE VALUE OF CREATIVE WORK
No. 22 FLAT FEES, FULL HEARTS, CAN'T LOSE
No. 23 EXPECT THE UNEXPECTED
No. 24 GOOD, FAST, CHEAP
No. 25 ALWAYS SIGN ON A DOTTED LINE
No. 26 TELL THE PEOPLE WHO DIDN'T GET THE JOB
No. 27 BEST PRACTICES WORK BEST WHEN THEY ARE FLEXIBLE
No. 28 DON'T WORRY IF YOU DON'T KNOW EXACTLY WHAT YOU WANT
No. 29 WHAT IF YOU HAVE A GOOD IDEA?
No. 30 SHOW-AND-TELL
No. 31 CUT OUT THE MIDDLEMAN
No. 32 WHITE SPACE IS YOUR FRIEND
No. 33 LET THE CREATIVES DRIVE THE FIRST PRESENTATION
No. 34 BE A FAIR JUDGE
No. 35 QUESTION EVERYTHING
No. 36 BE OPEN TO THINGS YOU DIDN'T IMAGINE
No. 37 DON'T SAY THAT, SAY THIS
No. 38 BEWARE OF GARANIMALS
No. 39 AN IMPORTANT NOTE ABOUT GIVING FEEDBACK
No. 40 I NOTICE / I WONDER
No. 41 IT'S OKAY TO LOVE SOMETHING RIGHT AWAY
No. 42 WHAT TO DO WHEN YOU KIND OF HATE WHAT YOU SEE
No. 43 SO YOU THINK YOU CAN MAKE IT BETTER?
No. 44 WHAT IF YOU DON'T KNOW WHAT YOU THINK?
No. 45 GIVE ALL FEEDBACK AT ONCE
No. 46 WE DON'T CARE WHAT YOUR SPOUSE THINKS
No. 47 ON FEAR AND INSECURITY
No. 48 WHY FOCUS GROUPS SUCK
No. 49 DON'T LET DATA DRIVE YOUR DECISIONS
No. 50 BE CONFIDENT, NOT ARROGANT
No. 51 PICK YOUR BATTLES
No. 52 THE POWER OF ENCOURAGEMENT
No. 53 ACCEPT THAT EVERYTHING IS EMOTIONAL
No. 54 TALK IT OUT
No. 55 PLEASE DON'T PISS ON THE CREATIVE
No. 56 NOTHING TAKES A SECOND
No. 57 DON'T ASK TO SIT WITH US WHILE WE MAKE CHANGES
No. 58 DON'T FALL OFF THE FACE OF THE EARTH
No. 59 IF IT'S JUST NOT WORKING
No. 60 WHEN CREATIVES ARE ASSHOLES
No. 61 DON'T BE RUDE TO MY STAFF (OR YOURS)
No. 62 SERVE LUNCH DURING LUNCHTIME MEETINGS
No. 63 ABOUT PRO BONO WORK
No. 64 GIVE CREDIT WHERE IT'S DUE
No. 65 DON'T USE THESE WORDS
No. 66 USE THESE WORDS
ACKNOWLEDGMENTS
ABOUT THE AUTHOR
INTRODUCTION
When my first graphic design company, Number 17, was only five years old, Oprah Winfrey (!) hired us to design a book dear to her heart. _Journey to Beloved_ combined the diary she kept while making the movie _Beloved_ with beautiful photographs from the film shoot. We began the design with trepidation: Honestly, her passion for the book was a huge red flag. Past experiences had taught us that it could be difficult for clients to hear objective opinions from consultants when a project had such deep personal meaning. Plus, there was Oprah's reputation as a demanding perfectionist with enough money to get whatever she wanted.
When we sent her our first pass of the book design, we assumed it would be rejected out of hand or covered with Post-it notes demanding changes without any diplomatic explanation. We waited anxiously for her assistant to call and say, "Please hold for Oprah" or to pass on to us what Oprah thought. Imagine our joy and surprise when Oprah called us herself. It got better: Instead of telling us what to do next, she asked questions about our creative choices. She listened to the answers, and a dialogue ensued. She accepted some of our choices after hearing our explanation and disagreed with others. But because she gave us the opportunity to make our case—and had the opportunity to make hers—the project and our relationship flourished. The book garnered glowing reviews. Most important, Oprah felt that it expressed what she wanted it to, and she cherished the final product. As did we.
If Oprah was an unexpected dream client, another high-profile celebrity (who shall remain nameless) was our nominee for Bad Client of the Year. The review process began with her telling us she loved the direction, but the next day we received a call from someone who worked for her telling us that the celebrity didn't really like what we had done and didn't really know why. She also asked us to retouch photographs she had supplied in impossible ways.*
Worse, instead of providing feedback we could use to design a second pass, she literally cut up our design and taped it together the way she thought it should look, which made for a mess. We were hamstrung, not to mention tongue-tied. Because it was our job, we continued. We took the elements of her pasteup that we could use and changed things that didn't make sense. Such demands increased the budget, lengthened the schedule, and produced cursing and unhappy people on all sides. After a process this fraught, it's a small miracle that the project turned out as well as it did.
Which kind of client would you like to be?
Whenever designers get together, we complain about difficult clients. We've all had them. Relationships that began with optimism and promise descended into bad feelings. Egos and insecurities are powerful negative forces. Some clients who want to appear smart confuse asking questions with appearing stupid. Or they think they should already know the answers. Others believe that since we work for them, we're simply obligated to just do what they want even when we think it is wrong. Still others don't understand the mysteries of the creative process, whether that of architecture, design, copywriting, or a host of other professions that are literally more art than science. All such thinking undermines the creative process and eliminates the opportunity for us to bring our strengths into play.
At the same time, we love our clients. And, of course, we need our clients. You allow us to do the work we adore. A fine artist loves a blank piece of paper with the freedom to do anything. Commercial artists (an old-fashioned term, I know) love a creative brief. I have now owned my own company for twenty-five years, although today it is called Eight and a Half after I split (amicably) with my partner at Number 17 a few years back. (Doesn't the name of my company make sense now?) I still love what I do, all of it: the process, the chaos, the anxiety, and the desire and opportunity to make something great. Sometimes it seems as if we care about the end product more than the client, who may just want the project to be completed. But we often get the most pleasure from obsessing about details that you might not even notice. Of course, I know we can be annoying . . . stubborn . . . irreverent . . . emotional . . . the list goes on. We understand the impulse some clients surely must have to wish they could just do it themselves so they wouldn't have to deal with us.
But you need us as much as we need you. The creative process is not just a matter of giving an assignment and getting a result. There are many phases. Every aspect of the journey needs care and attention. And any collaboration is only as good as the relationships, which take work. I realized long ago that my difficult clients weren't assholes or jerks or stupid. They simply don't know how to work with creative people, and that disconnect consistently leads to frustrations.
That's the topic of this book, the idea for which arose not long after I decided it was time to stop complaining. As Atticus Finch said, "You never really understand a person until you consider things from his point of view."
Ironically, there are many books for designers about how we can better work with clients, which are useful. Most of us want to understand you, so we can improve the process. But, as far as I know, there are no books to help clients better work with creative people, who are a unique species with a unique language and not-so-unique insecurities. Knowing their language and understanding how to talk about subjective concepts is sort of like preparing for foreign travel: You wouldn't go to Tokyo without learning a few words of Japanese. You'd want to be sure you were ordering a dish you could eat and would be able to get back to your hotel without getting lost. This book is meant to make sure you don't get lost in design translation.
I wrote _Dear Client_ to teach you how to interact with the creative professional. I approached it from a graphic designer's perspective, but I believe the lessons are applicable to most creative collaborations. I am also writing as a small-business owner. My clients range from entertainment organizations _(Saturday Night Live)_ to government entities (the National September 11 Memorial & Museum at the World Trade Center) to Fortune 500 companies (Scotts Miracle-Gro). We are, essentially, a client services company. As such, my goal is to help any client who's ever felt unsure or uneasy with a creative professional feel less conflict, less anxiety, and more joy.
After all, we are on the same side! We want the same thing! And it should be fun! Working with creatives really can be the best part of your day. Figuring out how to create better logos or make your dream kitchen or reinvent your website should be exciting. Together, we are making something out of nothing or improving something that wasn't working. Isn't that more enjoyable than most of your other tasks? Why not bring joy and gratitude to the process?
This book can help your business not only by saving you money and freeing up your time but also by getting you better results. It will also keep your hair from turning gray and reduce the risk of heart attacks.
This happens a lot, and I blame TV and movies. Both industries routinely make it seem like you can easily zoom in on one tiny aspect of a blurry photo and make it perfect instantly. In real life you just can't—but that doesn't stop people from asking you to do it.
DISCLAIMER
This book portrays hopes and dreams for ideal scenarios. They rarely occur in the real world, but when they do, it is a beautiful, magical thing. I hope this book serves as a guide for how working relationships can work most effectively. No one is perfect, nor will they ever be, but we can all keep trying.
The Thing About Creatives
No. 1
We do what we do because we can't _not_ do it. It's how we're wired. It's a passion. In fact, we feel lucky to get paid for doing what we love. But we also feel that clients question the value of what we do way more frequently than we'd prefer. This comes out in all sorts of ways—wondering if our fee was worth the time spent, for example, or failing to pay us—but whatever the manifestation, it's insulting and frustrating.
Creatives are more often than not sensitive souls, a quality that helps us create great work. But this quality also means that **we work better with people who are trusting and positive.** Although most creative work is about problem-solving, it's also about the human connection between us and the client. If you're enthusiastic, engaging, open, and optimistic, we will be too. (To be clear, you can be all of those things and still be a smart, tough critic.) And if you're suspicious, stressed out, and miserly, we may follow your lead. Our defenses will go up, and our inclination to put our hearts on the line will go down. That's not petulance; it's human nature.
Be Honest
No. 2
We had a client once who loved everything we did. While we were in the same room. The next day, we'd get a call telling us that he'd thought about it and changed his mind. He didn't like anything. It meant that we never believed anything he said when we were together. Which is bad.
Tell the truth. We can take it. In fact, we will appreciate your criticism, even if we don't agree. And if we understand what you're telling us, we'll find a way to implement the changes so they make sense for you, and for us.
And at every single stage of the creative process, **honesty helps more than it hurts** (and it does hurt sometimes). So be kind and considerate and professional and respectful and fair, but don't let any of those admirable qualities keep you from telling us what you really think and how you really feel.
Be honest about budgets.
Be honest about schedules.
Be honest about your company's odd ways.
Be honest about your troublesome colleague.
Be honest about your personal quirks.
Be honest about your boss's priorities.
Be honest about your fears.
Be honest about what you need to accomplish.
Be honest about your hopes and dreams.
Be honest about what you like.
Be honest about what you hate.
Be honest about what you know and don't know.
Be honest about whom we're trying to please.
Be honest about everything because, truth be told, that's the surest way to get the best work. And the alternative is just a waste of time, energy, and trust.
It's true.
Know Thyself
No. 3
Your taste plays a huge part in our work, so you should definitely make an effort to get to know it. Often, when I ask my clients what design work they respond to most strongly, they tell me they've never even considered the question. But everyone has personal preferences, and having a sense of what they are will make it easier to judge creative work with confidence.
Identifying what you like—What tickles you? What pleases you? What draws you in?—will be incredibly helpful in creative collaborations. **The better you understand your taste, the more you'll be able to engage in a useful dialogue throughout the process.** Of course, there may be differences between your personal taste and the needs of your company. A clear understanding of the former will help everyone understand your responses to work done to address the latter.
So before you start working with a creative team, start paying attention to what you like and what you don't like as you go about your day.
Look everywhere: the shelves of supermarkets and drugstores, the street, on television. Don't worry about why you like something, just note that you do. When you're online, focus on engagements that make you smile. Is hitting Facebook's "Love" button satisfying? Do you respond to oversized images or the simplicity of a scroll? Perhaps you appreciate hidden treats, like the dinosaur game that pops up on Google Chrome's "unable to connect" page (if you don't know about this, check it out). Leaf through magazines, tearing out compelling ads or page layouts. Think of magazines as catalogs of visual eye candy.
Now switch to the perspective of a brand custodian. Look for what you feel are successful representations of a brand; not your personal taste, but a good marriage of product and portrayal. Look for brands with visuals and messaging (pictures and words) that you think work cohesively to make the consumer engagement stronger.
Next, study your competition and determine what's working and, maybe more important, what's not. What makes you jealous? What makes you wonder, What were they thinking? Think about how their design choices relate to your project. Think about how you would respond to them were they presented to you.
Throughout these exercises, keep in mind that you are not looking for potential solutions to a specific problem. You are simply getting in touch with your own aesthetic personality to help us more easily reach a solution that will work for you.
Make Me Iconic
No. 4
Brands take time to become iconic.
Clients often tell us they want a logo that is instantly recognizable, "like Apple's or Nike's!" What I think they are really saying is that they want to be part of a huge and successful brand effort. What many don't necessarily realize with such entrenched images is that **saturation and time can make a design feel stronger.** That is, you may not have responded positively to the Nike logo in an initial presentation because it didn't necessarily communicate sneakers. You might have asked if it might be more appropriate for a boomerang company. Or maybe suggested that it looked like an odd check mark. But now, after almost fifty years and a cool moniker ("swoosh"), most would say it is one of their favorite logos. Its power reflects an intense familiarity, heroic spokespeople, and many, many marketing dollars.
Think about the New York Yankees logo, which is considered a perfect fit for that baseball franchise even though script typography like that is usually reserved for formal wedding invitations rather than professional sports teams. I don't think the logo is bad, but I am certain it would draw criticism if introduced today. After more than sixty years of use, however, the logo is indistinguishable from the team's identity—and our own emotional attachments.
Have Clarity of Purpose
No. 5
A clear understanding of your primary business objectives is crucial. And the time to identify them is before you involve us. Seems obvious? I can't tell you how many first calls with potential clients I've had that ended without a discussion of the underlying purpose of the design work to come.
Start by making a list of what you want to achieve or accomplish. Are you trying to increase sales—or make your brand cooler? Do you need your product to stand out on a shelf—or project an image of luxury? Is the idea to increase web traffic—or buzz?
More than likely you will have many dream objectives, but no design can meet every one. Choose the most important one, and then prioritize the others in order. How long should the list be? **If you have more than three priorities, you really don't have any.**
This thinking will be incredibly helpful to whomever you are working with, and they'll think you're amazing for being so organized about your objectives.
Jon Stewart attributed the success of _The Daily Show_ and its contributors to "a clarity of vision, but a flexibility of process." That combination allowed magic to happen while a clear focus was maintained. This is a pretty good start for all creative endeavors.
Who is Your Audience?
No. 6
Before you think it, let me stop you: **"Everyone" isn't an answer.** (You'd be surprised at how many clients begin there.) You must prioritize, and the better you can define your desired audience, the better the creative outcome will be.
So know whom are you trying to reach—and why. Are you targeting people who've never heard of your brand because you're trying to expand? Or are you focusing on those who are already part of the club because you don't want to lose them? Are you trying to connect with the people who decide to buy your product, service, or experience? Or are you trying to reach those who might influence that decision?
If your answers to all of the above are "Yes"—in other words, if you're still having trouble moving past "Everyone"—you might try instead to paint a picture (figuratively) of the attributes of your ideal customer. My guess is that this list will help you narrow your audience pretty quickly. If your desired consumer has disposable income, a college education, and children, "everyone" starts to look like someone very quickly.
After you decide whom you want to reach, figure out why you want to reach them. This will dovetail with your goals, and that's a good thing. Repetition of purpose only reinforces it.
There's one other audience you need to consider: the decision makers in the creative process. But keep in mind that those people—you, your colleagues, your staff, your bosses—are not always in the desired or targeted demographic. Design is always subjective. Knowing the difference between your taste and your audience's taste, as it relates to the solution, will be important information for you and for us.
Care About Every Audience
No. 7
There are two artificial audience distinctions in creative work, both of which result in less effective solutions. One is business-to-business. For some reason, people think such work should be more straightforward, serious, and, in our experience, less creative and fun. I have no idea why. **B2B consumers are the same people who are also spoken to daily through regular commercial marketing.** They may represent "business" to you and to their employer, but they are humans who are influenced by the same commercial forces as the rest of us—and we should speak to them in a way that shows we get that.
Another artificial distinction involves work done for an internal audience, within a company. Even in companies with tens of thousands of employees, work that is aimed "just internally" is deemed less important. Ironically, it's usually something meant to inspire or teach. It would seem to me that showing this audience that you care is at least as important as talking to strangers.
Every single audience likes to be entertained while being informed, and the extra effort will always pay off.
Decide Who Will Decide
No. 8
A number of years ago we were hired to help create a new identity for the National September 11 Memorial & Museum at the World Trade Center. Understandably, there were many important stakeholders, including the families of those killed, government officials, and the museum directors. Years had gone by without any decisions, until then–New York City mayor Michael Bloomberg announced that he would take on the role of decider. The branding process moved forward smoothly and efficiently from that point on. I am sure some people liked the final design more than others, and that is fine. It really is almost impossible to please all of the people all of the time, so choosing a representative makes progress possible. If no one hates it, most likely no one loves it either—but that's okay.
The plague of groupthink is not limited to creative work, but I can assure you that it is both particularly egregious in—and harmful to—creative collaborations. Because decisions around design, copy, video, and the like are subjective, people with little expertise tend to feel more confident sharing an opinion. And because each person will naturally have unique preferences, any decision made by committee will necessitate compromise and therefore lack singular vision. **Vision is not a group activity,** and the group inevitably interferes with the possibility of greatness.
Choose one person—maybe two—who will be the final decision maker. (Ideally, before we're involved.) Thus empowered, the final arbiter(s) will be more invested in the process and will ensure that it runs smoothly. That person will take their role much more seriously than ten people who each have one-tenth of the ownership.
Such an arrangement doesn't mean that others can't give feedback. In a good collaboration, there is ample opportunity for discussion among all involved. But we'll know how to weigh comments appropriately so that we can progress.
Equally important, make the decision maker's role—and the approval process in general—clear to all players, especially us. Our worst nightmare is a "faux decider." Once, my team went through several rounds of presentations, feedback, and changes before pleasing the person we thought had final say. Only then did we learn about a mystery person who had ultimate approval and an entirely different concept in mind. Had we known there was another layer of approvals, we would have structured our work and our time to reflect this step. Instead, we unexpectedly had to move in another direction. In certain cases, it's understandable that the person making the final call will never attend a meeting. In that case you should tell us who that person is—and who decides what that person sees. We can work with that arrangement . . . if we know that's the arrangement.
Do Not Send Out an RFP
No. 9
RFP stands for Request for Proposal, but **I think it really stands for Routinely Futile Paperwork.** Many clients send out a generic RFP because their company requires full vetting of potential vendors. That's totally understandable, but please do not use these RFPs as a way to choose a creative collaborator.
RFPs are just not the way to do that. They're often delivered without the information we need to fully understand a project's scope and type and without dialogue. And they are off-putting, letting us know that this client prefers paperwork to interpersonal relationships. A lengthy RFP—bios for everyone on the project, ten references, pages and pages of case studies—sends a message that we'll be dealing with a lot of bureaucracy. And it doesn't really give you the information you want. We could have a twenty-five-year-old wunderkind on our team whose bio may not impress but whose work certainly will. There is no place for that kind of understanding in an RFP.
More to the point, the person reading submitted RFPs will almost certainly not be the ultimate decision maker. Similarly, the lead creative is not likely to spend their time filling out a twenty-page document. Which means a huge decision is being filtered through people on both sides who aren't the real players. That doesn't make good business sense. If a designer can't convince you that they would be a good fit in two pages, they're likely not going to do it in twenty.
I recommend instead identifying a few firms, researching them (very easy to do on the interweb), and figuring out unique questions appropriate to each firm you are drawn to. Have a thirty-minute meeting with each of them and make your decision based on that.
A Brief Case for Writing a Brief
No. 10
A brief is a summary of a project's purpose. It will inform and remind everyone (including you) of the point of the project. (In-house art departments will find the document as valuable as outside creative consultants will.) Basically, it's a synopsis of everything we've just covered: the problem to be solved and the most important goals or aspects to be considered. It's a little more homework, but it will be worth it.
But before the creatives even see it, **it's crucial that key stakeholders agree on the contents of the brief.** Otherwise, everyone will still be debating essential aspects after work has begun. That saps momentum, turns us from optimists into cynics—and inevitably costs you money.
A brief doesn't need to follow a formal structure. It can be a well-crafted essay or a bulleted list. But it should contain the answers to most of these questions:
What is the challenge?
Why are you embarking on the project now? a little history, from your perspective, can be very helpful.
What are the objectives?
What is the current situation?
Who is the primary audience?
What do you know about them?
What is unique about your product or service?
What three adjectives describe the ideal response? anything from "beautiful" to "ah, now i understand."
What is the schedule?
What are the specific deliverables?
What are the technical or legal requirements?
What else should the creative know?
What are your hopes and dreams?
Yes, the goals may change, which is normal and okay. All creative work—graphic design, architecture, copywriting—is a process, but that process goes much more smoothly if we begin at the same starting point. And this way, no one is relying on their personal (and sometimes mistaken) recollection of what was discussed at the first meeting. It's all in the brief.
Tell Me the Problem, Not the Solution
No. 11
What the brief should not do is suggest solutions. That's our job. This is important to remember, because **a proposed direction or solution from a client is often difficult to forget** and may serve to limit a creative team's thinking. You don't want anyone saying, "Oh, they want that kind of solution." The other danger is that we'll judge our ideas against your suggestion and self-edit, which, again, is self-defeating. Your job is simply to communicate your official collection of hopes and dreams.
Get Buy-In
No. 12
Any collaboration will be rocky if your key stakeholders are not on the same page about the project's purpose, intended audience, goals, and budget. And the time to get buy-in is _before_ you brief the creative. Whether that means gathering everyone in a room or emailing a document for comments and sign-off, your job as the client is to **make sure that everyone in your organization agrees about the problem that needs to be solved . . .** before you hire someone to craft a solution.
Experience Isn't Everything
No. 13
When you call to talk about the possibility of working with us, there are plenty of things to chat about: our process, our staff, our clients, our availability.
Here's a question you shouldn't ask: Have you done a job like this before?
We hear it all the time. Have you ever designed toothpaste packaging? Or, How much experience do you have with websites devoted to interior decorating? In every case, the client is clearly looking for a positive response—and the comfort that comes from knowing we've already solved a problem like theirs. But it's a false comfort at best, for three reasons:
**1. The path to every solution should be unique.** That design you like on that similar product? You have no idea what the brief was that led the designers to it or why the client chose the direction they did. How we get to what you need may well take a very different approach. The client is the designer's collaborator, and working with you will undoubtedly be an entirely different experience. It is much more important that you discuss a potential designer's previous work and process holistically. Hear what they have to say about how they came up with the solutions they did—even if none of those solutions have to do with a bathroom product.
**2. Obsession with a specific kind of experience displays a lack of imagination—** and trust. It also shows an inability to understand the nature of creative problem-solving.
**3. Familiarity can breed laziness.** Designers who work a lot on one kind of thing tend to offer similar solutions each time. And why not? It pleased a client once, so it should again. But you should want us to do new and different thinking that addresses your specific needs. And not for nothing, for me (and a lot of people like me), work that is too similar to what I've done before just isn't as much fun to do.
That said, experience in a specific area isn't all bad either. It means the designer won't be learning on your job. Back to the toothpaste box: A designer who has done packaging work before will go into the project understanding dielines and bar code restrictions. But the truly important thing is the creativity and the thinking. If the designer is good, they can learn all the logistical stuff to complete your job to perfection, regardless of not having done it before. The thing that they can't google and get an answer to is how to problem-solve creatively.
Those Awkward First Phone Calls
No. 14
Think of your initial phone conversation with a potential creative hire as the beginning of the collaboration, whether you're considering one firm or ten. **The idea is to sow the seeds for a great partnership from the beginning** by setting a positive tone as you determine if your communication styles jibe.
The best approach is to just talk broadly about your company and your project: tell us how you got to where you are and what you hope to achieve; describe the culture, the people, the approval process. You'll ask questions and we'll ask questions and you'll see how well we communicate with each other. It's just like dating. See if you like the cut of our jib and how we think. See what it's like to have a conversation with us, because if we work together, you're going to have lots of conversations with us. When you get off the phone, you want to be able to answer "Yes" to most of the following questions:
Did we ask thoughtful questions?
Did we listen to your answers?
Did you understand what we said?
Did we seem to understand what you said?
Did we sound like we were responding specifically to you (as opposed to speaking in generic platitudes)?
Did we have the same cultural and/or business references?
If you're not sure what to say to a creative firm, start by asking them, "How can you help us?" Their answer should help you understand what they can do for you.
And pay attention to the questions they ask you. That will help you understand their process, what they need to know. This is a collaboration and, as with dating, you should both enjoy and learn whether you can work together from this conversation.
This is also the time to begin establishing trust (see No. 2, "Be Honest"). So tell us if you're making ten calls before deciding which three firms to meet with (perfectly okay) or if you already know that you want to hire us because you've heard great things (even better). This kind of information is valuable to us—but also to you, since it will help us to determine what to provide you to best assist in your decision.
The Importance of Meeting in Person
No. 15
Before you decide to work with a creative team, particularly on a major project, try your best to meet with prospective candidates in person. More so than a call or video chat, this lets both parties see the other in action. You get to read each other's body language. You get to have small talk, which can be the foundation for a (work) friendship. And one of you gets to see where the other works, which obviously can tell you a lot about a person and their organization. Just as crucially, a face-to-face meeting can set the tone for all that's to come. Here's a simple plan sure to get things going in the right direction.
**Be prepared.**
Know your goals. Arrive with your creative brief in hand; it will help you to articulate the mission. You should also be ready to discuss similar projects you've undertaken and why they were successful—or not. (We often learn more from failure than from success!)
**Be optimistic.**
Assume success and communicate that assumption. I'm told optimism is as contagious as a sneeze. (Gesundheit!)
**Be transparent.**
Tell us everything—even the bad stuff, like how the approval process might be a bit of an obstacle course. Tell us what you know about the timeline and budget too—and the flexibility around each. The more we understand, the better the odds of success, in both product and process.
**Be nice.**
Sorry to get all basic human decency on you; this is just one of my things. We're all busy and stressed, but we're also all human. So start with a compliment (we, like you, are insecure and needy). You're obviously considering this particular creative team for a reason. Tell them why. You want them on your side, and knowing that you believe in them will help to get them there. (I know I sound like your mother, but sometimes she did know what she was talking about.)
Get a Proposal
No. 16
Once you've spoken on the phone (and, ideally, met in person), ask any potential collaborator for a project proposal. A bare-minimum will include basics such as scope of services, cost, and timetable, but every firm or individual will have their own way of preparing this document—and that's the point. The proposal is another way in which we speak to you, and **it will offer a sneak peek into our working personality:** project understanding, preferred process, level of flexibility, and formality. All of this is useful information when making a decision.
Call References, For God's Sake
No. 17
We just met and you liked our work and what we had to say and you are thinking of working with us. That may be enough, especially if you were referred to us. But if you just aren't ready to pull the trigger, you are probably wondering what we're _really_ like to work with.
Please ask us to give you contact information for a couple of recent clients, and then please give them a call to discuss the experience of working with us. How did the project go? Did we respond well to feedback? Was it a pleasant relationship? Did we meet deadlines? Were they proud of the completed job?
Yes, each project is different, and we probably won't give you contact info for a client with whom we had a terrible relationship. Nevertheless, those with whom we worked well can still provide useful information, especially if you have specific concerns. Maybe you're worried about costs and overages. Ask. Maybe you're wondering whom at the firm you'll really work with. Ask.
And **feel free to come back to us with new questions** based on what you learned. Creatives want to start off on the best foot possible, which means we want you to trust us and not have nagging concerns as we begin this mysterious relationship.
Introduce Everyone at the Meeting
No. 18
I've sat at many long conference room tables with absolutely no idea as to who all the people staring at me were, let alone what their roles were or why they were there. And that's not cool, because **if we don't know who's who, we can't be sure which opinions and musings have value.** Obviously, we'll respond differently to a curious decision maker than we will to an intern who's simply expressing a personal preference. We'll be just as nice to the latter but will take more time addressing the concerns of the former.
So who's at this meeting? You tell us. No, seriously—you need to tell us, ideally beforehand. I get it. You may not settle on an invite list until the last minute. But if that's the case, tell us that too. And when we gather, introduce everyone, including the role each plays. Otherwise, all we'll know is that there are a bunch of people in the room who may or may not have names and are definitely there to judge us.
I totally appreciate the inclination to make meetings inclusive. Just include us too.
Don't SCHEDULE MEETINGS ONE RIGHT AFTER The OTheR SO that We're Bound to Run Into Each Other in the Lobby
No. 19
I often ask whom else a potential client is talking to. Sometimes they tell me, sometimes they don't. It helps me to get a sense of whom we are up against, but it is not necessary. Running into competitors at the elevator is a whole other thing. I once ran into an ex-boyfriend who was up for the same job. (It's a small world.) He was on the way out of the client's office; I was on the way in. As a result, I was a wreck during the interview, which I spent wondering what he had said and what work he had shown and what his life was like now.
Everyone's time is precious, so we understand how efficient it seems to knock out a bunch of interviews on a single day. But everyone feels uncomfortable and flustered after bumping into a competitor in the lobby—even if they never dated—which means you end up interviewing something other than the best version of what might very well have been an ideal collaborator. It feels a little too much like casting sessions where the struggling actor walks into the lobby and sees twenty other thirty-year-old blond men dressed in jeans and a leather jacket.
And, not for nothing, **meeting potential creatives in rapid-fire succession is not the best way for your brain to process personalities and presentations.** The best presentation may seem to be the one you saw right after lunch.
So, if you can, space out interviews with time to let all ships pass in the night.
Be Up Front About Money
No. 20
Creative people are at a little bit of a disadvantage, weirdly, because we love what we do. We feel lucky to get paid for it, and we would probably do it for free. But there are the realities of life, and while we are privileged to earn a living this way, earn money we must. Sure, we like to make money, but for the most part, we really want to kick ass creatively and yes, making money makes it all better. If we were really focused on making money, we'd probably be doing something else.
If you have a specific budget or range for your project, please tell us. **It will make us feel like we're on the same side** (which we desperately want to be) and will avoid protracted negotiations (which can sour the relationship). It will also save everyone time. Some projects are just too small for some creatives, no matter how much they think they might enjoy the work or the relationship—unless you explain that you care passionately about it but don't have the budget you would like. In that case we might just do it!
Some potential clients tell us they have no budget in mind, but there's always a rough number. And in the absence of any guidance, we may approach the project with a proposal that's way more than you expected. That's a quick way to kill what could have been a very rewarding collaboration.
Other would-be clients withhold their budget parameters in the hope that we will bid lower than what they have to spend. But most seasoned creatives don't even want to be the cheapest bidder. Most young creatives, meanwhile, will produce better work if they know you didn't hire them solely because they came in with the lowest bid.
A young colleague was asked to submit a proposal for a job he really wanted. No budget was given, leaving him agitated about having to make a wild guess. He decided to submit a very low bid—he landed on $5,000—hoping that after they saw how awesomely talented he was, he could raise his fees on the next project. The next day he got the job, but in reviewing his proposal and the contract the company sent he realized that in his nervousness, he had accidentally added an extra zero to his fee, making it $50,000—which the client had agreed to.
Maybe $50,000 was less than they planned on spending and everyone walked away happy, but the fact that this designer had _no idea_ is absurd. And maybe $50,000 was a stretch for them. If they had just given the designer a range, he still could have come in on the low end and saved the client lots of money.
**Having some sense of the budget will affect the way we think about the project from the get-go.** Starting out with a mystery between us means there's no way we can be on the same page, which is a terrible way to begin.
Please be up front about money.
The Value of Creative Work
No. 21
A true story: I was once hired to create a new brand identity for a New York City hospital. At one point, the hospital review committee, made up of six male surgeons, assembled to review our initial presentation. While we waited for the CEO to join the meeting, one of the surgeons told a story about a time he felt a designer had ripped him off. Apparently, the organization with which he was then affiliated had spent a lot of money on a new logo. After the work was completed, it was discovered that someone in their office—not a designer—had sketched a logo similar to the one the designer created. The surgeon's point, as I understood it, was that his previous company didn't need a fancy design firm when Johnny down the hall could make the same logo for free.*
I think this story resonates so strongly with me because it hits an issue that we deal with constantly. Because creative work is not easily quantified, some clients question the value of our work. This is not only galling; it also misses the point. **You're paying for our creativity, for our ability to create order from chaos,** to communicate your message, not for the time we need to solve your specific problem. The time it takes is our burden, not yours (so long as we meet deadlines). Is a brilliant logo worth less because we had the idea during our initial meeting? Is it worth more because we threw out a hundred ideas along the way?
Whether a solution takes us two days or two weeks or two months, the ultimate value to your business is the same—and that's what you're paying for.
An apocryphal story: A widget factory was brought to a halt by a piece of malfunctioning equipment. Management called a mechanic, who spent five minutes walking around the machine inspecting parts.
Then he pulled something out of his toolbox and tinkered for a moment in the back of the machine, which promptly started to work. Everyone was thrilled, until they got a bill for $5,000. The factory owner angrily asked the mechanic for a breakdown of the costs. The mechanic sent back the following itemization:
$10 for the replacement part
$4,990 for the 25 years of experience that allowed us to solve the problem in 10 minutes
Exactly.
After the fact, I realized what I should have said: "I know exactly how you feel. I once spent a ton of money on this fancy doctor and he could never make a diagnosis, but a neighbor of mine figured it out right away!"
Flat Fees, Full Hearts, Can't Lose
No. 22
Most designers (and many other creative types) worth their salt charge a flat fee for a project. This may or may not reflect some internal accounting for how many hours they expect to spend on your project, but it certainly includes a rough calculation of the number of people involved for a certain amount of time, their abilities, and the scope of the entire project. Whatever the case, I assure you that this structure benefits you. Here's why: Say my team is designing your logo, and we have an idea that requires drawing a typeface from scratch. If we're charging you by the hour, we have to consider your reaction to spending the extra money, especially if you end up not liking the direction. You would probably not want to invest more money in something that might not even work. If we're on a flat fee, we are more likely to forego such mental calculations and explore even time-consuming options that we think will teach us—or you—something important. **By paying a flat fee, you don't limit us to X hours of work.** The sky is the limit, which is right where you want it to be.
That said, I believe work required beyond the scope of the contract (see No. 23, "Expect the Unexpected") should generally be billed by the hour (at a rate stipulated in the contract). At this stage, hopefully, we will be executing precision strikes to address very specific issues. But whatever the reason, our time has a value and, like a lawyer, we need to charge for the hours we spend beyond what we agreed to. Know that we will work as efficiently as we can while staying the perfectionists you want us to be. To be honest, it's in our interest to work as quickly as possible: The faster a project goes down, the sooner we can move on to new jobs.
Expect The Unexpected
No. 23
Of course, you have the right to change your mind. (Personally, I think people who never change their minds aren't using them.) As we live with ideas, new thoughts inevitably enter the picture, and that affects the way we see the work. Sometimes a client changes their mind after receiving new information or sharing a presentation with a colleague or just after having a good night's sleep and reviewing it anew in the morning. It happens.
Do we sometimes wish the process were more of a straight line? Sure, but we know why it rarely is, and detours can lead to the best work. Just another reason we find our job so satisfying.
But a change of mind can mean a change of parameters. So every design project—from your annual report to my new kitchen—has the potential to take longer and cost more than anyone anticipated. By definition, **the thing that causes the delay is the thing you can't anticipate;** if you could, we'd have accounted for it in the initial schedule. By all means, think of as many contingencies as you can, but build in extra room for the unknown in both the schedule and budget anyway. (For the latter, an extra 10 percent in the lockbox is a comfortable cushion.)
Good, Fast, Cheap
No. 24
The best! Get it now! On sale! Sounds great, right? If you are buying deodorant, this trifecta is great. But with creative projects, **consider yourself lucky if you can get two out of three.** Getting them all is a near impossibility because:
If it's GOOD AND FAST,
more people need to be involved—so it won't be cheap.
If it's GOOD AND CHEAP,
it will take longer—so it won't be fast.
If it's FAST AND CHEAP,
it's probably not going to be good.
Always Sign on a Dotted Line
No. 25
Many creatives have learned hard lessons about the risks of working without a contract. My lesson wasn't even that hard, but it was still educational. We were chosen to design the identity and advertising for Air America, a media brand close to my heart (and politics). We were so excited about the project that we began working without a contract. But we refused to deliver the finished product until both parties had signed, despite a CEO who chided us for not accepting his handshake as assurance . . . like all the other vendors working with Air America had done. Well, we were very grateful for that contract when it turned out the CEO was a fraud and his handshake was worth less than his bank account. That paperwork meant that we were eventually paid in full, while all those vendors who simply shook on it were out of luck.
So please make signing a contract standard practice, whether we're talking about a huge job between two big companies or a relatively small project. I've had many clients—many of them at large organizations—tell me that we don't need a contract. Sometimes it's because they have a little extra money and don't want to call too much attention to the spend. And sometimes it's just in order to avoid the bureaucratic step. I understand this inclination, but it's not a good enough reason to go without. Contracts protect both sides and make expectations and obligations clear. There will undoubtedly be misunderstandings over the course of a collaboration; but if you've taken the time to review expectations in advance, they won't be about due dates, overages, or expenses.
A contract is also a signifier, telling all sides that this is a serious endeavor between two mutually respected parties. **For creative types, few things foster as much confidence at the start of a project** and few things do the opposite as quickly as a client's reticence to sign a contract.
If you don't have an attorney or a legal department, let your creative team draw up the document. It will almost certainly be simpler and more to the point. But regardless of who crafts it, the contract should include project scope (all services and deliverables included), fees, project and payment schedules, number of revisions, expenses, and final product ownership and usage rights. It should also include a "kill fee" in case the collaboration isn't working out and you want out (see No. 59, "If It's Just Not Working"). Hope for the best, plan for the worst.
Tell The People Who Didn't Get The Job
No. 26
Very few potential clients follow up with those in contention who didn't get the job. Don't be one of those clients. Here are three good reasons why:
**1. Because closure.** Everyone deserves to have it.
**2. Because it's the right thing to do.** Telling creatives that we didn't get the job will make us think more highly about you and your organization, improving your reputation and that of your brand and business.
**3. Because you never know . . .** Our firm once went through an extensive selection process for a large company. We didn't win the job, but the president called to explain her decision, the logic of which I understood. (I wished her well.) Three months later, she called again to ask if we were still interested in the project, which wasn't going as hoped. We jumped at the chance, because her initial display of openness, honesty, and respect told me that it would be a success. (It was.)
Best Practices Work Best When They are Flexible
No. 27
New clients always want to know what made other projects successful and how to replicate that process—in other words, best practices. But what worked with another company's policies, chain of command, and approvals will probably not be applicable in yours. We tend to follow a process that has evolved over time, but we always adjust and adapt it to each client's needs. Best practices are the ones that will work _in this case_.
But I can offer three general best-practice guidelines:
**1. Clarity.** If we have a clear brief and terms, we will have eliminated the cause of most problems before work has begun.
**2. Communication.** If you are open and honest from the outset, we will go above and beyond our obligations. The more we understand your goals, the approval process, and how your company works, the more we will surpass expectations. Give us the information and the space to do what we do best, and you should be very pleased with the results.
**3. Courage.** Nothing great happens when decisions are driven by fear (fear of failure, fear of losing one's job, fear of looking foolish, fear of getting it wrong . . .). Just keep in mind, even people who do take risks harbor those fears. I'm not saying that every solution needs to be risky. I am saying that you will benefit from a little bravery when encountering a direction you don't expect or haven't seen before.
Don't Worry if You Don't Know Exactly What You Want
No. 28
Here's the good news: It is really and truly not your job to know—or tell us—what you want. Your job is to figure out—and tell us—the problem you're trying to solve. Our job is finding the solution.
**Start by creating a list of adjectives** representing the emotions and responses you hope to elicit from our work. Those descriptors will serve as our North Star when we're deciding what we present to you.
It's our job to create something that elicits those emotions and responses—first from you, then from your audience. We explore possibilities not only to find the best solution but also to help identify your comfort level. Something that may help you get more focused is to ask your creative to choose a few past projects and walk you through the original objectives, the ultimate solution and how they got there. You will find both similarities and differences to your project, but doing this may give you ideas for how to frame the problem you're trying to solve.
Some creatives will present multiple solutions, covering a range of possibilities from safe to radical. Others will bravely show the solution they _know_ is right. There is no one right way to help you figure out what you want. But all good creatives will try, and your only obligation is to respond honestly.
What if You Have a Good Idea?
No. 29
**Tell us!** My saying that you don't need to come up with a solution doesn't mean I don't think you have good ideas. So feel free to share something that you think could work. At worst, it will tell us what type of solution you are imagining. Most creatives will explore that idea and, if it makes sense, try to make it work. Win-win. But keep in mind that we creatives tend to look at things differently than non-creatives. Most clients respond to things that they've seen before, because it gives them comfort and confidence.On the other hand, creatives—especially designers—gravitate to things they and you have never seen before.
Different is not always better, but better is always different. So while we're happy to hear your idea, remember that you are the expert at your job and we are the expert at ours. You hired us for that expertise, and you should trust us if we don't recommend your idea as the best direction. We only ask that you be as open-minded with our ideas as you'd like us to be with yours.
If you really do know what you want, tell us that up front. Or tell us that this is the idea to beat and we have one round to try. It's much better to know that before we begin to work, rather than after we struggle through trying to better an idea that in your mind can't be beat. Some firms may not want to accept that arrangement, but better to allow us to decide if we can make your idea work—or if you should find someone else who can.
Show-and-Tell
No. 30
It's one thing to know what you like, and another to communicate those preferences to your creative partner.
**Communicating your preferences early will save time and money,** while sparing everyone those awkward "first date" moments when common ground feels elusive. A creative person will want to know what you find pleasing, effective, off-putting, or ineffectual. As crucial as it is that you let us know what your brand stands for, it is equally important to let us know who you are.
One client of ours captured her favorite things with her phone's camera, showing them to us early in the process. She took assorted pictures of anything that caught her eye: street ads, art, wallpaper in a restaurant bathroom, a vintage travel poster hanging in her home. We immediately saw that those images shared a muted palette and a refined elegance, aesthetic leanings that became even clearer after we talked about what she showed us. Although our final design didn't actually incorporate anything she'd photographed, the overall aesthetic in her collection of images informed the direction we took and allowed us to start on common ground. We were collaborators from the start.
Reference images can also help where words fail—especially valuable in architectural or interior design projects. Understandings of what constitutes a "modern" look may differ, but concrete evidence of what you are picturing puts everyone on the same page.
Another client was equally effective at communicating her taste with a short list: "Everything Apple does, the branding for President Obama's campaigns, and the New York City subway signage." These examples told us that she liked straightforward, clean design—bright primary color palettes with little ornamentation. Chances are she would not have had the vocabulary to describe it like that.
One last thought on this subject: If you're struggling to articulate your aesthetic, your creative team can construct "mood boards" for you to respond to. Some firms even do this as a regular part of their process. A mood board is a collage of photographs, illustrations, materials, ads, and words that evoke a particular style or emotional response—and each one represents a different potential design direction. Their very purpose is to start a conversation about what feels most appropriate to you, generally speaking.
Cut Out The Middleman
No. 31
Large creative agencies often have a role called Client Coordinator (a title I loathe). Do you need to be coordinated? To be sure, projects require producers and strategists who are on top of every detail. But make sure that you also get to speak directly with, and express yourself to, those who are doing the actual creative work. **You don't want your words translated by a coordinator** all the time because something important could get lost in translation. After all, we're trying to thread the needle to find the perfect solutions to a long list of objectives, restraints, and considerations. How you communicate this information—both the casual and formal conversations about the project as well as your culture and insights—is what will lead us to the right solution. The more direct those conversations, from client to creative (and vice versa), the more effective they'll be.
Weirdly, such lines of communications are not always available. Many publishing houses, for example, don't allow authors to talk to the person designing their book cover. Sometimes, cover designers don't even get to read the book! This makes no sense to me. Just one chat could spark the perfect insight that translates into the all-important cover. Perhaps the publisher—who is the actual client—doesn't want the author to interfere in the process, give a specific direction that doesn't work, or fall in love with an impossible-to-execute idea. But if everyone is honest and transparent and understands that the publisher has the final say, there should be no problem. The possibility of a better cover should push everyone to have as many creative conversations as possible.
Think of yourself as the author. We need to hear the words directly from you and your fellow decision makers. You understand your hopes and dreams better than anyone else.
White Space is Your Friend
No. 32
White space is a design term that suggests "negative space"—aka space where there is no design element. It can work on a purely aesthetic level, but it also serves to tell the viewer where to look, what the hierarchy is, where to take breaks. It can also help an entire piece be more inviting.
A website, ad, or brochure that is chock-full of color, imagery, or type can be difficult to look at and read, let alone understand. Think of it this way: If someone throws a single tennis ball at you, you might catch it; if someone throws ten, chances are you won't catch anything. Sometimes I wonder if people think that if there is too much white space, they're not getting their money's worth. Every piece of available space should be filled, right?
Wrong.
**Do not be afraid of white space.** It serves a valuable purpose.
And while I'm at it, here are responses to seven other design misconceptions that can regularly trip up clients, hurt the collaboration, and weaken the final product.
1. Your logo doesn't have to be big to be seen.
2. Red is not the only color that stands out. Color choices communicate emotions and depend on everything else around them.
3. We can't "just sharpen" lo-res images in Photoshop.
4. We also can't "just change the font." At least, not without going back to the drawing board. Typeface choice and how it's used affects everything else.
5. If it looks small on your screen, you're probably not seeing it at the intended size.
6. Just because we can use all the colors in the world doesn't mean we should.
7. Yes, we really do need the "copy" (words) to start designing. It can be rough copy, but meaning affects design decisions.
Let the Creatives Drive The First Presentation
No. 33
The first meeting at which work is presented is often more pressure-filled than it needs to be. We have all been using words with each other and now we are all going to discuss how those words got translated into vision. Let the creative team drive the proceedings.
Some of us will recount things that were discussed early on. Let us. It will tell you how we arrived at our solutions.
Some of us will offer radically different solutions to the problem presented. Let us. There are usually many different and effective ways to achieve the priorities outlined in the brief, and we may want to gauge your responses to several of them.
Some of us will want to present straight through while you hold back responses until the end. Let us. Let us present however we feel most comfortable, because that will give _you_ the best opportunity to truly understand our thinking.
**Really, make an extraordinary effort to just listen.**
Presenting is a kind of performance. Much as you wouldn't interrupt a singer to tell them they sang a note out of tune, wait to tell a creative that you don't like that one aspect of the whole. You'll get your chance to respond. And when you do, the best initial approach is to ask questions.
Why did you use that color?
Why so much text?
Why did you start with that image?
The idea is to get more information about things you don't understand before you decide what you think. You want to make sure raw emotional responses don't prevent a beneficial problem-solving discussion. How you _feel_ matters, but what you _think_ matters more.
Focus (at this stage) on the intent of the design rather than the execution. Once you agree on the intent of each solution (the _why_ ) you can talk about the specific execution (the _how_ ). But it's very crucial (and very helpful to the process) to separate those two aspects of the work and address each independently.
One more thing: When multiple solutions are presented, clients often ask, "Am I allowed to ask which is your favorite?" The answer? "Yes!" But only after we hear your feedback. We're not being coy. It's just that the dialogue around the presentation might inform our choice, and we don't want that information to be influenced by our opinion.
Be a Fair Judge
No. 34
Sometimes, when given the role of design critic, especially for the first time, people think that criticism is required. And sometimes it is. But please keep in mind that your main goal is to collaborate with the creative to make the work better and not to be critical for the sake of it. To that end:
**Don't be hypercritical to get your money's worth.** Some clients will give lots of notes even when they love everything. You need only relate actual concerns, because if you think the work is terrific, you've already gotten your money's worth.
**Don't worry about the work solving absolutely everything (it never will).** This often surfaces when designing logos. Consider a successful company that's always had branding that is neither offensive nor communicative. They grow big enough to hire a professional designer to create a real identity. When judging the new logo—despite approval from everyone in the room—there is suddenly concern about whether it accomplishes everything. The goal is to solve the most important objectives, and then let time and successful business stewardship imbue the brand—and the logo—with everything else.
**Don't doubt your opinion. **Be brave and go with your gut—you know your company, the project, and, most important, what you do and don't like. For one thing, you have no choice. You're the final judge. Of course, if you can't commit to one direction at this particular moment, say that. The creatives spent a lot of time thinking and tinkering, so it's understandable if you need more space to consider all the angles.
A smart client once told me, "I like the first idea right now, but I think I'll like the second idea tomorrow, so let's go with that one."
QUESTIOn Everything
No. 35
Every industry has its own supersecret language and handshake. Designers (and other creative types) are no different. We tend to forget that whatever specialized knowledge we possess isn't shared by all. So if we throw around the word _responsiveness_ or assume you know the difference between PMS, CMYK, RGB, and Hex colors,* slow us down and ask us to explain ourselves. Sometimes there will be a technical reason for why a certain direction will save time and money. We know that because it's our job to know. There's no way you would, though, unless you ask us to break it down.
So ask a lot of questions, as often as you like. **Asking questions doesn't make you seem stupid.** It makes you seem like you want to understand things better. Pretending you know everything? Well, it can cause you to make stupid decisions, at the least. If you don't understand why we came up with the solution we did, how will you possibly be able to explain it to the next guy, or your boss, when they have the same questions you do? More important, for our selfish purposes, I've found that not understanding often leads a client to say No. Chances are, though, that if we can help you make sense of what we've done, we can change your mind. But we can't know what's confusing you unless you ask us about it.
PMS refers to the Pantone Matching System, a color system consisting of thousands of numbered swatches, used in printing. It allows designers to specify an exact color that will be clear to whoever is producing or printing the job. They are sometimes referred to as spot colors.
CMYK refers to Cyan, Magenta, Yellow, and Black. These four colors, when combined in different amounts, are the basis for printing all full-color images. And, yes, I know it seems like it should be CMYB, instead of CMYK. But the K likely stands for "key," to represent the key plate, which is black. Also, using a K means there's no chance the color will be confused with Blue.
RGB refers to Red, Green, Blue. It is the color system for video and computer monitors. There is a subset of 216 RGB colors considered safe for monitors, but even when using those some colors change from monitor to monitor, thus affecting the final visual experience.
Hex colors refers to three-byte hexadecimal numbers. It's another way to represent RGB colors in programming code.
Be Open to Things You Didn't Imagine
No. 36
You were expecting a big, powerful presentation, a solution that shouts your message throughout the land. But you hear only whispers. Or perhaps you thought subtlety was the way to go, and what you got instead was bold type in a thick red bar.
So . . .
Take a breath.
Or two.
Or three.
Don't dismiss the curveball outright just because it wasn't what you had in mind. Surprise may be your first reaction, but it shouldn't be your last. **Don't decide anything while you're still surprised.** Let the work sink in, then consider its potential only after its newness has worn off. While you're recovering, it may help to ask the designer to explain her thinking again. Voice your concerns and let her address them.
Someone said great architects don't build great buildings, great clients allow great buildings to be built. Change the nouns and verbs and the same goes for any creative profession. You make what we make possible, but when the solution is not what you expected, be open to the conversation. The situation calls for dialogue, not dictation.
To me, the best solutions break all the rules, all the preconceived notions of what they should be. As the old _Saturday Night Live_ character Stuart Smalley (played by the Honorable Al Franken, U.S. senator from Minnesota), liked to say, "Don't should all over yourself." ("Should" is a terrible driving force.) Those who do are likely to miss out on creating something great—or to prevent greatness from happening.
The noted entrepreneur and bestselling author Seth Godin says that the reason it's difficult to learn something new is that it changes you into someone who disagrees with the person you are. That's scary, particularly to those of us who like who we are. But questioning your beliefs keeps you growing, into not just a different version of you but a better one.
Don't Say that, Say This
No. 37
Sometimes it's not what you say but how you say it that derails a collaboration. Bluntness, specificity, vagueness—all of it can get in the way. So . . .
Don't say: Make it red.
Do say: I wish it were bolder and stronger.
Don't say: Make it bigger.
Do say: I wonder what this image would look like if it were more prominent.
Don't say: Use a handwriting font.
Do say: I like the feeling of handwriting.*
Don't say: I hate it.
Do say: Can you explain this to me?
Don't say: What I'm looking at makes no sense.
Do say: Can you explain why you decided on this direction?
Don't say: Can you try again and make it different?
Do say: I wish it were . . . [whatever you wish was different].
Don't say: I love it [if you don't actually love it].
Do say: I think I really like it, but I need some time to gather my thoughts.
Don't say: Here are the changes we want you to make.
Do say: Great effort, but there are some concerns we'd like addressed.
Don't say: We need you to do it like this.
Do say: We are hiring you to do what you do, so please tell us how you'd like this to work.
Don't say: What do you charge for a logo?
Do say: Here is what we are looking for and here's our ideal timeline. Please come back to us with a proposal.
Don't say: It's a little job; there's no need for a contract.
Do say: Would you like us to supply the contract or would you like to?
Don't say: We want it to look like this.
Do say: Here are a few examples of work we like and think is relevant.
Don't say: I'm not a fan of this typeface.
Do say: Can you show us some different type treatments?
Don't say: We can't pay you much, but we'll get you great exposure.
Do say: This is how much we can pay. We hope that works for you.
Don't say: This isn't what I pictured, so I don't think it works.
Do say: Let me live with this for a day or two.
Don't say: I showed your work to my friends last night at dinner, and they didn't like it.
Do say: I was talking to some colleagues and they brought up some issues I'd like to discuss with you.
Don't say: We need this project to accomplish these eight goals.
Do say: This is our most important goal, but there are secondary goals we'd love to achieve as well.
Don't say: Can you combine this version with that version?
Do say: This is what I like about this version and this is what I like about that one. What can you do with that information?
Don't say: Have you designed aseptic baby food packaging before?
Do say: Can you share other jobs you've had that are relevant to this project?
Don't say: We like both of these ideas, so we'll do an A/B test with them.
Do say: I like both of these ideas, but let's go with this one.
Real handwriting is amazing and beautiful and can communicate sincerity and (sometimes) urgency. Handwriting fonts tend to do the opposite. They are clearly, ironically pretending to be something "real." There are a few good handwriting fonts, but the tell is when each letter is exactly the same every time. That is never the case with real handwriting.
Beware of Garanimals
No. 38
Designers often present more than one idea. We do this for many reasons, but here's a big one: We have a few directions we like, but because it's our first time working with you, we can't predict which will work best for you. (Don't worry—we'd never show you a direction we wouldn't be happy for you to choose, even if we prefer another one.)
The downside of this strategy is that **sometimes clients see the various options as comprised of mix-and-match pieces instead of the coherent design whole each one is.** Of course, we know that clients will invariably like certain aspects of each idea, and describing what you like and don't like in terms of specific elements of particular design schemes is a worthy discussion to have. The problem occurs when you want us to take part of one and combine it with part of another. It creates a Garanimal, where the new solution is weaker than either original. (You're familiar with Garanimals, right? Those color-coordinated but mismatched pants and tops that were a staple of kids' wardrobes in the early '70s?)
Imagine using ingredients from different recipes because you love each taste in a certain dish. You already know that mozzarella and basil will probably not taste good in a Szechuan curry. Imagine how a designer will feel about randomly combining elements that each work well in their own context to create a weird, contextless mishmash.
Instead, allow us to consider your opinions about the strengths and weaknesses of each design, and let us create a new solution that may not incorporate all of your favorite elements but will nonetheless achieve the effect you are looking for. You don't want a cut-and-paste job; you want something greater than the sum of the parts.
Here's a perfect example of the Garanimals problem. At a brand identity presentation I gave at a production company, half the people in the room liked one logo that my team created, while the other half liked a different one. What they managed to agree on was that the two ideas should be combined. A terrible idea. They didn't understand that they were responding to the logos as a whole, not to their individual elements. After considering their responses to the presentation, we designed an entirely new option. When the once-divided room saw the new idea, they appreciated the differences in the original choices and agreed to go back to one of those. It remains the company logo to this day.
Another encounter with the Garanimals problem didn't work out as well. We were asked to come up with a new retro look and feel for a seaside hotel. We worked with an illustrator to create old-fashioned paintings of the building and designed a logo and typographic system that felt equally vintage. It was a beautiful package, if I do say so myself. When we had finished designing almost everything, the client told us they had just decided they wanted to keep their current very modern logo after all, and asked that it be put on all of the new material. Surprise—it didn't work; the elements contradicted each other. We strongly recommended creating a whole new campaign around the original logo or going with the "vintage" campaign we had produced. They decided to do neither. It was a huge waste of time and money.
Of course, there are cases in which a detail from one design solution can be incorporated into another. But **I promise it's almost always better to consider creative solutions as they were meant to be—as a whole.** What works for dressing children doesn't work for dressing your brand.
An Important Note About Giving Feedback
No. 39
Being a good client is not synonymous with being an "easy" client. In fact, oftentimes it's the clients who challenge and question designers who get the best results. **You can be opinionated and assertive** and probing and still be the ideal client. That is what makes collaboration brilliant.
I Notice / I Wonder
No. 40
One of the most challenging aspects of a creative collaboration is reacting to the big reveal when you see the work for the first time. The whole room turns to you, the client, seeking words of wisdom. Maybe you'll instantly know what you like or don't like and why, but more often you aren't sure how you feel. Meanwhile, we are at a vulnerable moment in our collaboration, and your response—and how you deliver it—will greatly impact the next phase. **Here is a foolproof way to work through your feelings out loud** while also considering those of your creative collaborator.
Begin with an "I notice __________________ " statement.
Examples:
"I notice how powerful that image is now, and you really followed our request for color."
"I notice you handled the logo in lots of different ways across the solutions. Lots to choose from."
"I notice how happy this whole presentation makes me."
Fill in the blank with virtually anything you notice about the work without passing judgment (yet). You can even notice that the presentation was comprehensive or that the presenter was excited about the work. And if you can't think of anything, try this: "I notice you guys really put a great deal of work into this presentation." It may feel like you are stating the obvious, but trust me, what's "obvious" to you is valuable for us to hear.
This not only gets you out of an awkward moment, it can be revelatory to both you and the creative, who gleans a lot from the simple articulation of what you see. Maybe they meant to convey something else entirely. Maybe what stood out to you was intended to be a minor element. Maybe they didn't even notice it was there before.
Next, seamlessly move on to an "I wonder __________________ " statement.
Examples:
"I wonder what you might have done if I hadn't asked you to begin with that image of the horse."
"I wonder what this would look like with a different palette."
"I wonder if we should rethink our hierarchy. What do you think?"
"I notice" and "I wonder" statements allow for the conversation to unfold openly without criticism on your part or defensiveness on theirs. You aren't telling the creative to do something. You're giving him feelings to respond to. You are wondering, not directing. **"I notice" and "I wonder" statements can be the difference between having a constructive creative dialogue and a combative one.**
And yes, feel free to use words that feel more natural to you, like "I can't help but notice" or "What do you think would happen if?" The point is to be conversational, but with constraints that can help keep you in the right lane.
It's Okay to Love Something Right Away
No. 41
This may not seem like a problem, but it can confound clients. It gets them thinking that it was all too easy or that they aren't getting their money's worth. Yeah, I know it sounds weird. But in a standard project, with a process that includes two rounds of revisions, even the best client might be hesitant to admit in the first presentation that we nailed it.
So think of immediate success as a reflection of how well you briefed us—and how well we connected with your needs as you expressed them.
**That's cause to celebrate! And reason to move on.**
What to Do When You Kind of Hate What You See
No. 42
This can happen, even with a fantastically talented creative. But how you offer your reaction will make a big difference in what happens next. So try not to give in to the urge of an automatic No.
Instead, start by asking a lot of questions, especially if we haven't sufficiently explained our thinking. Try to understand what you are looking at more completely. Asking why we chose that particular photograph or those specific colors may help you see advantages to an approach that you might otherwise miss. Even if you hate the execution, you may very well fall in love with the intent.
Consider also that you might be responding negatively simply because you are surprised. The human brain is an expectation machine, which has evolved to make decision-making as easy as possible by confirming what we already know (or believe) and discounting what is new or unfamiliar. In other words, sometimes the best ideas take a little getting used to (seeNo. 36, " Be Open to Things You Didn't Imagine").
One way to handle immediate disappointment is to just **be honest and say you're not sure if it's working for you,** then ask for time to think about it. Maybe you'll feel differently the next day, after you separate your expectations from reality. Maybe you won't—but you'll have a clearer head with which to explain your issues.
Another tactic in the moment is to begin talking about some tiny aspect you like—a typographic choice, the pacing, anything. Ask yourself, or us, why you like that thing. Why does it speak to you? In addition to softening the blow, finding one area of agreement is a good first step on a journey forward.
So You Think You Can Make It Better?
No. 43
Although the impulse is understandable, it's important to remember that you're not the creative. I often make it a point to ask clients to communicate the goal rather than identify even one possible solution. For example, I'll say, **"Don't ask me to make it yellow. Tell me you want it to be sunnier."**
I promise I'm not trying to stifle your creativity. But if you communicate what you're trying to achieve rather than offer a specific solution, you give us room to do our job. Maybe a change in color isn't the best solution. Maybe using yellow would make the copy more difficult to read and recede on the screen. So maybe we change the background image or redesign the typography instead. Requesting a design that feels more upbeat allows us room to explore—and actually make it look sunnier.
What if You Don't Know What You Think?
No. 44
At some point in a creative process, you're likely to find yourself in one of the following situations:
1. You like something but worry it's not actually good.
2. You don't like something but don't know why.
You hired us, in part, for our level of taste and ability to differentiate between good and bad and the gray areas in between. But we understand not having the words to articulate why you do or don't like something. Just tell us that.
We'll ask you a lot of questions to help you speak in full paragraphs, guiding you through the discomfort to reach a conclusion we can work with. **Even if there are no specific conclusions, talking about it will help us respond.** We will ask more questions, maybe look at some other work together, and try to understand more fully how you're feeling.
Remember this: There is no single right or wrong answer. Coming up with the solution that works for you and the project is the goal. Work with us to get there.
And keep your eyes on the prize—a successful collaboration. Either everyone wins or no one wins. Together we can make it better, if you give us the room to do it.
Give All Feedback at Once
No. 45
I have a client who sends me an email every time they chat with someone else about the project. They introduce new thoughts, new changes, new perspectives. As you'd expect, some of the ideas are interesting food for thought and some are terrible. That's okay—separating the signal from the noise is what we do. But no feedback is helpful if it comes in dribs and drabs over the course of a week.
It makes no sense for us to begin revisions after a presentation until we have all your comments. Otherwise, we'll just be waist-deep in a reactive and inefficient two-steps-forward-one-step-back process. Deliverers of piecemeal feedback appear indecisive or undiscriminating or both. It's pretty clear to us that they aren't thinking that much about what they are sending along. They certainly aren't comparing new comments to previous ones to see if they contradict each other or even support the same goal. Which unintentionally leaves the decisions up to us.
It will be much better to tell us it will take you a week to gather feedback from each of the stakeholders and then put it all in writing for your own review. Then you can be sure that all points are valid and there are no contradicting directions. You then weigh all the opinions and decide which are worth our consideration. This is no small responsibility. One tossed-off comment that you didn't even feel so strongly about can mean days of work for us. On the other hand, if it's a serious comment with a real possibility, it will be well worth the exploration.
Here's another pitfall: **The greater the number of emails we have to field, the greater the chance of something important getting lost in the shuffle.** (I know you know what I mean.) If instead we have one email to work from, not only can we use it as kind of a checklist but it will also give us a chance to consider how all of the comments will work together and propose thoughtful solutions about our next steps.
My favorite way to receive feedback is a combination of a phone call and a follow-up with a written list, from you or us. The call is necessary because we all get to be heard and have the opportunity to ask questions and make comments. The list is crucial because it summarizes what was discussed on the call and what we think was agreed upon. You don't want to rely on any one person's memory for a call because sometimes people walk away with different conclusions.
I tell my designers to follow my feedback precisely and _then_ also do what they think is right based on how the work is shaping up. We do the same in turn with clients. Maybe you really want us to add a floral element, but when we do it, we know it isn't working. We'll show you what you asked for, and then show you what we think could work better, keeping your desired effect in mind.
Another difficult situation is when clients change their mind after giving a go-ahead. Think of it like a construction project. After the ground has been broken, it is expensive (and wasteful of time and energy) to go backward, reconsidering what has already been built. It also messes with our heads and throws the possibility of a single-vision creation out the window.
That said, it can and does happen even with all the best intentions in place. If you preface a change of direction with an acknowledgment of the emotional toll of the change, whatever follows will go down easier.
WE Don't Care What Your Spouse Thinks
No. 46
The call from the client typically goes something like this: "I showed my husband/wife/partner/son/daughter/second cousin what you did—they know much more about this stuff than I do—and he/she/they thought we should go in another direction."
While we are sure that your life partner and/or progeny are wonderful people with excellent taste—and maybe even do know "more about this stuff" than you do—what you show them is likely their first interaction with the project. They haven't read the creative brief, heard you discuss the project with us or your colleagues, had any conversations with us, or attended the meeting at which we explained our thinking. So hearing from them is more than a little frustrating.
Don't get me wrong. Their opinion is valid because it's their opinion. Everyone has new thoughts and perspectives that come at random, even inconvenient times. (Sometimes I wake up with different solutions to projects long complete. This is not a discouragement of new ideas or directions or thoughts.) Moreover, the opinions of those close to you are even more relevant if you, the client, truly believe they have brought up interesting points. So once you discuss your loved one's thinking with your colleagues and any other relevant stakeholders, you are welcome—even encouraged—to raise any points that survive that gauntlet with your creative professional.
We ask only one thing: Don't tell us it came from your spouse!
Own it. Don't bring up the mister or missus. **Instead, explain it to us in light of the original brief** and all the conversations we've had. Because few things are more frustrating to a creative (or anyone, I would imagine) than the idea that all our hard work—not to mention our collaboration with you, dear client—can be undone by dinner table or pillow talk. It's maddening, and it can quickly undo the trust we've built together.
Oh, one other thing: If you tell us that your spouse had a new idea, suggesting that we now follow this new direction, well, we now have a new de facto client. So it's only fair that we meet with said spouse, and that he or she attend meetings going forward.
Won't that be fun for everyone?
On Fear and Insecurity
No. 47
The emotions that drive creatives are hope and optimism. We believe we can make a difference. We know we can make a difference. For you. That is why we do what we do. If we didn't believe in it, we couldn't do it. Too often, the emotion that drives clients is fear and insecurity. When those two sets of feelings get together, there is bound to be dissatisfaction and frustration.
But hard choices are hard precisely because there is no one right answer. That is especially true when working with creative people.
Don't let fear drive. It's an especially terrible driver in creative endeavors. **Fear usually drives people to make the most cautious choices.** I'm not saying you should always go with the riskiest choice, but if your only reason not to do something is fear, you need to step back and analyze it again.
What are you afraid of? What is the worst thing that can happen? Try to put the choice in perspective and understand whether there is a single element that is keeping you up at night—or if it's the whole thing. You are in the driver's seat. If you decide the best solution is to begin again, that's fine. Just make an extraordinary effort to understand what is driving that decision. And make sure you can explain that decision so the creatives can understand and respond effectively.
Why Focus Groups Suck
No. 48
**Truly great work is not achieved by committee or consensus.** Great work is achieved by someone with a strong vision or an original idea—and the leadership skills necessary to convince others to take the creative journey with her. They have the support of teams both above and below, people who trust and believe in them. That journey should not pass through the sterile, one-way-mirrored rooms that house focus groups.
It's not that the people in those groups don't take the responsibility seriously. Quite the opposite: An executive at a multinational brand company once told me that Americans really look forward to that decisive moment in the store aisle when they get to choose which box of tissues to buy. So being asked (and paid!) to weigh in on the aesthetic qualities of anything is a pretty big deal to most people.
A crowded table of strangers wanting to do good without really knowing what "good" means as they respond to a facilitator's leading questions is not conducive to creative input. Add to that the fact that in a group of strangers, a dynamic inevitably develops in which a single strong personality articulates a position and the rest of the group follows. The result is that in a room of, say, ten interviewees, you're probably getting no more than a couple of reasoned opinions. That's not a focus group; that's a focus pair.
Worse, **group settings often lead people to mistake criticism for intelligence.** A guy who says, "Hey, that's cool" doesn't seem as smart as those with something negative to say. So critical comments rule the room in focus groups, even absurd insights like "That shade of red is weird." And while many clients understand the psychology at play, it's hard to ignore negative feedback. It's an act of bravery to continue to like that "weird" shade of red after the group has spoken.
And of course, we all know that in real life, the person who will really be respected is the one who is not afraid to be honest about her feelings even if they are not consistent with the group's. That bravery is rare. Watch _12 Angry Men_ for the perfect illustration.
George Lois, the legendary art director best known for creating iconic _Esquire_ magazine covers, famously said, "Great ideas can't be tested. Only mediocre ideas can be tested." That's because most of us don't have the framework to respond to revolutionary originality (or even plain old originality). Focus groups rate only what the people in them are already comfortable with or what we already understand as being "good." But good design should be distinct and specific to particular client needs. Imagine the advice Apple would have heard had they focus-grouped the packaging of the iPhone: "That sure is a lot of white space." Or "You should put a picture on the outside so I know what I'm getting." Instead, unboxing those first iPhones felt like revealing a beautiful, sui generis object. That experience of delight simply could not be properly valued in a "test" setting. Gathering opinions in a focus group leaves no room for a visionary solution or a revolution in design that is not yet quantifiable.
If you insist on focus-grouping a concept, make sure the moderator steers the discussion away from generalizations. Better yet, conduct focus groups before you have a design in order to learn what the public thinks about your company or the product in question or the competition. Established consumer beliefs should inform a creative brief, not a creative solution.
Twelve publishers (about the size of your average focus group) rejected _Harry Potter and the Sorcerer's Stone_. In the end, what it took was one person of vision—the thirteenth publisher, who considered the idea independently, rather than based on the consensus of a roomful of random people—to turn one woman's brilliant idea into a global phenomenon.
Don't Let Data Drive Your Decisions
No. 49
The data we all now have access to is so cool, but we shouldn't be slaves to it. Successful businesses cannot be run by data exclusively. They'd never keep up with it. But judging creativity or being a slave to the data in creating a brief is even more absurd. Data doesn't have room for a visionary outlook that is not yet quantifiable. It can't anticipate imagination and joy and the role they play.
Some decision makers like to settle creative debates with an A/B test because it relieves them of the responsibility of making the hard choice themselves. But it means that they also miss out on the enlightening discussions that precede decisions, when you can decide on the relationship between A and B and the benefits of each. That's their loss. My loss is that A/B tests don't account for the possibility of impact over time.
Worse, **data doesn't leave room for the most unquantifiable of qualities: vision.** If creativity defeats habit, data testing reinforces it. People tend to respond to the familiar, feeling more comfortable with something they have seen before. But the familiar has no magic. It is known and predictable, and—yes—quantifiable by data. But you are presumably in this for the long haul and want to (or need to) differentiate your brand. Not in a way that alienates, of course, but A/B testing is a terrible way to assess the impact and possibilities of creativity.
Be Confident, Not Arrogant
No. 50
Confidence is a beautiful thing. It's based on reality—you know who you are, what you're doing, and, most important, what you don't know. Someone who is confident brings out the best in everyone. When you get praise from a confident person, you work harder to get that praise again. When you are criticized by a confident person, you take it seriously because you know they only do so with good reason.
Arrogance, on the other hand, rarely gets you what you want from a creative. It's based on insecurity or fear, both terrible drivers. You (subconsciously?) need to put other people down to give the impression that you, in fact, know everything and everyone else is inferior to you. It never works. When creative people work with someone arrogant, it makes them withdraw rather than strive. **No one wants to be yelled at or scolded,** whether they are five or fifty years old.
With an arrogant person, we tend to ignore both praise and criticism, feeling it is all self-serving. We go about our business doing the best we can to get through and around it. This doesn't create great collaborations or, more to the point, great work. I would try two other modes on for size. One is self-doubt. Question yourself. You may learn something new by wondering, listening, being curious about what others think. The other is empathy. Imagine how we're feeling/what we're thinking. It works wonders in every situation.
Pick Your Battles
No. 51
Compromise, that lovely and noble salvager of relationships—how valuable it can be. Especially if we think of it not as "caving" but rather as letting go of something that doesn't matter nearly as much to us as it does to our partner. (An accommodation, if you will.)
Make no mistake: I'm not suggesting that you relinquish your insistence on anything important to you. But when you're dealing with a list of issues and your creative partner feels very strongly about a couple of the items, it means one of two things:
1. We may very well be right; this is, after all, our field of expertise.
2. You will make us happy if you let us have our way every once in a while.
**A satisfied creative partner is much more likely to find the best solutions** for those changes that you do feel most strongly about. It's win-win: two people concocting a mutually beneficial arrangement from two competing opinions and needs—as if you're the only two people in the world that matter. Because, at that moment, you just might be!
The Power of Encouragement
NO. 52
A little love goes a long way if your aim is to get the best results. The power of encouragement can't be overstated. Creative brains thrive on psychic payments, so I recommend you heed this advice in good times and bad.
The time span of any creative project provides ample opportunity for a random email praising our work and appreciating our effort. This out-of-the-blue message puts a swing in our step and encourages the extra late-night push to live up to the praise. Also, it costs you nothing.
This approach may feel harder when things go wrong, but even then, carrots are simply more effective than sticks.
Consider the different responses to a difficult first presentation in which, due to miscommunication or misunderstanding, the creative missed the boat by a mile. One client was discouraging and one was encouraging. I've experienced both.
client number one
"Looks like we might have made a mistake when choosing your firm. We are really disappointed. Contractually, we have to give it another try, but I'm skeptical this will work out."
client number two
"Obviously, this went badly, but we still have faith in you. We are fans of the work you've done for others. Please consider all we have discussed."
Berating the creative is of no use—especially since the client has nothing to gain from a second failure. Yet that's the likely outcome, as I can safely say it is very difficult to give our heart and soul to a client who doesn't believe in us.
**I'm not encouraging false praise.** In fact, if that's the only type of praise you can offer, sit down over coffee or a stiff drink and try to figure out how to get the collaboration back on track.
A graphic designer colleague posted a note on Facebook recently that simply said: "Will work for thank-you cards."
I know he's not alone.
Accept that Everything IS Emotional
No. 53
People behave differently at work than they do at home or with friends. More reserved, more "professional"—in short, less human. But their emotions are still there, simmering just underneath the surface.
For creatives, who are doing something that seems a bit mysterious to non-creatives, this is even more true.
Acknowledging and accepting that **emotions are a normal part of the creative process** and the resulting client dynamic will help everyone in any collaboration.
This kind of work requires that we share the inner workings of our brains. Doing it well means we've made an emotional connection with your audience, which we can only do by pouring our emotional selves into the work. Those emotions sometimes overflow, especially—again—if it's not going well.
Our professional persona will try to remain calm and cool, but another part of us—the one that stayed up all night to make it perfect—will be devastated. We may get emotional. We may even cry. And that's okay. It's part of the process.
You too may find yourself more emotional and insecure in these projects. Creative work can seem elusive and confounding to non-creatives. Especially when we are shaping the part of your business that will be exposed to the public. There's an unknown factor, and it's a problem you can't solve yourself. Clients will get more upset with us than other collaborators, especially when they feel it's not going well and their job is on the line. And that's okay too—also part of the process.
Talk It Out
No. 54
Someone once said a creative's work is only as good as the number of uncomfortable conversations she is willing to have with her client. Positive results are dependent on the successful navigation of a variety of fraught topics—expectations, budgets, deadlines—and breaking them down takes guts. From both parties.
So you need to be as devoted to dialogue as we will be.
Talking through misunderstandings, misgivings, mistakes, and whatever other human issues may arise helps to dispel momentum-killing and emotional awkwardness. Not talking through them only makes it worse.
**This is not about being confrontational. It's about being conversational.**
Yes, it can be frustrating when you ask for a change and the person you're paying doesn't want to make it. But if you don't give us the chance to explain our point of view, how will you convince us? Or vice versa?
So have the hard, honest conversation. Don't avoid emotions (see No. 53, "Accept That Everything Is Emotional"), and don't be afraid to raise fears. Talking defuses emotional impasses, stress, and frustration. And when I say "talking," I literally mean talking. Don't get into email exchanges about important issues; the tone of written messages is frequently misinterpreted, and once the damage is done, unintentional or not, it will be hard to repair. And never, ever start a fight over email; that's like breaking up with someone on a Post-it. Show you care by having a real conversation with a real person—without eye rolling or table pounding or hanging up.
Some people think they will spare our feelings if they withhold the truth, but if you know how you feel, pull the Band-Aid off quickly. It will save time and strengthen our relationship. While it can be scary to tell someone how you feel, take comfort in the fact that the creative likely knows how you are feeling already. We are always reading you and your emotions. The biggest surprise will be your willingness to discuss the feelings. Once you reveal your vulnerability (a universal condition)—someone we're working _with_ on a project and not a suit we are working _for_ —I promise the results will always be better.
This is a relationship. Invest in it.
Please Don't Piss On the Creative
No. 55
This may sound funny, but the client's need to mark their territory on a creative work for the sake of it happens way more often than it should (which is never). This is why we get requests for a small change that seems to fall under the heading "just because" . . . or a huge change that influences everything. I presume this instinct comes from the client's (subconscious?) desire to feel that they're an integral part of the creative work—to mark their territory. But the crazy thing is that the client has already marked the work in a huge way. The whole project wouldn't be what it is without them. There is no need for this step.
Just be sure to keep your ego in check. Will this change really make the work better? If yes, then great! That's what we all want. If you have a funny feeling in your tummy that you are doing it to assert your authority, then take a deep breath and realize you already have the authority; no need to assert it here. You are the client.
There are a few key warning signs to look for:
The change is minimal and doesn't really impact the job, but you want it anyway.
It comes after we have worked through all the major decisions but before you would incur change costs.
You are giving us a directive rather than engaging in a conversation.
If you still believe a change is necessary, **all we ask is that you call us to discuss and deliberate.** Explain your reasoning, and let us think about the suggestion. In the end, it may turn out to be a great last-minute fix.
Nothing Takes a Second
No. 56
Clients sometimes ask us to make changes or explore a path that will "just take a second." We can't read minds, so we don't know for certain if they truly believe that what they're asking is as simple as flicking a light switch or if they are trying to downplay extra work so it doesn't feel like an imposition or if what they really mean is "I want you to do something extra, but I don't think this should cost more."
But whatever the actual intent, I'm here to tell you that nothing takes a second. In the request, **we often hear sentiment that's at best dismissive of our time and at worst dismissive of our value.**
That change you think will take no time at all? Sorry, but it will. Everything does. Knowing and respecting that will make a huge difference.
Ask yourself this: How good would the result be if the change did take just a second? Certainly it wouldn't give us the time to put any thought into how the specific change might affect the coherence of the full project. You wouldn't want that. You _shouldn't_ want that.
A client once asked us to change a few images in a design scheme, suggesting that it would only take a second. But a raft of factors had gone into choosing the images that made it into the work: color vs. black and white, page balance, subject diversity. We had also designed the typography to complement certain photos; in some cases, the swapped-in photos clashed with the type. We made the changes—we heard what the client was telling us—but it took a lot longer than a second to make the new photos look right.
This too is a two-way street. We're asking you to recognize how much time each task takes, so you can expect us to give you the time you need to consider each iteration of the work. It doesn't help us if you rush past mistakes that you're going to need us to fix later on. So go ahead, take your time—or at least more than a second.
Don't Ask to Sit With Us While We Make Changes
No. 57
I can promise you that we will politely answer No. (Maybe not so politely.)
**I can't imagine you would like it if someone sat behind you while you wrote a report at your desk,** chiming in every once in a while with a "helpful" suggestion. Neither do we.
Clients generally propose this scenario figuring that it will save time. "We could eliminate the back-and-forth," they say. What it will also eliminate is our ability to do our job well. That often involves creating hundreds of ugly things before the beautiful thing comes along.
You do not want to see how the sausage gets made, but the truth is, in this case, you can't. The truly exciting part often happens in our heads anyway. We may need to just sit and stare at the work for a while, spend some time thinking about it. Nothing to see.
Don't take it personally. Designers don't even like their art directors to "sit with them" while they work. There's a photo blog called _Hovering Art Directors_ , a living tribute to that awful moment when art directors stand behind designers and tell them to make a change while they are being watched. No one can use their creative brain fully when someone is putting pressure on them to "create." No one.
Don't Fall Off The Face of the Earth
No. 58
Every contract should include a schedule so that everyone knows how much time each phase of the project should take. If the process goes a bit off track, fine. The schedule is just a guideline. As long as we confer about shifting time frames, things should continue along smoothly.
But if that conferring doesn't happen—if communication stops or gets drawn out beyond reason—all bets are off.
Creative professionals—like most everyone else but especially if they're freelancers—schedule their workflow around agreed-upon schedules. When that schedule goes off the rails, it makes it hard to plan for other projects we need to do to make our rent. In fact, we might have turned down work to be available for the agreed-upon schedule. When you ignore the schedule, you are disrespecting our business arrangement. How eager do you think we'll be to jump back in when you do finally call? More to the point, who's to say whether our schedule will allow us to?
Communication blackouts also suck the momentum out of the process. After being put on indefinite hold, it takes time to get back into a project's particular rhythm. There's an emotional toll too. When we don't hear back from you, it's a little like getting stood up. We've worked hard to do the right thing; of course we're anxious to hear what you think of it. But if you don't get back to us within a reasonable time frame, you're kind of saying you don't care about the work as much as we do.
We aren't asking for much. Even a simple sentence of explanation via email will suffice: "Apologies, but we're actually going to need a couple of months to reevaluate everything, so we'll get back to you the week of May twentieth." Another perfectly fine response: "We received the email but won't have a chance to look at it until later this week."
Here's another easy one: "Thank you." That's all we need to know that actually you received what we sent. A simple acknowledgment of effort is worth more than you know. Having to write to a client to ask if she got the stuff we sent a week ago is crazy-making.
**Shit happens. We get it.** But a quick email to concede that will make a huge difference in the ongoing relationship.
If It's Just Not Working
No. 59
You're trying to make this work, and the creative you've hired is clearly talented, but something about the working relationship just isn't clicking. Maybe the conversations aren't productive. Or the creative doesn't respond in a timely enough fashion. Maybe you find yourself talking only to junior members of the creative team. Or maybe the work is just terrible. You've begun to dread getting on the phone with them. Maybe you've lost confidence in the fundamental direction of the project.
Those are all good reasons to cut bait. But before you give up . . .
**Talk it through one more time.** Definitely tell the creative how you're feeling, but do it with empathy for their position and with an honest desire to find a better way forward. They may well have a legitimate, and resolvable, beef. As I said earlier, a good creative can be measured by the number of difficult conversations she is willing to have. You have to be willing too.
**Take a look in the mirror.** Be honest: Are you sure you've been a good collaborator? Is it possible you've been unreasonable? Have you been pushing too hard? Without realizing it, you might have started to act more like the creative than like a client.
**Try shifting your approach.** I once had a client—call her Natalie—whose boss forced her to work with us. She wasn't happy about it and made it clear that she didn't like me. And I didn't like her right back. One day I decided to conduct an experiment: If I really made an effort, could I make her like me and make myself like her? So instead of dreading getting on the phone with her, I looked forward to another opportunity to change our relationship. I listened more attentively. I did not take anything she said personally. I complimented her ideas and approaches.
And it worked! We began to appreciate each other and even became friendly. And since she now liked me, she trusted me, and our collaboration flourished. Yes, it took work and a little swallowing of pride, but it was worth the effort. (She later hired us herself for many other projects.) I have since "Natalied" others as well. Perhaps it's a tactic that will work for you.
Of course, it may be that you've done all you can and you're still not where you want to be. In such cases, don't hesitate. Because if you're unhappy, chances are the designer is too. Hopefully, you've prepared for the worst and there's a "prenup" (kill fee) in place. If not, a phone call between reasonable, soon-to-be-ex-collaborators should yield an amicable agreement. The creatives should keep in mind that they have essentially failed you. You should keep in mind that they paid employees to work for you. You hold the checkbook, so you have the power. Err on the side of fairness, not bitterness. Both sides should be equally content (and possibly annoyed) when you part ways.
When Creatives are Assholes
No. 60
As much as this book is meant to explain how designers, architects, writers, and other creatives might need special care and feeding to get the best results, I don't have any patience for creatives who think of themselves as "artists" first.
So don't fall for any temperamental genius crap.
I know of one colleague who refused to include a visual remembrance of a client's deceased partner in a project because it didn't fit his design.
Can you imagine? Well, I'm here to tell you that this is not the way it's supposed to work. Clients shouldn't treat creatives badly—and **creatives shouldn't treat clients badly.** But it happens. Creatives are humans, and some humans are mean, manipulative, and holier-than-thou. Maybe they offer one solution and expect you to just take it. Maybe they belittle your ideas or play off your insecurities or refuse to make changes. Maybe they throw things. Whatever the behavior—and this is yet another reason to do your homework (see No. 17, "Call References, for God's Sake")—run at the first sign of assholishness. Life is too short
Don't Be Rude to My Staff (Or Yours)
No. 61
Being nice is one of those things you learned in kindergarten that becomes even more important in a professional, collaborative context. Regardless of what else is going on—in your project, your personal life, or the world—you control how you treat others. Use that control.
**Clients usually have the sense to not be rude to senior members of a team. **But too often that sense of decency flies out the window when more junior people are involved. It's as though the client thinks those people are working for them. They're not—although it would hardly be okay to treat them badly if they were. They work for us; we work for you. If they screw up, we can fire them. You can't.
I know a private school principal who makes sure she is the one answering the phone when parents of prospective students call for applications. She doesn't identify herself, though, because she wants callers to assume she is the receptionist; she wants to see how they act with people they don't think they have to impress. Or people they assume they are superior to. She can't know how far the acorns fall from those trees, but by the end of the conversation she has a good idea of the kind of values those trees have instilled.
We feel the same way about clients who berate their own employees in front of us. We're not impressed by leaders who bully the people they have power over. It only makes them look less competent as a leader and makes us respect them less. And that has a terrible ripple effect.
**No one likes a bully,** and since it will make us respect you less, it certainly won't encourage us to go the extra mile for you. We file that information away and know that one day, that anger may be turned on one of us.
That's if we decide to work for you at all. Some people are so obnoxious so early in a process that they never get a chance to be a client. Like the record company executive my partner and I once pitched. We were in the middle of presenting our physical portfolio (that's how long ago it was) to this guy in his office, when his (giant) cell phone rang. Explaining that he had to take the call, he excused himself. That's annoying, but it happens. Right before he closed the door, though, he turned to us and said, "Keep going."
Huh? We were pitching to him! There was no one else in the room! Keep going for whom?
At that moment we knew we'd never work with him. He had revealed that he neither understood—nor cared to understand—what we do. I sometimes think about how funny it would have been if when he returned to the room, we had told him that the presentation went great and he had given us the assignment.
Serve Lunch During Lunchtime Meetings
No. 62
Everyone has too many meetings. It's the number one complaint of Corporate America. I don't disagree, but I'm not going to go there right now. I do think, however, that we should make those meetings we must have as enjoyable and productive as possible. I formally submit this simple request: If you've called people together for a meeting at mealtime, **feed us.**
It's hard enough for a roomful of people to focus and cooperate long enough to accomplish anything. Hunger and its corresponding grumpiness exponentially lessen any chance of accomplishment. So for our stomachs'—and your project's—sake, give us something to chew on.
About Pro Bono Work
No. 63
Creatives get many requests to work gratis for a good cause. Most of us love doing these projects, since it's a chance to make a difference by doing what we love. And equally important and somewhat liberating is lending our talents to an organization whose goal is _not_ making money. But the joy will quickly fade if your actions do not reflect—and make up for—the lack of pay. **Pro bono projects should not follow the normal way of doing business,** but rather should be handled with unusual consideration and thoughtfulness. For example, whereas multiple (sometimes unlimited) iterations and presentations are standard in paid creative work, that's asking a bit too much from someone who's doing such work for free.
So it is even more important to strictly follow the guidelines in this book for a wonderful and joyful collaboration (yes, they apply to paid projects as well, but they are of even more importance in these situations). And I would place even more emphasis on giving credit whenever and wherever you can (see No. 64, "Give Credit Where It's Due") and sending samples of the work to the creative so they can show it off too.
With this kind of mind-set, everyone wins.
Give Credit Where It's Due
No. 64
A while back, we spent a year on a project with a famous person. When the project was finished, and she was interviewed about it, she said she had done the work herself, including the design. It made no sense—she isn't even a designer—but she said it anyway.
Creatives, especially designers and copywriters, are used to being an invisible partner. Companies proudly announce a new identity as though it appeared out of the ether, landing on their desk complete. Rarely do they announce the creative collaboration that culminated in the brand reboot or a new slogan. This has always seemed odd to me. How cool would a company appear if it bragged not only about what it does but also about how they appreciate what others do and work really well to get the best out of everybody they deal with? Instead they go the stealth designer route and don't mention it.
I guess they want you to assume it was done in-house, which I get. But if it was done in-house, even more reason to name names. Mention the creative director as you would the executive who makes the announcement. There's even more reason to acknowledge your own employees. **It creates loyalty **and lets them know they are appreciated. The next time, they'll work even harder and other creatives will be attracted to a company that acknowledges their talent.
I wrote a nice email to "Famous Person" suggesting how great it would be for our company if the next time she talked about the project, she mentioned that we had worked on it together. I never heard back.
If you're a bit shocked at how badly Famous Person behaved, think back on whether you always share credit on your collaborations. Few omissions are as glaring and public as what happened to us. But quieter oversights sting too.
**Sharing credit takes nothing away from your achievement.** If anything, it makes you look like a bigger, better person.* To be fair, more than a few clients who appreciate our work and the effort we put into it include us in their press releases (which of course makes them look smart for hiring well and takes nothing away from them).
While I'm on the subject, we'd also like you to allow us to put our link on the website or a credit at the end of the TV show we just helped you with. This will also help you, since more people will be exposed to you, your company, the project, and your appreciation of good design.
Some companies not only discourage this but also actually forbid it in their contracts. Fortune 500 companies. The ones that are supposed to lead. Again, I guess it's because they don't want anyone to peek behind the curtain and see the elves doing the actual work. The thing is, we're not elves.
This seems like the perfect time for me to thank everyone who has ever worked at Eight and a Half and Number 17.
Don't Use These Words
No. 65
Terms like these are often meant to simplify complex concepts, but they can end up complicating simple notions. Also, I find that sometimes people use this kind of jargon to cover up their own lack of understanding or insecurity. So please don't use these words—they make everything overly formal and overly complicated for no good reason.
Disruption matters
Adaptable infrastructures
Emergent systems
Recontextualization
Shifting paradigms
core competency
datafication
synergize
Leverage best practices
open the kimono
Use These Words
No. 66
Please.
Thank you.
Can we speak privately?
Good job.
Wow!
Thank your team for us.
Drinks?
this is the
beginning of a
beautiful collaboration.
XOXO
ACKNOWLEDGMENTS
I am grateful to Lia Ronnen for believing in this book from the very beginning and for being such a great collaborator and client and friend all these years. A huge thank-you to Lisa DiMona for being my amazing agent who made so much else possible. Thank you to Gary Belsky, Leslie Koren, and Neil Fine of Elland Road Partners for their wisdom, insight, and incredible skill. Thank you to Anne Kreamer for her sage counsel and friendship these many years. Thank you to Seth Godin for all of his encouragement and support. Thank you to my besties, Emma Cookson, Judy Goldberg, and Penny Shane; my sisters, Rayna Dineen and Nomi Joy Parker; and my parents, Helen and Steve Siegler. Thank you to my brilliant colleagues who shared their stories with me: Sean Adams, Keira Alexandra, Eric Baker, Matteo Bologna, Stefan Bucher, Brian Collins, Louise Fili, Stanley Hainsworth, Alexander Isley, Jennifer Morla, Kristen Ren, Christopher Simmons, and Ann Willoughby. And a very special thank-you to my partner at Number 17, Emily Oberman, for living through eighteen years of this with me. Lastly and most importantly, hugs and kisses and gratefulness to my incredible husband, Jeff Scher, and our children, Buster Scher and Oscar Scher, for putting up with me and for their constant support, love, and inspiration.
And a final thank-you to all my current and past clients. Every last one of them.
ABOUT THE AUTHOR
ryan christopher jones
Bonnie Siegler, voted one of the fifty most influential designers working today by _Graphic Design USA_ , founded and runs the award-winning design studio Eight and a Half. She is best known for her design work for _Saturday Night Live_ , the Criterion Collection, HBO, _Late Night with Seth Meyers_ , StoryCorps, Participant Media, and _Newsweek_. Most recently, she was the creative director of the Trump parody memoir _You Can't Spell America Without Me_ by Alec Baldwin and Kurt Andersen and created the main title sequence for _Will & Grace_. She also writes an advice column for designers called Dear Bonnie at AIGA.org. She has taught at the graduate level for many years at the School of Visual Arts and Yale University, has conducted workshops at the Maryland Institute College of Art and Rhode Island School of Design, and lectures and judges design competitions all over the place.
Copyright © 2018 by Bonnie Siegler
All rights reserved. No portion of this book may be reproduced—mechanically, electronically, or by any other means, including photocopying—without written permission of the publisher.
Library of Congress Cataloging-in-Publication Data is available
ISBN 9781579658557
Design by Bonnie Siegler
8point5.com
Published by Artisan
A division of Workman Publishing Co., Inc.
225 Varick Street
New York, NY 10014-4381
artisanbooks.com
Artisan is a registered trademark of Workman Publishing Co., Inc.
Published simultaneously in Canada by Thomas Allen & Son, Limited
## Contents
1. Introduction
2. No. 1: The Thing About Creatives
3. No. 2: Be Honest
4. No. 3: Know Thyself
5. No. 4: Make Me Iconic
6. No. 5: Have Clarity of Purpose
7. No. 6: Who is Your Audience?
8. No. 7: Care About Every Audience
9. No. 8: Decide Who Will Decide
10. No. 9: Do Not Send Out an RFP
11. No. 10: A Brief Case for Writing a Brief
12. No. 11: Tell Me the Problem, Not the Solution
13. No. 12: Get Buy-In
14. No. 13: Experience Isn't Everything
15. No. 14: Those Awkward First Phone Calls
16. No. 15: The Importance of Meeting in Person
17. No. 16: Get a Proposal
18. No. 17: Call References, For God's Sake
19. No. 18: Introduce Everyone at the Meeting
20. No. 19: Don't Schedule Meetings One Right After The Other So that We're Bound to Run Into Each Other in the Lobby
21. No. 20: Be Up Front About Money
22. No. 21: The Value of Creative Work
23. No. 22: Flat Fees, Full Hearts, Can't Lose
24. No. 23: Expect The Unexpected
25. No. 24: Good, Fast, Cheap
26. No. 25: Always Sign on a Dotted Line
27. No. 26: Tell The People Who Didn't Get The Job
28. No. 27: Best Practices Work Best When They are Flexible
29. No. 28: Don't Worry if You Don't Know Exactly What You Want
30. No. 29: What if You Have a Good Idea?
31. No. 30: Show-and-Tell
32. No. 31: Cut Out The Middleman
33. No. 32: White Space is Your Friend
34. No. 33: Let the Creatives Drive The First Presentation
35. No. 34: Be a Fair Judge
36. No. 35: Question Everything
37. No. 36: Be Open to Things You Didn't Imagine
38. No. 37: Don't Say that, Say This
39. No. 38: Beware of Garanimals
40. No. 39: An Important Note About Giving Feedback
41. No. 40: I Notice / I Wonder
42. No. 41: It's Okay to Love Something Right Away
43. No. 42: What to Do When You Kind of Hate What You See
44. No. 43: So You Think You Can Make It Better?
45. No. 44: What if You Don't Know What You Think?
46. No. 45: Give All Feedback at Once
47. No. 46: We Don't Care What Your Spouse Thinks
48. No. 47: On Fear and Insecurity
49. No. 48: Why Focus Groups Suck
50. No. 49: Don't Let Data Drive Your Decisions
51. No. 50: Be Confident, Not Arrogant
52. No. 51: Pick Your Battles
53. No. 52: The Power of Encouragement
54. No. 53: Accept That Everything IS Emotional
55. No. 54: Talk It Out
56. No. 55: Please Don't Piss On the Creative
57. No. 56: Nothing Takes a Second
58. No. 57: Don't Ask to Sit With Us While We Make Changes
59. No. 58: Don't Fall Off The Face of the Earth
60. No. 59: If It's Just Not Working
61. No. 60: When Creatives are Assholes
62. No. 61: Don't Be Rude to My Staff (Or Yours)
63. No. 62: Serve Lunch During Lunchtime Meetings
64. No. 63: About Pro Bono Work
65. No. 64: Give Credit Where It's Due
66. No. 65: Don't Use These Words
67. No.66: Use These Words
68. Acknowledgment
69. About the Author
70. Copyright
## Landmarks
1. Cover
2. Cover
3. Table of Contents
| {
"redpajama_set_name": "RedPajamaBook"
} | 6,711 |
"""This code example updates a creative set by adding a companion creative.
To determine which creative sets exist, run get_all_creative_sets.py.
The LoadFromStorage method is pulling credentials and properties from a
"googleads.yaml" file. By default, it looks for this file in your home
directory. For more information, see the "Caching authentication information"
section of our README.
"""
# Import appropriate modules from the client library.
from googleads import dfp
# Set the ID of the creative set to update.
CREATIVE_SET_ID = 'INSERT_CREATIVE_SET_ID_HERE'
COMPANION_CREATIVE_ID = 'INSERT_COMPANION_CREATIVE_ID_HERE'
def main(client, creative_set_id, companion_creative_id):
# Initialize appropriate service.
creative_set_service = client.GetService('CreativeSetService',
version='v201508')
# Create statement to select a single creative set by ID.
values = [{
'key': 'creativeSetId',
'value': {
'xsi_type': 'NumberValue',
'value': creative_set_id
}
}]
query = 'WHERE id = :creativeSetId'
statement = dfp.FilterStatement(query, values)
# Get creative set.
response = creative_set_service.getCreativeSetsByStatement(
statement.ToStatement())
if 'results' in response:
updated_created_sets = []
for creative_set in response['results']:
creative_set['companionCreativeIds'].append(companion_creative_id)
updated_created_sets.append(creative_set)
# Update the creative sets on the server.
creative_sets = creative_set_service.updateCreativeSet(updated_created_sets)
# Display results.
for creative_set in creative_sets:
print (('Creative set with ID \'%s\', master creative ID \'%s\', and '
'companion creative IDs {%s} was updated.')
% (creative_set['id'], creative_set['masterCreativeId'],
','.join(creative_set['companionCreativeIds'])))
else:
print 'No creative sets found to update.'
if __name__ == '__main__':
# Initialize client object.
dfp_client = dfp.DfpClient.LoadFromStorage()
main(dfp_client, CREATIVE_SET_ID, COMPANION_CREATIVE_ID)
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,595 |
How to choose the best web hosting in sri lanka ?
Price Considering price does not mean that you should choose any web-hosting provider that does offer CHEAPEST hosting solutions, they can affect your website. Thefore check following details from your web hosting provider. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,076 |
\section{Introduction}
\setlength{\parskip}{\smallskipamount}
Understanding the relation that connects trade imbalances and price changes is arguably one of the main goals of market microstructure theory. By leveraging a \emph{data deluge} that increased both quantity and quality of financial data over the past 20 years, many empirical results have shed light on market impact (see e.g.~\cite{Bouchaud2018TradesPrices,Almgren2005DirectImpact,Torre1997BARRAHandbook}). Further, it lead to an adjustment of the theoretical framework underpinning the foundations of market microstructure~\cite{Kyle1985ContinuousTrading,Glosten1985BidTraders}, and it drove a more data-driven community to build novel settings in which to accommodate these findings (see e.g. ~\cite{Bouchaud2018TradesPrices,Taranto2018LinearModels}).
On the other hand, only sparse attention has been given in the literature to the related problem of establishing a relation between order flows and price changes in a multi-instrument setting (\emph{cross-impact}). Compared to its univariate counterpart, cross-impact is much harder to characterize empirically, due to the larger number of degrees of freedom involved, and the consequently smaller signal-to-noise ratio~\cite{Hasbrouck2001CommonLiquidity,Pasquariello2015StrategicMarket,Schneider2017Cross-impactNo-dynamic-arbitrage,Wang2015PriceResults}. The challenge of cross-impact modeling also raises from genuinely new effects that only appear in the multivariate setting, such as the possible presence of cross-sectional arbitrages. Accounting for these problems requires building some dedicated theoretical infrastructure~\cite{Alfonsi2016MultivariateFunctions,Mastromatteo2017TradingExecution}, and it led us to investigate in~\cite{Tomas2020HowResults} the principles by which a cross-impact model should abide in order to be free from basic inconsistencies and arbitrages.
This works aims precisely at illustrating the consequences of such a principled approach in a limit case that exposes both the flaws of inconsistently formulated models and the benefits of having strong theoretical guarantees on the behavior of a cross-impact model. In fact, we focus our study on cross-impact in a universe of instruments that comprises potentially illiquid derivatives. This is the prototypical case in which a univariate approach to modeling impact and liquidity falls short, due to two main reasons respectively related to \emph{prices} and \emph{liquidity}. Indeed, in an efficient market the \emph{prices} of derivatives should be locked by non-arbitrage, and hence they are not expected to respond to trades independently of their underlying. Regarding \emph{liquidity}, it is intuitive that in presence of many strongly correlated and individually illiquid financial instruments (e.g. options), it is necessary to aggregate the liquidity of multiple products into common liquidity pools in order to have a satisfactory description of the price response, which would otherwise appear anomalously strong. Both points indicate that in order to have a viable model to describe impact on derivative markets in presence of fragmented liquidity it is unavoidable to take a multivariate perspective on the system, namely one that is able to single out the relevant liquidity factors.
Our approach allows to map this problem onto a dimensionality reduction one, showing that one can replace a high dimensional space of instruments (say, option surfaces) with a lower dimensional representation of underlying factors (spot, implied volatility), which are the only degrees of freedom allowed to respond to order flow imbalances.
It is worth emphasizing at this point that, although other models for cross-impact of derivatives (in particular for options) have already appeared in the literature, our focus is different in several respects. A first stream of works aims at the \emph{characterization} of non-arbitrage properties in cross-impact models \cite{Alfonsi2016MultivariateFunctions}, aiming at defining necessary conditions that should be satisfied in the general case. Here, we study a specific instance of such class of models, which leads to a very rich phenomenology that cannot be fully appreciated in a completely generic setting. A second series of works focuses on the \emph{implications} that some specific cross-impact models have in the context of option replication and hedging~\cite{Loeper2018OptionEquations,Bouchard2017HedgingConstraint}, due to the fact that in presence of cross-impact non-linear effects arise, and potentially dangerous feedback loops emerge. Finally, in \cite{Toth2016TheMarkets} the emphasis is given to the \emph{empirical determination} of cross-impact; one of its findings of interest to us is the identification of impact along a non-trivial underlying factor (level of implied volatility) that does not mechanically correspond to any individual option, and yet emerges from the aggregation of the whole volatility surface.
An important contribution that pushes this approach even further is \cite{Said2019HowImpact}, which indicates that other factors (skew of the volatility surface) are also necessary to accurately describe cross-impact on options.
Even though the last two references strongly relate to our work, there are several differences that characterize our approach. First, we try to infer from data the rules to be used to aggregate liquidities, rather than postulating them. Second, our approach can easily accommodate multi-factor cross-impact models, whereas in such references only one factor at the time was considered.
Third and last, the theoretical foundations our our approach are strongly grounded in the classical market microstructure literature~\cite{Caballe1994ImperfectNeutrality,Pasquariello2015StrategicMarket}, and in particular in~\cite{delMolino2018TheDifferent}, which provides a solid micro-foundation of our model (see also~\cite{Tomas2020HowResults}).
The paper is organized as follows. In \cref{sec:nota} we introduce the notations used. \cref{sec:setup} presents our modeling framework. \cref{sec:examples} provides illustrative examples of its applications. \cref{sec:empirical} presents the empirical results of cross-impact on options. In \cref{sec:conclusion} we conclude on the contributions of the paper, open questions, and directions for future work.
\section{Notations}
\label{sec:nota}
Throughout the paper, we write scalars in roman lower cases, vectors in bold lower cases and matrices in roman upper cases. The set of $n$ by $n$ real-valued square matrices is denoted by $\mat{n}(\mathbb{R})$, the set of orthogonal matrices by $\orth{n}$, the set of real non-singular $n$ by $n$ matrices by $\gln{n}(\reals{})$, the set of real $n$ by $n$ symmetric positive semi-definite matrices by $\spd{n}$, and the set of real $n$ by $n$ symmetric positive definite matrices by $\pd{n}$. Further, given a matrix $A$ in $\mat{n}(\mathbb{R})$, $A^\top$ denotes its transpose. Given $A$ in $\spd{n}$, we write $A^{1/2}$ for a matrix such that $A^{1/2} (A^{1/2})^\top = A$ and $\sqrt{A}$ for the matrix square root, the unique positive semi-definite symmetric matrix such that $(\sqrt{A})^2 = A$. We write $\ker{(M})$ for the null space of a matrix $M \in \mat{n}$, $\Pi_V$ for the projector on a linear subspace of $V \in \mathbb{R}^n$ and $\bar \Pi_V = \mathbb{I} - \Pi_V$ for the orthogonal projector. Finally, given a vector $\boldm{v} \in \reals{n}$, we write $\boldm{v} = (v_1, \dots, v_n)$ and $\diag{\boldm{v}}$ for the diagonal matrix with diagonal components the components of $\boldm{v}$.
All stochastic processes in the text are defined on a probability space $(\Omega, \mathcal{F}, (\mathcal{F}_t)_{t \in \reals{}}, \mathbb{P})$ and will be adapted to the filtration $(\mathcal{F}_t)_{t \in \reals{}}$ unless stated otherwise. Standard Brownian motions are defined with respect to the probability measure~$\mathbb{P}$. All stochastic differential equations introduced will be assumed to have a unique strong solution and correspondingly the functions appearing in these equations will be assumed to be sufficiently regular for this to be true. We denote by $\mathbb{E}$ the expectation with respect to the probability measure $\mathbb{P}$ and $\mathbb{E}_t[\dots]$ will denote the conditional expectation $\mathbb{E}[\dots | \mathcal{F}_t]$.
\section{The model}
\label{sec:setup}
We consider a universe comprising two classes of financial instruments, that we will refer to as \emph{underlying} and \emph{derivatives}. With some abuse of language, the notion of \emph{underlying} will apply to a set of $N$ stochastic processes, that might describe indistinctly a set of tradable financial instruments or an ensemble of stochastic factors. The prices of these $N$ instruments will be denoted ${\bm p}_t =(p^1_t, \dots, p^N_t)$. We define as \emph{derivatives} a set of $M$ instruments, whose prices ${\bm P}({\bm p}_t, t) = (P^1({\bm p}_t, t), \dots, P^M({\bm p}_t, t))$ are deterministic functions of the underlying price process ${\bm p}_t$.
We assume that impact is linear in the traded order flows and we denote by ${\bm q}_t = (q^1_t, \dots, q^N_t)$ the stochastic process corresponding to the net traded order flows on the underlying and by ${\bm Q}_t = (Q^1_t, \dots, Q^M_t)$ the stochastic process corresponding to the net traded order flows on derivatives. Such flows are not associated to any specific agent, and rather denote aggregate market order flow. Since only the non-predictable component of order flows contributes to impact, up to replacing ${\bm q}_t$ by ${\bm q}_t - \mathbb{E}_{t-}[{\bm q}_t]$ and ${\bm Q}_t$ by ${\bm Q}_t - \mathbb{E}_{t-}[{\bm Q}_t]$ in the following, we assume that $\mathbb{E}_{t-}[{\bm q}_t] = 0, \mathbb{E}_{t-}[{\bm Q}_t] = 0$.
\cref{sec:price_dynamics} introduces the underlying and derivative price dynamics with cross-impact. \cref{sec:impact_model} presents the proposed cross-impact model and \cref{sec:properties_impact} discusses the properties of this cross-impact model.
\subsection{Price dynamics}
\label{sec:price_dynamics}
We assume that the dynamics of the underlying are
\begin{align}
\label{eq:underlying_dynamics}
\textrm{d} {\bm p}_t =& {\bm \mu}_p({\bm p}_t, t) \textrm{d} t + \mathcal{G}_p({\bm p}_t, t) \textrm{d} {\bm w}_t + \Lambda_{pq}({\bm p}_t, t) \textrm{d} {\bm q}_t + \Lambda_{pQ}({\bm p}_t, t) \textrm{d} {\bm Q}_t \, ,
\end{align}
where ${\bm w}$ is a standard $N$-dimensional Brownian motion, ${\bm \mu}_p \colon \reals{N} \times \reals{} \to \reals{N}$ is the drift, $\mathcal{G}_p \colon \reals{N} \times \reals{} \to \gln{N}(\reals{})$ is the diffusion matrix, $\Lambda_{pq} \colon \reals{N} \times \reals{} \to \mat{N,N}(\reals{})$ is the underlying-underlying cross-impact matrix and $\Lambda_{pQ} \colon \reals{N} \times \reals{} \to \mat{N,M}(\reals{})$ is the underlying-derivative cross-impact matrix. The underlying dynamics of \cref{eq:underlying_dynamics} could be enriched by jump processes, but for the sake of simplicity we chose a simple continuous framework which covers several well-known models of derivatives pricing.
Since derivative prices are deterministic functions of the underlying, without loss of generality, the derivative dynamics can be written as
\begin{align}
\label{eq:derivative_dynamics}
\textrm{d} {\bm P}_t =& {\bm \mu}_P({\bm p}_t, t) \textrm{d} t + \mathcal{G}_P({\bm p}_t, t) \textrm{d} {\bm w}_t + \Lambda_{Pq}({\bm p}_t, t) \textrm{d} {\bm q}_t + \Lambda_{PQ}({\bm p}_t, t) \textrm{d} {\bm Q}_t \, ,
\end{align}
where ${\bm \mu}_P \colon \reals{N} \times \reals{} \to \reals{M}$ is the derivative drift, $\mathcal{G}_P \colon \reals{N} \times \reals{} \to \mat{M,N}(\reals{})$ is the derivative diffusion matrix, $\Lambda_{Pq} \colon \reals{N} \times \reals{} \to \mat{M,N}(\reals{})$ is the derivative-underlying cross-impact matrix and $\Lambda_{PQ} \colon \reals{N} \times \reals{} \to \mat{N,M}(\reals{})$ is the derivative-derivative cross-impact matrix.
For convenience cross-impact matrices can be compactly rearranged into a single matrix, $\Lambda$, which we refer to as the cross-impact matrix since it describes the cross-impact of the complete system
\begin{equation}
\label{eq:grouped_impact}
\Lambda({\bm p}_t, t) := \begin{pmatrix} \Lambda_{pq} & \Lambda_{pQ} \\ \Lambda_{Pq} & \Lambda_{PQ} \end{pmatrix} ({\bm p}_t, t) \, .
\end{equation}
Similarly drift and diffusion terms can be grouped as
\begin{equation}
\label{eq:grouped_drift_diff}
{\bm \mu}({\bm p}_t, t) = ({\bm \mu}_p({\bm p}_t, t), {\bm \mu}_P({\bm p}_t, t))
\quad \quad \quad\quad
\mathcal{G}({\bm p}_t, t) = (\mathcal{G}_p({\bm p}_t, t), \mathcal{G}_P({\bm p}_t, t)) \, .
\end{equation}
Obviously, not all the terms appearing in \cref{eq:grouped_impact,eq:grouped_drift_diff} are independent, given that the function ${\bm P}({\bm p}_t, t)$ fixes the derivative prices as a function of the underlying.
In Sec.~\ref{sec:price_efficiency} we will discuss the conditions required to prevent arbitrage.
\\ \\
We also draw the reader's attention to the fact that one may directly obtain an equation for the derivatives' prices by applying Ito's formula and using the underlying dynamics of \cref{eq:underlying_dynamics}. This would yield expressions for $\Lambda_{Pq}$ and $\Lambda_{PQ}$ as a function of $\Lambda_{pq}$ and $\Lambda_{pQ}$. However, not all cross-impact models give expressions of $\Lambda_{Pq}$ and $\Lambda_{PQ}$ consistent with Ito's formula and it is thus more convenient to choose a cross-impact model which, by construction, yields this result instead of imposing it \textit{a priori}. Our choice of cross-impact model is discussed in the next section.
\subsection{Impact model}
\label{sec:impact_model}
The impact model we propose involves two parameters, the return covariance matrix and the order flow covariance matrix. The underlying-underlying return covariance matrix $\Sigma_{pp} \colon \reals{N} \times \reals{} \to \spd{N}$ is defined as
\begin{equation}
\label{eq:covariance_udr}
\Sigma_{pp}({\bm p}_t, t) \textrm{d} t :=
\mathbb{E}_t[\textrm{d} {\bm p}_t \textrm{d} {\bm p}_t^\top] - \mathbb{E}_t[\textrm{d} {\bm p}_t]\mathbb{E}_t[\textrm{d} {\bm p}_t^\top] \, ,
\end{equation}
and we similarly denote $\Sigma_{pP}, \Sigma_{Pp}=\Sigma_{pP}^\top, \Sigma_{PP}$ for the underlying-derivative, derivative-underlying and derivative-derivative return covariance matrices. Naturally, since derivative prices are deterministic function of the underlying, these matrices are all related to $\Sigma_{pp}$. We denote by $\Omega_{qq} \colon \reals{N} \times \reals{} \to \spd{N}$ the underlying-underlying order flow covariance matrix
\begin{equation}
\label{eq:covariance_qq}
\Omega_{qq}({\bm p}_t, t) \textrm{d} t :=
\mathbb{E}_t[\textrm{d} {\bm q}_t \textrm{d} {\bm q}_t^\top] - \mathbb{E}_t[\textrm{d} {\bm q}_t]\mathbb{E}_t[\textrm{d} {\bm q}_t^\top] \, ,
\end{equation}
and we denote $\Omega_{qQ}$, $\Omega_{Qq}=\Omega_{qQ}^\top$ and $\Omega_{QQ}$ for the underlying-derivative, derivative-underlying and derivative-derivative order flow covariances. Contrary to return covariance matrices, there are no constraints betweeen these order flow covariance matrices and $\Omega_{qq}$. The covariance structure of returns and flows for the whole system can be arranged compactly as
\begin{equation*}
\Sigma({\bm p}_t, t) = \begin{pmatrix} \Sigma_{pp} & \Sigma_{pP} \\ \Sigma_{pP}^\top & \Sigma_{PP} \end{pmatrix} ({\bm p}_t, t)
\hspace{1cm}
\Omega({\bm p}_t, t) = \begin{pmatrix} \Omega_{qq} & \Omega_{qQ} \\ \Omega_{qQ}^\top & \Omega_{QQ} \end{pmatrix} ({\bm p}_t, t) \, .
\end{equation*}
The impact model that we propose, first derived in~\cite{Caballe1994ImperfectNeutrality}, has been analyzed in this context in~\cite{delMolino2018TheDifferent,Tomas2020HowResults}, where it was referred as the \emph{Kyle cross-impact} model. The model prescribes using a $\Lambda$ of the form
\begin{equation}
\label{eq:kyle_model}
\Lambda = \sqrt{Y} \Lambda_{\textnormal{kyle}}(\Sigma, \Omega) := \sqrt{Y} (\Omega^{-1/2})^\top \sqrt{(\Omega^{1/2})^\top \Sigma \Omega^{1/2}} \Omega^{-1/2} \, ,
\end{equation}
where we have omitted the dependence on $({\bm p}_t, t)$ for convenience, and where we have introduced $\Lambda_{\textnormal{kyle}} \colon \spd{N+M} \times \pd{N+M} \to \mat{N+M,N+M}(\reals{})$. We introduced $0 < Y < 1$ whose interpretation will appear clearly in the next section. The next section emphasizes the properties that motivate the usage of the Kyle cross-impact model.
\subsection{Properties}
\label{sec:properties_impact}
The Kyle cross-impact model (i) ensures derivatives are priced consistently with the underlying dynamics, (ii) reduces the dynamics of the system to a classic SDE when flow degrees of freedom are integrated inside volatility terms, (iii) allows for dimensionality reduction, (iv) properly aggregates liquid and illiquid instruments and (v) does not need to know which instruments belong to the set of underlyings and which ones are derivatives. We show these properties below and discuss their implications.
\subsubsection{Price efficiency}
\label{sec:price_efficiency}
In order for the model to be self-consistent (i.e., for the derivative to be efficiently priced at all times), one should make sure that the dynamics that we have postulated in \cref{eq:derivative_dynamics} are consistent with the one obtained by applying Ito's formula to the dynamics of the underlying via the relation ${\bm P}({\bm p}_t, t)$ . This requirement prescribes that the following conditions should hold.
\begin{description}
\item[Diffusion] In order for the diffusion dynamics to be consistent, one should have
\begin{equation}
\label{eq:necess_cond_diff}
\mathcal{G}_P({\bm p}_t, t) = \Xi({\bm p}_t, t) \mathcal{G}_p({\bm p}_t, t) \, ,
\end{equation}
where $\Xi \colon \reals{N} \times \reals{} \to \mat{M,N}(\reals{})$ is a \emph{sensitivity matrix} defined as
$$
\Xi_{ij}({\bm p}_t, t) = \dfrac{\partial P_i}{\partial p_j}({\bm p}_t, t) \, .
$$
\item[Impact] By the same token, the cross-impact matrix should satisfy the condition
\begin{equation}
\label{eq:necessary_cond_impact}
\Lambda({\bm p}_t, t) = \begin{pmatrix} \Lambda_{pq} & \Lambda_{pQ} \\ \Xi \Lambda_{pq} & \Xi \Lambda_{pQ} \end{pmatrix} ({\bm p}_t, t) \, ,
\end{equation}
indicating that the price response of the derivative should be completely fixed by the one on the underlying.
\item[Drift] Finally, the drift term should also match the one obtained via Ito's formula, so that
\begin{equation}
\label{eq:necess_cond_drift}
{\bm \mu}_P({\bm p}_t, t) = \bm{\Theta}({\bm p}_t, t) + \Xi({\bm p}_t, t) {\bm \mu}_p({\bm p}_t, t) + \frac{1}{2} \sum_{jk} \bm{\chi}_{jk}({\bm p}_t, t) (\Sigma_{pp}({\bm p}_t, t))_{jk} \, ,
\end{equation}
where
\begin{align*}
\Theta_i({\bm p}_t, t) &= \dfrac{\partial P_i}{\partial t}({\bm p}_t, t) \\
\chi_{i,jk} ({\bm p}_t, t) &= \dfrac{\partial P_i}{\partial p_j \partial p_k}({\bm p}_t, t) \, ,
\end{align*}
are sensitivities, of nature similar to $\Xi$ defined above.
\end{description}
We will assume in the following that the conditions for drift and diffusion hold by construction, taking \cref{eq:necess_cond_diff,eq:necess_cond_drift} as definitions of respectively $\mathcal{G}_P$ and ${\bm \mu}_P$.
On the other hand, since \cref{eq:necessary_cond_impact} is not guaranteed \emph{a priori} under our choice of the cross-impact model, we will be required to prove that our model satisfies \cref{eq:necessary_cond_impact} above, and thus that our construction is consistent.
In order to do so, we need to discuss a crucial property of the Kyle model, that is referred in ~\cite{Tomas2020HowResults} as \emph{strong fragmentation invariance}. With strong fragmenation invariance, we denote the fact that for any $\emptyset \subset V \subseteq \ker(\Sigma)$ we have
\begin{align}
\label{eq:weak_frag}
\Pi_V \Lambda_{\textnormal{kyle}}(\Sigma, \Omega) &= 0 \\
\label{eq:semi_frag}
\Lambda_{\textnormal{kyle}}(\Sigma, \Omega) \Pi_V &= 0 \\
\label{eq:strong_frag}
\Lambda_{\textnormal{kyle}}(\Sigma, \bar \Pi_{V} \Omega \bar \Pi_{V}) &= \Lambda_{\textnormal{kyle}}(\Sigma, \Omega) \, .
\end{align}
\cref{eq:weak_frag} shows that linear combinations of instruments with constant price (zero volatility) are not impacted by the order flow. In our setting, this guarantees that derivatives are always priced efficiently even in the presence of order flow pressure. \cref{eq:semi_frag} maintains that order flow pressure on non-fluctuating modes should not be able to influence the price of any other combination of products. This prevents pushing the price of fluctuating instruments by trading zero-volatility (free) linear combination of instruments. Finally, \cref{eq:strong_frag} shows that the way non-fluctuating modes are traded has no influence the price of any instrument.
In our context, strong fragmentation invariance and symmetry imply that
\begin{equation}
\label{eq:kyle_fragm}
\Lambda({\bm p}_t, t) = \begin{pmatrix} \Lambda_{pq} & \Lambda_{pq} \Xi^\top \\ \Xi \Lambda_{pq} & \Xi \Lambda_{pq} \Xi^\top \end{pmatrix} ({\bm p}_t, t) \, .
\end{equation}
Thus the Kyle model satisfies the condition of \cref{eq:necessary_cond_impact} above, thus guaranteeing that (along with the conditions of \cref{eq:necess_cond_diff,eq:necess_cond_drift} which we impose and are independent of the impact model) the derivative is efficiently priced.
At this moment, it is worth emphasizing a central point of our approach: we are postulating that derivatives are efficiently priced at all times despite the presence of finite liquidity. This hides the implicit assumption that some market actors are able to arbitrage away the spread between underlying and derivatives very quickly, and that those market directions are effectively frictionless for such actors. Inefficiencies can be implemented in this framework by relaxing the assumption that ${\bm P}_t = {\bm P}({\bm p}_t, t)$, rather assuming that derivative prices mean-revert with a finite velocity to their theoretical value. On long enough time scales, we expect the empirical estimate for $\Sigma$ to nevertheless be close to the value given by no-arbitrage so that these considerations can be ignored. For pedagogical clarity, hereafter we will stick to the idealized case in which derivatives are efficiently priced.
\subsubsection{Consistency of frictionless and impacted dynamics}
\label{sec:covariance_consistency}
We now want to show that the dynamics with impact are consistent with the \emph{frictionless} dynamics that would be observed when disregarding the flows degrees of freedom. The term frictionless in this context does not indicate absence of impact, but rather identifies the effective system in which the degrees of freedom related to flows (${\bm q}_t$ and ${\bm Q}_t$) are integrated inside volatility contributions.
To prove this, we first remark that the Kyle model is the only linear, symmetric positive definite impact model that is consistent with the covariance structure of the system (see \cite{Tomas2020HowResults}), namely the fact that
\begin{equation}
\label{eq:covariance_consistency}
Y \Sigma({\bm p}_t, t) = \Lambda({\bm p}_t, t) \Omega({\bm p}_t, t) \Lambda^\top({\bm p}_t, t) \, .
\end{equation}
This property is not surprising, given ubiquity of the \emph{inconspicous equilibrium} property in theoretical frameworks in which market efficiency is achieved by rational agents that attempt to forecast future returns~\cite{Caballe1994ImperfectNeutrality,delMolino2018TheDifferent}. In these frameworks, predictions are optimal when \cref{eq:covariance_consistency} is verified. The prefactor $Y$ expresses that a fraction $Y$ of the total covariance is due to trading activity while the remainder comes from shocks unrelated to the order flow.
Now, let us relate a frictionless dynamics to the one that we have postulated in our model thanks to the covariance consistency condition (\cref{eq:covariance_consistency}).
To do so, consider the dynamics without impact
\begin{align}
\label{eq:underlying_dynamics_frictionless}
\textrm{d} \td{{\bm p}}_t =& \td{{\bm \mu}}_p(\td{{\bm p}}_t, t) \textrm{d} t + \td{\mathcal{G}}_p(\td{{\bm p}}_t, t) \textrm{d} \td{{\bm w}}_t \, \\
\label{eq:derivative_dynamics_frictionless}
\textrm{d} \td{{\bm P}}_t =& \td{{\bm \mu}}_P(\td{{\bm p}}_t, t) \textrm{d} t + \td{\mathcal{G}}_P(\td{{\bm p}}_t, t) \textrm{d} \td{{\bm w}}_t \,
\end{align}
where $\td{{\bm w}}$ is a standard Brownian motion, $\td{{\bm \mu}}_p \colon \reals{N} \times \reals{} \to \reals{N}$ is the frictionless underlying drift, $\td{{\bm \mu}}_P \colon \reals{N} \times \reals{} \to \reals{M}$ is the frictionless derivative drift, $\td{\mathcal{G}}_p \colon \reals{N} \times \reals{} \to \gln{N}(\reals{})$ and $\td{\mathcal{G}}_P \colon \reals{N} \times \reals{} \to \mat{M,N}(\reals{})$ are the frictionless diffusion matrices.
Then it is simple to verify that thanks to \cref{eq:covariance_consistency} one can recover the equivalence between frictionless and impacted dynamics if $\mathcal{G} = \sqrt{1 - Y} \td{\mathcal{G}}$ and ${\bm \mu} = \td{{\bm \mu}}$. In intuitive terms, our price dynamics reduces to the vanilla stochastic evolution of derivatives and underlying for any observer that does not possess information about the order flows. This stems from the Gaussian nature of both order flow processes and underlying increments, along with the covariance consistency condition (\cref{eq:covariance_consistency}) that is implicitly contained in the definition of the Kyle model.
\subsubsection{Dimensionality reduction}
\label{sec:low_dimensional_ximpact}
The strong fragmentation property introduced in Sec.~\ref{sec:price_efficiency} has another important implication in our setting: by imposing the structure of the impact matrix to the form of \cref{eq:kyle_fragm}, it explicitly shows that $\textrm{rank}(\Lambda) = \textrm{rank}(\Lambda_{pq})=N$. This has the consequence of making explicit that no more than $N$ distinct liquidity pools are necessary in order to compute impact. In particular, we will show that it is enough to estimate $\bar \Pi_{V} \Omega \bar \Pi_{V}$ instead of the (potential) rank $N+M$ matrix $\Omega$ in order to fully determine the cross-impact matrix, where with $V$ we denote the subspace spanning the direction ${\bm P}_t - {\bm P}({\bm p}_t, t)$, which obviously belongs to $\ker(\Sigma)$ if we assume that derivatives are consistently priced.
In intuitive terms, it is only the liquidity in the direction of the fluctuating degrees of freedom that contributes to the overall liquidity pool, whereas any trading in the direction of the mispricing has no effect on the system.
To show this, remark that \cref{eq:kyle_fragm} allows us to express the full cross-impact matrix $\Lambda$ once an expression for the lower-rank $\Lambda_{pq}$ object is available. We will thus derive the expression of $\Lambda_{pq}$. Writing $\hat{{\bm p}}$ and $\hat{{\bm P}}$ for the underlying and derivative impact component of the price, one has $\textrm{d} \hat{{\bm P}}_t = \Xi \textrm{d} \hat{{\bm p}}_t$ and
\begin{align*}
\begin{pmatrix}
\textrm{d} \hat{{\bm p}}_t \\
\textrm{d} \hat{{\bm P}}_t
\end{pmatrix}
=
\begin{pmatrix}
I & 0 \\
\Xi & I
\end{pmatrix} \begin{pmatrix}
\textrm{d} \hat{{\bm p}}_t \\
0
\end{pmatrix} &= \begin{pmatrix}
I & 0 \\
\Xi & I
\end{pmatrix} \begin{pmatrix}
\Lambda_{pq} & 0 \\
0 & 0
\end{pmatrix} \begin{pmatrix}
I & \Xi^\top \\
0 & I
\end{pmatrix} \begin{pmatrix}
\textrm{d} {\bm q}_t \\
\textrm{d} {\bm Q}_t
\end{pmatrix} \, ,
\end{align*}
so that the impacted underlying price is
\begin{align*}
\textrm{d} \hat{{\bm p}}_t =& \Lambda_{pq} (\textrm{d} {\bm q}_t + \Xi^\top \textrm{d} {\bm Q}_t) \, .
\end{align*}
Since $\Lambda$ is symmetric and positive-definite, one can easily show that $\Lambda_{pq}$ is symmetric and positive-definite. Furthermore, $\Lambda_{pq}$ is covariance-consistent and
$$
Y \Sigma_{pp} = \Lambda_{pq} \Omega_{\Xi} \Lambda_{pq}^\top \, ,
$$
where we have introduced the aggregated order flow covariance matrix
$$
\Omega_{\Xi} := \mathbb{E}_t[(\textrm{d} {\bm q}_t + \Xi^\top \textrm{d} {\bm Q}_t) (\textrm{d} {\bm q}_t + \Xi^\top \textrm{d} {\bm Q}_t)^\top] = \Omega_{qq} + \Xi^\top \Omega_{QQ} \Xi + \Xi^\top \Omega_{Qq} + \Omega_{qQ} \Xi \, .
$$
Therefore, since these properties imply that $\Lambda_{pq}$ is the Kyle cross-impact model with return covariance $\Sigma_{pp}$ and order flow covariance $\Omega_{\Xi}$ one has
$$
\Lambda_{pq} = \sqrt{Y} \Lambda_{\textnormal{kyle}}(\Sigma_{pp}, \Omega_{\Xi}) = \sqrt{Y} (\Omega_{\Xi}^{-1/2})^\top \sqrt{(\Omega_{\Xi}^{1/2})^\top \Sigma_{pp} \Omega_{\Xi}^{1/2}} \Omega_{\Xi}^{-1/2} \, .
$$
This property is very useful in practice since it gives a recipe for computing $\Lambda_{pq}$. It also tells us that the aggregated order flow covariance matrix combines direct trading of underlying and indirect trading through derivatives exposures to the underlying. In particular, even if an underlying is not tradeable,
as long as derivatives which are exposed to that factor are tradeable its aggregated liquidity will be non-zero.
\subsubsection{Cross-stability and spurious liquidity effects}
The Kyle-model is also \emph{cross-stable} (see~\cite{Tomas2020HowResults}), meaning that trading an illiquid combination of products cannot move liquid products by a disproportionate amount. To make this property explicit, let us introduce a subset of illiquid instruments $W$, on which we assume to measure a modified covariance matrix
\begin{align*}
\Omega_{\epsilon} &:= (\bar \Pi_W + \epsilon \Pi_W) \Omega (\bar \Pi_W + \epsilon \Pi_W) \, ,
\end{align*}
where $\Pi_W = \mathbb{I} - \bar \Pi_W$ is a projector on the space $W$. The covariance matrix above is the one we would have observed if liquidities of instruments belonging to $W$ were multiplied by $\epsilon$.
Then, for any $(\Sigma, \Omega) \in (\spd{n} \times \pd{n})$, the Kyle model satisfies
\begin{align}
\bar{\Pi}_W \Lambda_{\textnormal{kyle}}(\Sigma, \Omega_{\epsilon}) \Pi_W \underset{\epsilon \to 0}{=}& O(1) \label{eq:cross_stab_liq_ill}\\
\bar{\Pi}_W \Lambda_{\textnormal{kyle}}\left(\Sigma, \Omega_{\epsilon}\right) \bar \Pi_W \underset{\epsilon \to 0}{\to}& \bar{\Pi}_W \Lambda_{\textnormal{kyle}}\left(\bar \Pi_W \Sigma \bar \Pi_W, \bar \Pi_W \Omega \bar \Pi_W \right) \bar \Pi_W \, . \label{eq:cross_stab_liq_liq}
\end{align}
\cref{eq:cross_stab_liq_ill} indicates that volumes traded on illiquid products cannot move by a disproportionate (diverging in $\epsilon$) the price of liquid instruments, whereas \cref{eq:cross_stab_liq_liq} indicates that the impact of the flows of liquid instruments is not affected by the presence of other, illiquid, instruments.
These properties allow one to include non-tradeable instruments (such as implied volatilities) within the definition of the underlying because even though the quantities $\Omega^{-1/2}$ appearing in \cref{eq:kyle_model} are divergent whenever an illiquid product appears, this property implies that the divergence is restricted to the subspace of zero-liquidity products. This is convenient also for cases in which liquidity is fragmented in a large set of products that might display weak liquidity (e.g., out-of-the money options) as this property guarantees that such behavior won't induce spurious features on the overall liquidity pool of the system.
\subsubsection{Universality}
Throughout our approach, we have split instruments between underlyings and derivatives. However, a compelling property of the chosen cross-impact model is that \cref{eq:kyle_model} does not need to know which is which in the universe of instruments. This may be convenient when dealing with a large number of instruments where it would be time-consuming to make explicit which instruments are derivatives and the associated sensitivity matrix $\Xi$.
\section{Examples}
\label{sec:examples}
To illustrate the flexibility of our setup and the usefulness in practice of the properties of the Kyle cross-impact model, we discuss examples in increasing complexity below.
\subsection{Futures}
For our first example, we consider a universe of $N=M=1$ instruments, consisting in a spot with price $p_t$ and a futures contract expiring at a later time $T$, quoting a price $P(p_t, t)$.
By assuming a constant, continuously compounded, deterministic interest rate $r$ one has
$$
P(p_t, t) = e^{r(T-t)} p_t \, .
$$
In this case $\Xi(p_t, t) = \partial_p P(p_t, t) = e^{r(T-t)}$ and \cref{eq:kyle_fragm} yields
$$
\Lambda(p_t, t) = \sqrt{Y} p_t \frac{\sigma(p_t, t)}{\omega(p_t, t)} \begin{pmatrix} 1 & \ e^{r(T-t)} \\ e^{r(T-t)} & e^{2r(T-t)} \end{pmatrix},
$$
where
\begin{align*}
\sigma^2(p_t, t) &:= \frac{\mathbb{E}_t[p_t^2] - \mathbb{E}_t[p_t]^2}{p_t^2} \\
\omega^2(p_t, t) &:= (1, e^{r(T-t)})^\top \Omega(p_t, t) (1, e^{r(T-t)}) \, .
\end{align*}
The meaning of this formula is rather simple: when dealing with a spot and a future market, there is a single relevant liquidity pool. Such liquidity pool should mix the flow traded on the future and the one traded on the spot. Volumes traded on the futures market should be properly adjusted for the interest rate.
\subsection{Black-Scholes model}
\label{sec:black_scholes_model}
We now consider a system with a single underlying $N=1$ and $M$ derivatives. The underlying is a spot with price $p_t$, whereas the derivatives are a set of European call or put options labeled by $i=1, \dots, M$, differing for either their strike or their maturity. We assume the price $p_t$ follows the usual log-normal dynamics, with risk-free rate $r$ and implied volatility $\sigma$
$$
\textrm{d} p_t = r p_t \textrm{d} t + \sigma p_t \textrm{d} w_t \, .
$$
Then, with the usual notation for the Black-Scholes $\Delta$, we have
$$
\Xi^i(p_t, t) = \partial_p P^i(p_t, t) := \Delta^i_t(p_t, t) \, ,
$$
and, writing $\bm{\Delta} := (\partial_p P^1(p_t, t), \cdots, \partial_p P^M(p_t, t))$, \cref{eq:kyle_fragm} yields
$$
\Lambda(p_t, t) = \sqrt{Y} p_t \frac{\sigma}{\omega(p_t, t)} \begin{pmatrix} 1 & \ \bm{\Delta}^\top \\ \bm{\Delta} & \bm{\Delta} \bm{\Delta}^\top \end{pmatrix} (p_t, t) \, ,
$$
where
$$
\omega^2(p_t, t) = (1, \bm{\Delta}(p_t, t))^\top \Omega(p_t, t) (1, \bm{\Delta}(p_t, t)) \, .
$$
Thus, as in the previous example, there is a single liquidity pool, with volumes traded on options adjusted for the options' $\Delta$. Volume traded on deep in-the-money options ($\Delta^i \approx 1$) contribute to the overall liquidity pool as if it was the spot itself that was traded, whereas deeply out-of-the-money options ($\Delta^i \approx 0$) give negligible contributions.
\subsection{Volatility factors}
\label{sec:vol_factors_example}
Building on our previous example, we want to focus on the same class of instruments (one spot and a strip of $M$ European options) in the case in which it is necessary to add an implied volatility term to the Black-Scholes formula to obtain their price. One is required to use a pricing formula $P^i(p_t, \hat \sigma^i_t, t)$ in order to accurately describe the price of the options, where $\hat \sigma^i_t$ is an \emph{implied volatility}.
\\ \\
In order to reduce the dimensionality of the $M$ implied volatilities $\hat \sigma^i_t$, we assume that they lie on a low dimensional surface, so that we are allowed to write
$$
\hat \sigma^i_t = F^i({\bm \varsigma}_t) \, ,
$$
where ${\bm \varsigma}_t = (\varsigma^1_t, \dots, \varsigma^Q_t)$ is a set of volatility factors that completely describe the volatility surface through a set of $M$ functions $(F^i({\bm \varsigma}))_{i=1}^M$.
Note that with some abuse of notation, we will often write
$$
P^i(p_t, \hat F^i({\bm \varsigma}_t), t) =
P^i(p_t, {\bm \varsigma}_t, t) \, ,
$$
and we will employ a similar notation for other functions of the implied volatility $\hat \sigma^i_t$. We then have an underlying consisting of $N = 1 + Q$ instrument, of which only one is tradeable (the spot), and where the other $Q$ factors correspond to non-tradeable volatility factors. The sensitivities of the system in this case correspond to
\begin{align*}
\Xi^{i1}_t (p_t, {\bm \varsigma}_t, t)
&=
\Delta^i_t (p_t, {\bm \varsigma}_t, t)
:=
\frac{
\partial P^i(p_t, {\bm \varsigma}_t, t)
}{\partial p_t} \\
\Xi^{i(q+1)}_t (p_t, \hat \sigma^i_t, t)
&=
\frac{
\partial P^i(p_t, \hat\sigma^i_t, t)
}{\partial \hat\sigma^i_t}
\frac{
\partial F^i({\bm \varsigma}_t)
}{\partial \varsigma^q}
:=
\mathcal{V}^i_t (p_t, {\bm \varsigma}_t, t)
\beta^{iq}(p_t, \varsigma_t, t) =: \Upsilon^{iq}
\, ,
\end{align*}
where $q=1, \dots, Q$ and where, as it is customary in the literature on option pricing, we have introduced the \emph{vega}
$$
\mathcal{V}^i_t (p_t, \hat \sigma^i_t, t) =
\frac{
\partial P^i_t(p_t, \hat\sigma^i_t, t)
}{\partial \hat\sigma^i_t} \, ,
$$
and the sensitivities of the volatility surface to $ {\bm \varsigma}_t$
$$
\beta^{iq}(p_t, {\bm \varsigma}_t, t) = \frac{
\partial F^i({\bm \varsigma}_t)
}{\partial \varsigma^q} \, .
$$
For convenience, we write the sensitivity matrix in block
$$
\Xi = \begin{pmatrix}
\bm{\Delta} \mid \Xi^{\cdot 1} \mid \cdots \mid \Xi^{\cdot Q}
\end{pmatrix} =: \begin{pmatrix}
\bm{\Delta} \mid \Upsilon
\end{pmatrix} \, .
$$
At this point, the most general expression for the cross-impact matrix that we can write is
$$
\Lambda(p_t, {\bm \varsigma}_t, t) = \begin{pmatrix}
\Lambda_{pp} & \Lambda_{p\varsigma} & \Lambda_{pp} \bm{\Delta}^\top + \Lambda_{p\varsigma} \Upsilon^\top \\
\Lambda_{p\varsigma}^\top & \Lambda_{\varsigma \varsigma} & \Lambda_{\varsigma \varsigma} \Upsilon^\top + \Lambda_{p \varsigma}^\top \bm{\Delta}^\top \\
\bm{\Delta} \Lambda_{pp} + \Upsilon \Lambda_{p \varsigma}^\top & \Upsilon \Lambda_{\varsigma \varsigma} + \bm{\Delta} \Lambda_{p\varsigma} & \bm{\Delta} \Lambda_{pp} \bm{\Delta}^\top + \Upsilon \Lambda_{\varsigma \varsigma} \Upsilon^\top + \bm{\Delta} \Lambda_{p \varsigma} \Upsilon^\top + (\bm{\Delta} \Lambda_{p \varsigma} \Upsilon^\top)^\top
\end{pmatrix}\, .
$$
\paragraph{Single-factor model}
It is instructive to understand the behavior of the system in the case in which $Q=1$, and the volatility surface is parametrized by a single level factor:
$$
\hat\sigma^i_t(\varsigma_t) = F(\varsigma_t) = \varsigma_t \, ,
$$
so that one has
$$
\Xi^{i1}(p_t, \varsigma_t, t) = \mathcal{V}^i_t (p_t, \varsigma_t, t) \, .
$$
In this case the rank two cross-impact matrix can be written as
$$
\Lambda(p_t, \varsigma_t, t) = \begin{pmatrix}
\Lambda_{pp} & \Lambda_{p\varsigma} & \Lambda_{pp} \bm{\Delta}^\top + \Lambda_{p\varsigma} \mathbfcal{V}^\top \\
\Lambda_{p\varsigma} & \Lambda_{\varsigma \varsigma} & \Lambda_{\varsigma \varsigma} \mathbfcal{V}^\top + \Lambda_{p \varsigma} \bm{\Delta}^\top \\
\bm{\Delta} \Lambda_{pp} + \mathbfcal{V} \Lambda_{p\varsigma} & \mathbfcal{V} \Lambda_{\varsigma \varsigma} + \bm{\Delta} \Lambda_{p\varsigma} & \Lambda_{pp} \bm{\Delta} \bm{\Delta}^\top + \Lambda_{\varsigma \varsigma} \mathbfcal{V} \mathbfcal{V}^\top + \Lambda_{p \varsigma} (\bm{\Delta} \mathbfcal{V}^\top + \mathbfcal{V}^\top \bm{\Delta})
\end{pmatrix} \, .
$$
In the case where the $\Delta$ order flow and $\mathcal{V}$ order flow are not correlated, i.e. writing $\bdelta_{\textnormal{c}} := (1, 0, \frac{\partial P^1}{\partial p}, \cdots, \frac{\partial P^M}{\partial p})$, $\mathbfcal{V}_{\textnormal{c}} := (0, 1, \frac{\partial P^1}{\partial \varsigma^1}, \cdots, \frac{\partial P^M}{\partial \varsigma^1})$ we have $\bdelta_{\textnormal{c}}^\top \Omega \mathbfcal{V}_{\textnormal{c}} = 0$, we can obtain the expression of the kyle cross-impact matrix for the underlying:
\begin{equation}
\label{eq:kyle_leverage}
\begin{pmatrix}
\Lambda_{pp} & \Lambda_{p \varsigma} \\
\Lambda_{p \varsigma} & \Lambda_{\varsigma \varsigma}
\end{pmatrix}(p_t, \varsigma_t, t) = \dfrac{1}{\sqrt{\sigma^2 \omega_{\Delta}^2 + \xi^2 \omega_{\mathcal{V}}^2 + 2 \sigma \xi \rho \omega_{\Delta} \omega_{\mathcal{V}}}}
\begin{pmatrix}
\sigma^2 + \frac{\omega_{\mathcal{V}}}{\omega_{\Delta}} \sigma \xi \sqrt{1-\rho^2} & \sigma \xi \rho \\
\sigma \xi \rho & \xi^2 + \frac{\omega_{\Delta}}{\omega_{\mathcal{V}}} \sigma \xi \sqrt{1-\rho^2}
\end{pmatrix} (p_t, \varsigma_t, t) \, ,
\end{equation}
where $\omega_{\Delta}^2 := \bdelta_{\textnormal{c}}^\top \Omega \bdelta_{\textnormal{c}}$ is the delta-aggregated liquidity, $\omega_{\mathcal{V}}^2 := \mathbfcal{V}_{\textnormal{c}}^\top \Omega \mathbfcal{V}_{\textnormal{c}}$ is the vega-aggregated liquidity, $\sigma^2(p_t, \varsigma_t, t) := \mathbb{E}_t[p^2_t] - \mathbb{E}_t[p_t]^2$ is the spot volatility, $\xi^2(p_t, \varsigma_t, t) := \mathbb{E}_t[\varsigma_t^2] - \mathbb{E}_t[\varsigma_t]^2$ is the volatility of volatility and $\rho$ is the spot-vol correlation.
\section{Empirical Results}
\label{sec:empirical}
We now illustrate \cref{sec:setup} with an empirical analysis of cross-impact on derivatives markets. \cref{sec:setupemp} describes the universe of instruments and the chosen derivative modeling. \cref{sec:relevant_observables} shows the empirical observables $\Sigma_{pp}$ and $\Omega_{\Xi}$ used in \cref{sec:cross-impact-models} to compute the resulting cross-impact matrix $\Lambda_{pp}$. Finally, \cref{sec:quality_fit} stress-tests the fit of cross-impact models and \cref{sec:aggregate_impact} examines non-parametric evidence of cross-impact.
\subsection{Setup}
\label{sec:setupemp}
The universe of instruments is made up of (i) the front-month E-mini future, (ii) the two front-month VIX futures, (iii) a set of $M-2$ call and put options on the E-mini. We thus have $M$ derivatives. We model the implied volatility surface with $Q$ volatility factors, as discussed in \cref{sec:vol_factors_example}. We aggregate returns and order flows on a time window of five minutes, so that $\textrm{d} {\bm p}_t$ is approximated by the price change on the timeframe of five minutes and $(\textrm{d} {\bm q}_t, \textrm{d} {\bm Q}_t)$ is approximated by the signed traded order flow during this time window. To avoid confusion, we write $\delta {\bm p}_t$, $\delta {\bm q}_t$ and $\delta {\bm Q}_t$ for these empirical quantities in the rest of this section. Prices and order flows for these instruments are taken from trades and quotes data and more detail on the dataset is provided in \cref{app:data}.
We consider a linear approximation of the implied volatility surface with volatility factors, so that using the notations of \cref{sec:vol_factors_example}, we have $F^i({\bm \varsigma}) = \sum_{q=1}^{Q} \beta^{iq}\varsigma^q$ where $i=1,\dots,M$. To fit surfaces, we choose $M=3$ and describe volatility factors in \cref{fig:volatility_factors}. The first factor is a classic implied volatility level factor and we make the rough approximation that VIX futures are solely explained by such \emph{level} factor. The second factor corresponds to the skew of the implied volatility surface, referred to as the \emph{skew} factor hereafter. The third factor explains the term structure of the implied volatility, hence the name the \emph{term} factor in the following.
\begin{figure}[h!]
\centering
\centering
\includegraphics[width=0.95\textwidth]{figures/volatility_factors.pdf}
\caption{\textbf{Effect of the different volatility factors on the implied volatility surface.} \\
Starting from a historical implied volatility $\hat{\sigma}^i$, we show the modified implied volatility surface after with a small contribution from the factor $q$: $\hat{\sigma}^i + \epsilon \beta^{iq}$. The original (non-modified) implied volatility surface is shown in light opacity for reference.}
\label{fig:volatility_factors}
\end{figure}
\subsection{Relevant observables}
\label{sec:relevant_observables}
Using \cref{sec:low_dimensional_ximpact}, it suffices to compute the Kyle model associated to the underlying return covariance matrix $\Sigma_{pp}({\bm p}_t, t)$ and the aggregated order flow covariance matrix $\Omega_{\Xi}({\bm p}_t, t)$ to obtain the full cross-impact matrix. As we have approximated the behaviour of the system with 4 underlyings, these observables are 4 by 4 matrices. To estimate them, we make the additional assumption that $\Sigma_{pp}$ and $\Omega_{\Xi}$ are stationary and independent of ${\bm p}_t$. \cref{fig:covariance} displays the underlying return correlation matrix $\varrho_{pp} := \diag{\bm{\sigma}}^{-1} \Sigma_{pp} \diag{\bm{\sigma}}^{-1}$ and the risk order flow covariance matrix $\Omega_{\Xi}^{\text{risk}}:= \diag{\bm{\sigma}} \Omega_{\Xi} \diag{\bm{\sigma}}$ where $\bm{\sigma} = ((\Sigma^{11}_{pp})^{1/2}, \cdots, (\Sigma_{pp}^{NN})^{1/2})$ is the underlying volatility.
The traded risk (volatility times liquidity) is concentrated on the spot and level directions. This justifies approximating cross-impact on options using solely spot and level underlyings, which we delve in more detail in \cref{sec:cross-impact-models}. The traded risk in the skew direction is much smaller than all other directions and skew order flow is thus expected to contribute less to cross-impact. The underlying return correlation matrix correlation matrix shows strong negative correlation between the spot and level mode. This is a well-known stylised fact, sometimes referred to as the "leverage effect". This will play an important role in the form of the cross-impact model, as highlighted in \cref{eq:kyle_leverage_approx_emp}. Unsurprisingly, the correlation between spot and level order flow is much smaller, although still noticeable (around -0.15\%).
\begin{figure}[h!]
\centering
\centering
\includegraphics[width=0.5\linewidth]{figures/covariances.pdf}
\caption{\textbf{Empirical estimates of return correlation matrix $\varrho$ and order flow covariance $\Omega$.} \\
The return correlation matrix $\varrho$ (left) and the order flow covariance matrix $\Omega$ (right) estimates on our dataset. The order flow is reported in thousands of dollars of risk.}
\label{fig:covariance}
\end{figure}
\subsection{Cross-impact models}
\label{sec:cross-impact-models}
We can now use the empirical estimates of $\Sigma_{pp}$ and $\Omega_{\Xi}$ from the previous section to compute the cross-impact matrix $\Lambda$. For comparison purposes, we also introduce other cross-impact models. The first cross-impact model used for comparison is the Black-Scholes cross-impact model introduced in \cref{sec:black_scholes_model} which has a single underlying: the spot. It is defined as
\begin{equation}
\Lambda_{\textnormal{bs}}({\bm p}_t, t) := \frac{\sigma}{\sqrt{\bdelta_{\textnormal{c}}^\top \Omega \bdelta_{\textnormal{c}}}} \bdelta_{\textnormal{c}} \bdelta_{\textnormal{c}}^\top \, .
\end{equation}
The Black-Scholes model coincides with the Kyle cross-impact model if all the liquidity is concentrated on the spot. In particular, this model is unable to account for changes in the volatility factors. We thus introduce the two-dimensional direct model $\Lambda_{\textnormal{direct-2d}}$ which accounts for the spot and implied volatility factor but ignores cross-sectional effects, defined as
\begin{equation}
\Lambda_{\textnormal{direct-2d}}({\bm p}_t, t) := \frac{\sigma}{\sqrt{\bdelta_{\textnormal{c}}^\top \Omega \bdelta_{\textnormal{c}}}} \bdelta_{\textnormal{c}} \bdelta_{\textnormal{c}}^\top + \frac{\xi}{\sqrt{\mathbfcal{V}_{\textnormal{c}}^\top \Omega \mathbfcal{V}_{\textnormal{c}}}} \mathbfcal{V}_{\textnormal{c}} \mathbfcal{V}_{\textnormal{c}}^\top \, .
\end{equation}
To account for all underlyings without correcting for cross-sectional effects, we introduce the four-dimensional direct model
\begin{equation}
\Lambda_{\textnormal{direct-4d}}({\bm p}_t, t) := \frac{\sigma}{\sqrt{\bdelta_{\textnormal{c}}^\top \Omega \bdelta_{\textnormal{c}}}} \bdelta_{\textnormal{c}} \bdelta_{\textnormal{c}}^\top + \frac{\xi}{\sqrt{\mathbfcal{V}_{\textnormal{c}}^\top \Omega \mathbfcal{V}_{\textnormal{c}}}} \mathbfcal{V}_{\textnormal{c}} \mathbfcal{V}_{\textnormal{c}}^\top + \sum_{i=3}^{Q+1} \sqrt{\frac{\Sigma^{ii}_{pp}}{\Omega_{\Xi}^{ii}}} \Xi^{\cdot i}({\bm p}_t, t) (\Xi^{\cdot i}({\bm p}_t, t))^\top \, .
\end{equation}
Direct models ignore the off-diagonal structure of $\Sigma_{pp}$ and $\Omega_{\Xi}$. In particular they do not account for the leverage effect, which is an essential characteristic of the underlying return covariance matrix $\Sigma_{pp}$. To fix this, we introduce the two-dimensional Kyle cross-impact model $\Lambda_{\textnormal{2d}}$ which captures the two dominating underlyings of the system: the spot and level factor. Since \cref{fig:covariance} shows that the delta and vega order flow correlation is small (around $-0.15\%$) and $\xi \omega_{\mathcal{V}} \ll \sigma \omega_{\Delta}$, we can use \cref{eq:kyle_leverage} to obtain the approximation
\begin{equation}
\label{eq:kyle_leverage_approx_emp}
\Lambda_{\textnormal{2d}}(p_t, \varsigma_t, t) \approx \frac{\sigma}{\sqrt{\bdelta_{\textnormal{c}}^\top \Omega \bdelta_{\textnormal{c}}}} \bdelta_{\textnormal{c}} \bdelta_{\textnormal{c}}^\top + \frac{\xi \sqrt{1-\rho^2}}{\sqrt{\mathbfcal{V}_{\textnormal{c}}^\top \Omega \mathbfcal{V}_{\textnormal{c}}}} \mathbfcal{V}_{\textnormal{c}} \mathbfcal{V}_{\textnormal{c}}^\top + \frac{\xi \rho}{\sqrt{\bdelta_{\textnormal{c}}^\top \Omega \bdelta_{\textnormal{c}}}} (\mathbfcal{V}_{\textnormal{c}} \bdelta_{\textnormal{c}}^\top + \bdelta_{\textnormal{c}} \mathbfcal{V}_{\textnormal{c}}^\top).
\end{equation}
The two-dimensional Kyle cross-impact model predicts that when trading options, one pushes the price in the amount of notional $\mathcal{V}$ traded divided by the typical $\mathcal{V}$ liquidity, which is compatible with findings from the meta-order study \cite{Toth2016TheMarkets}. The prefactor $\sqrt{1-\rho^2} \approx 0.4$ is close to the empirical value of $0.33-0.4$ reported in \cite{Toth2016TheMarkets}. Further, because of the leverage effect, trading delta-hedged portfolio impacts the spot price.
The full, four-dimensional Kyle cross-impact model $\Lambda_{\textnormal{4d}}$ is shown in \cref{fig:kyle-4d}. Compared to the two-dimensional Kyle cross-impact model, it decouples the contribution of options on the level mode depending on the direction. This increases the explanatory power of the model, as shall be evidenced in \cref{table:scores}.
\begin{figure}[h!]
\centering
\centering
\includegraphics[width=0.3\linewidth]{figures/kyle_skew.pdf}
\caption{\textbf{Four dimensional Kyle cross-impact model on options.} \\
We report the four dimensional Kyle model estimated using empirical estimates of the covariances of \cref{fig:covariance}. The cross-impact matrix are reported in units of risk and in basis points so that $\Lambda_{ij}$ encodes by how many basis points of volatility Asset $i$ is pushed by trading one dollar of risk on Asset $j$.}
\label{fig:kyle-4d}
\end{figure}
\subsection{Explanatory power of cross-impact models}
\label{sec:quality_fit}
For practical applications, a good cross-impact model should explain realized price changes from order flows. Thus to compare the models previously introduced, we now examine their explanatory power on empirical data. Given a realization of the underlying price process $(\delta {\bm p}_t)_{1 \leq t \leq T}$ of length $T$, a corresponding series of predictions $(\widehat{\delta {\bm p}}_t)_{1 \leq t \leq T}$ and a symmetric positive semi-definite matrix $M$, we introduce the generalized $R^2(M)$ error as
$$
R^2(M) := 1 - \dfrac{\sum_{1 \leq t \leq T} (\delta {\bm p}_t - \widehat{\delta {\bm p}}_t)^\top M (\delta {\bm p}_t - \widehat{\delta {\bm p}}_t)}{\sum_{1 \leq t \leq T} \delta {\bm p}_t^\top M \delta {\bm p}_t} \, .
$$
The matrix $M$ is used to examine a model's predictive power for different portfolios. As the underlyings of our system are natural directions to consider, we report the $R^2(M)$ in \cref{table:scores} for $\Pi_{(1,0,0,0)} =: \Pi_{\textrm{spot}}$, $\Pi_{(0,1,0,0)} =: \Pi_{\textrm{level}}$, $\Pi_{(0,0,1,0)} =: \Pi_{\textrm{skew}}$ and $\Pi_{(0,0,0,1)} =: \Pi_{\textrm{term}}$.
\begin{table}[h!]
\centering
\scalebox{0.9}{\begin{tabular}{lcccccc} \toprule
\multicolumn{1}{c}{Model} & \multicolumn{4}{c}{Scores} \\
\cmidrule{2-5} & $R^2(\Pi_{\textrm{spot}})$ & $R^2(\Pi_{\textrm{level}})$ & $R^2(\Pi_{\textrm{skew}})$ & $R^2(\Pi_{\textrm{term}})$ \\
\midrule
$\Lambda_{\textnormal{bs}}$ & $ 0.18 \pm 0.01 $& $ -0.00 \pm 0.02 $& $ -0.00 \pm 0.01 $& $ -0.00 \pm 0.02 $ \\
$\Lambda_{\textnormal{direct-2d}}$ & $ 0.18 \pm 0.01 $& $ -0.03 \pm 0.02 $& $ -0.01 \pm 0.01 $& $ 0.00 \pm 0.02 $ \\
$\Lambda_{\textnormal{direct-4d}}$ & $ 0.18 \pm 0.01 $& $ -0.03 \pm 0.02 $& $ -0.14 \pm 0.02 $& $ -0.26 \pm 0.02 $ \\
$\Lambda_{\textnormal{2d}}$ & $ 0.20 \pm 0.01 $& $ 0.12 \pm 0.01 $& $ -0.01 \pm 0.01 $& $ 0.01 \pm 0.02 $ \\
$\Lambda_{\textnormal{4d}}$ & $ 0.20 \pm 0.01 $& $ 0.14 \pm 0.01 $& $ -0.12 \pm 0.02 $& $ 0.04 \pm 0.01 $ \\
\bottomrule
\end{tabular}}
\caption{\textbf{Scores of different cross-impact models.\\}
All scores were computed in-sample using the same data used for the calibration of the cross-impact models.}
\label{table:scores}
\end{table}
Looking at $R^2(\Pi_{\textrm{spot}})$, we see that all models show similar scores on the spot, with cross-impact models being slightly better. Furthermore, there is no difference between $\Lambda_{\textnormal{2d}}$ and $\Lambda_{\textnormal{4d}}$. This is consistent with the liquidity reported in~\cref{fig:risk_liquidity}. Indeed, most of the liquidity is placed on the spot and the order flow traded on other factors is small in comparison. Models which only take into account the spot thus capture most of the order flow explanatory power. There is also a small advantage in using order flow on the level mode since $\Lambda_{\textnormal{2d}}$ and $\Lambda_{\textnormal{4d}}$ score better, but using term and skew order flow provides no improvement.
While using solely spot liquidity to explain spot returns is a good approximation, $R^2(\Pi_{\textrm{level}})$ shows the same is not true for the level underlying. Indeed, only models with spot-level cross-impact are able to account for returns of the implied volatility level. Therefore, to explain price changes on the level underlying we need to use order flow traded on the spot. This is natural as most of the traded order flow is on the spot but there is a high negative correlation between spot and level underlying (see~\cref{fig:risk_liquidity}). Unfortunately, all models fail to explain skew returns. We suspect this comes from the low signal to noise ratio and low liquidity (in risk terms) of the skew underlying (see~\cref{fig:risk_liquidity}).
On all metrics, $\Lambda_{\textnormal{4d}}$ performs at least as well as $\Lambda_{\textnormal{2d}}$, which shows that the model is able to combine additional factors without suffering from noise. The additional underlying also help weigh trades appropriately on the implied volatility surface, which improves the $R^2(\Pi_{\textrm{level}})$ score.
Finally, we report the expected realized return conditional on the prediction of $\Lambda_{\textnormal{4d}}$ in~\cref{fig:kyle_agg}. This shows that, skew aside, $\Lambda_{\textnormal{4d}}$ provides a good fit for the realized returns of the different underlying as $\avg_t[\delta {\bm p}_t \mid \delta \hat{{\bm p}}_t] \approx \delta {\bm p}_t$.
\begin{figure}[h!]
\centering
\centering
\includegraphics[width=0.8\linewidth]{figures/kyle_agg.pdf}
\caption{\textbf{Predictions of the four-dimensional Kyle model on the main directions of the system.} \\
We report the expected price change conditional on the predicted price change of the four-dimensional Kyle model for the four main directions of the system: in red for the spot, blue for the level, green for the skew and purple for the term structure. Predicted price changes and conditional averages are both normalized by the standard deviation of price changes along the given direction.}
\label{fig:kyle_agg}
\end{figure}
\subsection{Evidence of cross-impact on options}
\label{sec:aggregate_impact}
\cref{sec:quality_fit} showed that only cross-impact models are able to explain returns for the level and term underlying. Aside from this explanatory power, this section tests their ability to explain other features of our data. To do so, we introduce the cross aggregate impact metric. The cross aggregate impact induced from the portfolio $\bm{u} \in \reals{N+M}$ on the return of the portfolio $\bm{v} \in \reals{N+M}$ is
$$
\textnormal{Agg}_{\bm{u},\bm{v}}(x) := \mathbb{E}_t [ \bm{v}^\top (\delta {\bm p}_t, \delta {\bm P}_t) \mid \bm{u}^\top (\delta {\bm q}_t, \delta {\bm Q}_t) = x] \, .
$$
If returns are given by a linear cross-impact model $\Psi$ and if we further assume $(\delta {\bm q}_t, \delta {\bm Q}_t)$ is a zero-mean Gaussian, then
\begin{align*}
\textnormal{Agg}_{\bm{u},\bm{v}}(x) &= \mathbb{E}_t [ \bm{v}^\top \Psi (\delta {\bm q}_t, \delta {\bm Q}_t) \mid \bm{u}^\top (\delta {\bm q}_t, \delta {\bm Q}_t)] := \textnormal{Agg}_{\bm{u},\bm{v}}^{\Psi}(x) = a_{\Psi} x \, ,
\end{align*}
where the slope $a_{\Psi}$ depends on the cross-impact model $\Psi$ and on the order flow covariance. Even in the absence of cross-impact, the presence of order flow correlations between two portfolios $\bm{u}$ and $\bm{v}$ may lead to a non-zero cross aggregate impact. Thus, to test whether there is cross-impact, we compare the empirically measured $\textnormal{Agg}_{\bm{u},\bm{v}}$ to the prediction $\textnormal{Agg}_{\bm{u},\bm{v}}^{\Psi}$ for different cross-impact models $\Psi$. We differentiate models between those which have no off-diagonal contributions ($\Lambda_{\textnormal{bs}},\Lambda_{\textnormal{direct-4d}},\Lambda_{\textnormal{direct-2d}}$) and thus ignore cross-impact and those that take it into account ($\Lambda_{\textnormal{2d}},\Lambda_{\textnormal{4d}}$).
We report $\textnormal{Agg}_{\bm{u},\bm{v}}$ in \cref{fig:kyle_agg} for different portfolios $\bm{u},\bm{v}$ described in \cref{table:directions}. Diagonal plots show aggregate direct impact. As expected, buying the E-Mini increases, on average, the price of the E-Mini as shown by the $\bm{u}, \bm{v} = \text{spot}$ plot (first row, first column). We see from the $\bm{u},\bm{v} = \text{level}$ plot (second row, second column) that buying options and VIX futures increases, on average, the implied volatility. Furthermore, buying options and VIX futures decreases, on average, the E-Mini price as shown by the $\bm{u} = \text{level}, \bm{v}= \text{spot}$ plot (first row, second column). This same plot, among others of \cref{fig:kyle_agg}, shows that direct models provide a poor fit for cross aggregate impact. This suggests that the cross aggregate impact can only be explained by using a cross-impact model with off-diagonal elements, such as $\Lambda_{\textnormal{4d}}$. Further, the fit is noticeably better for $\Lambda_{\textnormal{4d}}$ than $\Lambda_{\textnormal{2d}}$ which highlights the importance of taking into account the skew and term factors.
\begin{table}[h!]
\centering
\scalebox{0.9}{\begin{tabular}{lcccccc} \toprule
\multicolumn{1}{c}{Name} & \multicolumn{4}{c}{Components} \\
\cmidrule{2-5} & spot & $\text{VIX}_0$ & $\text{VIX}_1$ & options \\
\midrule
spot & $(1,$ & $0,$ & $0,$ & $0, \cdots, 0)$ \\
level & $(0,$ & $\beta^{11},$ & $\beta^{21},$ & $\beta^{31}, \cdots, \beta^{M1})$ \\
skew & $(0,$ & $\beta^{12},$ & $\beta^{22},$ & $\beta^{32}, \cdots, \beta^{M2})$ \\
term & $(0,$ & $\beta^{13},$ & $\beta^{23},$ & $\beta^{33}, \cdots, \beta^{M3})$ \\
\bottomrule
\end{tabular}}
\caption{\textbf{Description of different directions used in this section.}
}
\label{table:directions}
\end{table}
\begin{figure}[h!]
\centering
\centering
\includegraphics[width=\linewidth]{figures/agg_impact_4d.pdf}
\caption{\textbf{Normalized cross aggregate impact curves.} \\
We report the cross aggregate cross impact curves for the spot, level, skew and term structure directions. Aggregate traded volumes are normalized by the typical deviations $\omega_{u}^2 := \avg_t[(\bm{u}^\top (\delta {\bm q}_t, \delta {\bm Q}_t))^2]$ and portfolio returns by the typical deviations $\sigma_{v}^2 := \avg_t[(\bm{v}^\top (\delta {\bm p}_t, \delta {\bm P}_t))^2]$. Estimated cross aggregate impact $\textnormal{Agg}_{\bm{u},\bm{v}}$ is reported along with predicted cross aggregate impact $\textnormal{Agg}_{\bm{u},\bm{v}}^{\Psi}$ for different choices of linear cross-impact models $\Psi$.}
\label{fig:kyle_prefactor_agg}
\end{figure}
\section{Conclusion}
\label{sec:conclusion}
Let us summarize what we have achieved. Our main objective was to examine cross-impact when some instruments, derivatives, are deterministic functions of others, underlying. This posed modeling challenges on two fronts. First, derivative prices with impact must be locked-in by no-arbitrage. Second, the liquidity of derivative instruments may be very small and heavily non-stationary.
Leveraging the results of~\cite{Tomas2020HowResults}, we introduced the Kyle cross-impact model on derivatives. We showed in \cref{sec:properties_impact} that this model (i) prevents arbitrage, (ii) provides impact dynamics which can be factored to recover frictionless dynamics, (iii) aggregates traded order flow to a few liquidity pools, (iv) is well-behaved even if some instruments are highly illiquid, and (v) can be applied without specifying which instruments are derivatives. The Kyle cross-impact model is thus theoretically satisfying and practical for applications. This justifies its use compared to other cross-impact models (see~\cite{Tomas2020HowResults} for examples of other models).
To stress-test our framework on empirical data, we used the front-month E-Mini future, E-Mini vanilla options and VIX futures. Despite our simplistic approach to model implied volatility dynamics, we showed (see \cref{fig:kyle_prefactor_agg,table:scores}) that the Kyle model better explains returns than models which ignored cross-impact, and that the Kyle model can be improved by more precise modeling of the implied volatility surface. This points at the effectiveness of the proposed framework to aggregate liquidity and suggests more sophisticated implied volatility modeling may further improve results. Aside from explanatory power, cross-impact models are consistent with some empirical observations noted in \cite{Toth2016TheMarkets,Said2019HowImpact}. We provided evidence of cross-impact in derivative markets by studying price responses conditional on traded order flow and showing models which ignore cross-impact are unable to provide an adequate fit (see \cref{fig:kyle_prefactor_agg}).
On both theoretical and empirical grounds, the simple static, linear framework presented here thus accounts for important properties of impact on derivative markets. The methodology is flexible and can be readily adapted to handle complex price dynamics and exotic derivatives. The cross-impact estimates may be used in practice for estimating execution costs, in particular hedging costs.
While this work provides a first proof of concept which captures many features of cross-impact on derivatives, it fails to capture the auto-correlations of order flows. A multi-period cross-impact model, apart from providing more accurate descriptions of cross-impact, would yield insight into the cross-impact of meta-orders, another topic left unexplored to this date and particularly difficult to measure on options. We leave this extension to future work since it raises new challenges. For example, multi-period, cross-sectional arbitrages yield new constraints for the chosen cross-impact model. Furthermore, to remain tractable, such models need to find the proper way to aggregate traded order flow in liquidity pools.
\section{Acknowledgments}
We warmly thank J.-P. Bouchaud, Z. Eisler and B. Toth and M. Rosenbaum for fruitful discussions. This research was conducted within the \textit{Econophysics \& Complex Systems} Research Chair under the aegis of the \textit{Fondation du Risque}, a joint initiative by the \textit{Fondation de l'\'Ecole polytechnique, l'\'Ecole polytechnique} and Capital Fund Management.
\bibliographystyle{plain}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,902 |
Should Mortgage Debt Forgiveness be Taxed?
Today, President Bush signed into law a new tax law that puts in place a three year exclusion from income of mortgage debt forgiveness. Currently, individuals who receive forgiveness of their mortgage must claim the forgiveness as income on their IRS tax forms. This change in tax law is bad tax policy for two reasons. First, it's temporary. If mortgage debt forgiveness should not be taxable income, then why should somebody who is in financial trouble in 2008 be more deserving of somebody who is in financial trouble in 2012? Such a provision defies logic and basically shows that the politicians are just trying to appease the short-run concern of voters, void of any true principle.
But then again, tax policy in Washington is rarely driven by principle. And that brings us to the second reason why this is bad tax policy mortgage debt forgiveness is income and should be taxed under an income tax. There is a reason that the IRS lawyers have ruled that this type of mortgage debt forgiveness should be treated as ordinary income.
Now on the issue of debt forgiveness, if an individual seeks to purchase a $450,000 home and needs to borrow $450,000 to do so, the interest expenses should be deductible under the pure income tax assuming the imputed rental income is taxed. For simplicity, however, assume there was a zero percent interest rate. Suppose one year later, the value of the home now falls to $200,000 given the market and the bank forgives the remainder of the loan. $15,000 has been paid off, but the bank now forgives the person of the remaining $435,000 and takes the home. Should that $435,000 be taxed?
From a Haig-Simons perspective, the person's change in net wealth is zero relative to the starting point (before the investment). Ignoring the imputed rental income (the consumption portion of HSI), the person would be forced to claim the forgiveness as income but also be allowed to deduct from income the huge capital loss as a result of the house depreciation. However, the U.S. tax system does not tax the capital gains from housing nor does it allow for housing-related capital losses to be deducted against income. Therefore, the forgiveness should still be treated as income and the person should have a positive tax liability.
Finally, it is worth noting that this will cost $1 billion. So how do we pay for that? Raise taxes on somebody else of course. Bloomberg News reports that "the $1 billion cost of the bill will be offset by raising penalties on partnerships and small businesses that fail to file tax returns." That is not sound tax policy either. The penalties on partnerships and small businesses for not filing tax returns should be set in order to ensure proper compliance, and should not be increased merely because politicians want to raise revenue to pay for something else. (Same principle as Virginia drivers' fees and cigarette taxes.) There is an optimal fine amount, which is independent of the need to raise money to help bailout homeowners who happen to be struggling when others are struggling. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,954 |
\section{Introdução}
O século XXI tem sido um grande momento para o desenvolvimento da física e da ciência como um todo. Grandes passos foram dados e grandes revoluções nas ideias sobre o funcionamento do Universo foram geradas e/ou reafirmadas, trazendo a sensação de que a física se mantém inovadora a ponto de ainda modificar nossas concepções sobre o conhecimento do Universo.
O final do ano de 2015 e início de 2016 trouxe consigo essa sensação de trabalho contínuo da física, em comprovar, algo predito por Albert Einstein há mais de 100 anos, 1916, a existência das Ondas Gravitacionais (OG) pelo LIGO (Laser Interferometer for Gravitational Waves Observatory)~\cite{ligo} em colaboração com o Virgo Interferometer~\cite{virgo} e outros detectores. A detecção foi possível com a ocorrência da fusão de um sistema Binário de Buracos Negros (BBN's), como abordado por Cattani e Bassalo~\cite{Cattani} em afirmar que BBN's podem ser um fonte potencial para essas ondas e um meio pelo qual poderiam ser comprovadas. Essa detecção certamente marca uma nova fase da astronomia, a chamada \textit{Astronomia de Ondas Gravitacionais}.
A formulação da existência de OG e principalmente da sua elaboração como teoria passou por um processo árduo, principalmente devido as interrupções sofridas pela eclosão tanto da 1º Guerra mundial (1914-1918), quanto da 2ª Guerra mundial (1939-1945) e seu respectivo pós-guerra, fazendo com que boa parte das pesquisas da época entrassem em modo \textit{stand by}, afim de que praticamente todo e qualquer financiamento, desenvolvimento científico e dedicação de cientistas fossem direcionados a guerra, resultando em que muitas dessas pesquisas entrassem no total esquecimento. Um caso em particular que praticamente entrou em parcial esquecimento foi justamente a teoria da Relatividade Geral (RG) de Einstein, por ser, na época, uma teoria especulativa, sem uma formulação matemática convincente e um pouco vazia de conteúdo físico, como menciona Saa~\cite{Saa}. No entanto, devido à grande indagação para a comunidade científica, sobre a existência das ondas gravitacionais, a RG, posteriormente, foi retomada.
Além da imposição das guerras nos países europeus, muitas discordâncias, até do próprio Albert Einstein, ainda persistiam, possuindo em contrapartida muitas aprovações e crenças de sua existência, envolvendo uma gama de físicos empenhados em trazer para comunidade científica algo tão vislumbrado pela sua ideia inicial de unificação e resolução de problemas que a mecânica newtoniana não era capaz de resolver. Esse é o embate característico do desenvolvimento das OG citado por Kennefick~\cite{Kennefick}.
Sendo uma previsão resultante da Relatividade Geral, como afirma Saa~\cite{Saa} em dizer que, "esta deve ser uma previsão de qualquer teoria que rejeite interações instantâneas à distância, como as presentes na Gravitação Universal de Newton", ainda não estava concretizada e aceita por boa parte da comunidade científica. Muitos foram os incrédulos à teoria das ondas gravitacionais e principalmente a sua comprovação experimental, mas aparentemente essa incredulidade e alto nível de ceticismo foi o combustível primordial para fazer com que a sua comprovação saísse de apenas especulações para fatos incontestáveis.
A formulação da teoria das OG, mesmo sendo proposta em 1916 por Einstein, só foi começar a encontrar caminhos fortificados para sua estruturação nos anos de 1950 e mesmo assim muitos anos à frente de intensas discussões e debates até então dar início, verdadeiramente, da tentativa de detecção dessas ondas.
O próprio LIGO demorou décadas para ter a sua primeira comprovação, 14 setembro de 2015, a chamada GW150914 e no mesmo ano, em 26 de dezembro, a segunda comprovação, chamada de GW151226, ambas em interferômetros de mesma base de funcionamento, uma situada em Hanford, Washington (EUA), e a outra em Livingston, Louisiana (EUA), para então chegar a impressa mundial e divulgar seus dados e comprovações, impactando de forma positiva e estimulante a sociedade científica, trazendo novas portas de pesquisas e campos de conhecimento como a astronomia gravitacional.
Como mencionado anteriormente, essas descobertas e comprovações trazem a sensação vívida do trabalho da física na continuidade de modificar o pensar humano, mas em contrapartida o seu ensino não desperta essa sensação nos discentes, por se manter preso e estagnado a conceitos ultrapassados e antigos da ideia de funcionamento da física e do Universo, como menciona Moreira~\cite{Moreira},
" (...) o ensino da Física estimula a aprendizagem mecânica de conteúdos desatualizados. Estamos no século XXI, mas a Física ensinada não passa do século XIX".
Sem quase nenhum espaço para apresentação de conceitos novos, ideias novas e concepção da Física Moderna e Contemporânea em sala de aula, a física tende a ser direcionada de forma errônea, gerando uma concepção desvirtuada da ideia de conhecimento do discente que tem contato com o ensino de física. Temos conhecimento que essa deficiência da presença do ensino da Física Moderna e Contemporânea nas escolas, não se dá apenas por um único fator, mas sim, por uma série de fatores e variáveis que em conjunto auxiliam na desconstrução do pensamento físico e principalmente científico dos discentes, sendo assim, o ponto de discussão deste trabalho.
Pensando nessa problemática, o respectivo trabalho tem como objetivo fundamental levar para sala de aula a ideia das ondas gravitacionais e o seu impacto perante o ensino, quebrando e desmistificando o pensamento de que alunos, "leigos à ciência", não possuem capacidade de absorver tais ideias e que esse é um tipo de conhecimento destinado apenas para um grupo seleto de cientistas. Também discutimos a relação entre a descoberta das ondas gravitacionais e assuntos que eles (discentes) veem em sala de aula, como fundamentos de óptica e gravitação, que servem como uma porta de entrada desse conteúdo em sala de aula, como também gerar conceitos novos sobre o funcionamento do Universo, mostrando a importância da renovação do conhecimento e escolhendo formas didáticas de aplicá-las como explica Moreira~\cite{Moreira} sobre a interação cognitiva entre conhecimentos novos e prévios como chave da aprendizagem significativa.
Outro enfoque que o respectivo trabalho traz é confirmar a importância da experimentação em sala de aula que surge como "(...) uma forma do aluno entrar em contato com a realidade, com a intenção de comprovar modelos ou teorias, ou ainda com o objetivo de motivar o aluno e despertar seu interesse pelo tema"~\cite{Silva}. Visando isso, além de ter a proposta de levar para a sala de aula a ideia da fundamentação teórica das ondas gravitacionais, também tem como enfoque mostrar o modelo experimental do interferômetro de Michelson-Morley, construído com materiais de baixo custo, que traz a mesma concepção de funcionamento que o LIGO utilizou para a detecção das OG, fazendo com que o aluno elucide suas ideias sobre o tema e entenda que conceitos físicos não são meras ideias prontas e matematizadas, mas sim que passam por um processo cientifico robusto e uma experimentação aguçada a fim de trazer a verdade sobre o funcionamento da natureza.
Para uma melhor apresentação, este trabalho está organizado da forma como segue. Na seção 2, apresentaremos uma breve discussão sobre a teoria da Relatividade de Einstein e o desenvolvimento histórico e científico das ondas gravitacionais como teoria e consequentemente o seu achado e dada comprovação. Após uma apresentação concisa do objeto deste trabalho, na seção 3 discutiremos a aplicação do conceito de ondas gravitacionais dentro da sala de aula, com o auxílio do experimento de Michelson-Morley, onde coletamos dados e discutimos ideias fundamentais ao desenvolvimento do ensino de física apresentados na seção 4. Por fim, na seção 5 apresentaremos nossas considerações finais.
\section{Apresentação histórica, conceitual e experimental das ondas gravitacionais}
Nessa seção iremos abordar de forma concisa os principais acontecimentos históricos que contribuíram para o desenvolvimento teórico e experimental das ondas gravitacionais. Após essa abordagem, discutiremos sobre as possibilidades de inserção da temática para o ensino médio.
\subsection{Noções sobre a teoria da relatividade de Einstein}
Em 1905, ano conhecido como \textit{annus mirabilis}~\footnote{Expressão do latim que significa \textit{ano miraculoso}.} da física, Einstein traz ao mundo novas concepções sobre a ideia de movimento que até então tinha se estagnado como teoria pronta e completa, advindo de cientistas importantes como Galileu Galilei e Sir Isaac Newton. As leis fundamentais da mecânica pareciam funcionar de forma coerente a realidade em qualquer aspecto, tratando o estudo dos movimentos como algo natural à condição humana. Com o advento do desenvolvimento da física, principalmente na área do eletromagnetismo, com respeito à constante da luz em 1865 por James Clerck Maxwell, muitos conceitos relacionados ao movimento tiveram que mudar ou serem revistos.
Surgiu então a conhecida questão de Einstein que foi responsável por umas das primeiras e grandiosas formulações físicas do mesmo, em se questionar: Se pudéssemos então viajar em um feixe de luz, como observaríamos um raio de luz? Essa indagação paradoxal levantou de forma icônica o questionamento de Einstein. Como resposta, forneceu a seguinte afirmação: veríamos esse feixe de luz imóvel e sem alterações, como algo em repouso. A resposta parecia um tanto absurda, pois sabia-se na época que um feixe de luz não era imóvel e nunca estaria em repouso. Einstein parecia um pouco duvidoso do seu pensamento, mas atribuiu que se trabalhasse com a ideia de referencial talvez essa resposta duvidosa não parecesse tão perturbadora. Entra então, na física, um dos primeiros momentos em que o termo referencial apareceria como algo decisivo. Einstein gerou outro questionamento, agora sobre as características de movimento em diferentes referenciais inerciais, questionando alguns parâmetros que até então eram considerados absolutos. Einstein então teve um artigo publicado na revista alemã, \textit{Annalen der Physik}, intitulado \textit{"Sobre a eletrodinâmica dos corpos em movimento"}, em 1905, com base em trabalhos de Lorentz e Poincaré, trazendo consigo o fundamento da chamada teoria da Relatividade Restrita ou Especial.
O pensamento de Einstein não era algo tão novo e revolucionário como parecia ser. Galileu Galilei já se questionava a presença ou não de referenciais para então se fundamentar um movimento, quando formalizava a teoria inercial, mencionando que de fato a ideia de movimento absoluto não era algo a se crer, mas que dependia incisivamente de um referencial para ser então formulado. A questão de corpos inerciais em movimento uniforme não ter a condição de percepção e distinção entre movimento e repouso sem um dado referencial já era debatida, como menciona os autores da Ref.~\cite{Porto} em dizer que "em outras palavras, Galileu incorporou o conceito de relatividade do movimento, formulando-o, em forma de princípio". O próprio Galileu~\cite{Galileu} reafirma essa ideia também por um trecho de seu livro \textit{"Diálogo sobre os dois máximos sistemas do mundo ptolomaico e copernicano"}, na pele do personagem Salviati afirmando que "o movimento é movimento e como movimento opera, enquanto tem relação com coisas que carecem dele; mas entre as coisas que participam todas igualmente dele, nada opera e é como se ele não fosse".
Tais pensamentos influenciariam de forma direta a formulação da Relatividade Especial para referenciais inerciais, gerando dois postulados fundamentais:
\begin{enumerate}
\item As leis da Física são as mesmas em todos os referenciais inerciais;
\item A velocidade da luz no vácuo tem o mesmo valor de $c$ em qualquer referencial inercial, independente da velocidade da fonte de luz.
\end{enumerate}
O primeiro postulado tem como principal característica trazer à física o caráter invariante, formulando então uma ideia de teoria unificada para a concepção física. O segundo postulado foi o mais robusto conceito capaz de dar fim, de uma vez por todas, à ideia de \textit{"éter luminífero"}~\footnote{A ideia de éter luminífero surgiu, no Séc. XIX, da necessidade de algo que pudesse preencher o espaço dando à luz um meio na qual pudesse se propagar, da mesma forma que acontece ao som, por exemplo, que necessita de um meio material para se propagar; utilizando-se sempre de analogias iniciais para a formulação teórica da ideia física.}, que já tinha sido questionado experimentalmente por Michelson-Morley em 1887, de forma indireta, com o experimento de interferômetro de luz.
Tudo apresentado na idealização da Relatividade Especial, que não será diferente na formulação futura das ondas gravitacionais onde reafirma-se como resultado do desenvolvimento da teoria da Relatividade, possui um caráter unificador e com uma influência direta de interferômetros para a sua concretização experimental. No caso das OG dada pela LIGO, tendo como diferencial a correlação direta com a gravitação de Newton, se formula uma nova visão sobre a gravidade que não tem mais como característica primordial a ação direta e instantânea de corpos por efeitos gravitacionais como era apresentado na gravitação do século XVIII.
Claro que um dos enfoques do respectivo trabalho é dar um embasamento teórico da Relatividade Geral de Einstein, em caráter de familiarização, para fornecer ao leitor uma mínima condição de entendimento das ondas gravitacionais. Mas é quase que impossível falar de Relatividade Geral sem mencionar os avanços de pensamento trazidos pela Relatividade Especial.
Aparentemente, Einstein não estava satisfeito com a particularidade que a Relatividade Restrita trazia ao tratar o movimento apenas em referenciais inerciais, como reafirma os autores da Ref.~\cite{Peruzzo} em dizer que "Einstein ficou insatisfeito com a Relatividade Restrita. Sentia uma forte necessidade de generalizar o princípio da relatividade dos movimentos uniformes a todos os movimentos". Einstein era um grande defensor da ideia de unificação, sendo isso já mostrado no desenvolvimento da Relatividade Especial, e então vivificado mais ainda na formalização da Relatividade Geral, em 1916, publicando na revista Alemã, \textit{Annalen der Physik}, um artigo de 60 páginas com o título \textit{"Fundamentos da Relatividade Geral"}, que segundo o próprio Einstein, "a teoria da Relatividade Especial, comparada com a Relatividade Geral, é brincadeira de criança" e Videira~\cite{Videira} relatando que "a teoria da Relatividade Geral é uma das mais profundas, deslumbrantes e belas produções do espírito humano de todos os tempos".
Einstein trazia consigo toda uma incorporação matemática e idealista sobre a generalização da Relatividade Especial, tornando-a mais completa e abrangente, tentando responder a dois princípios fundamentais que aqui serão apresentados:
\begin{enumerate}
\item A compatibilidade com a teoria gravitacional, após o avanço das leis de Maxwell;
\item Sobre a movimentação de corpos que não eram considerados referenciais inerciais, a fim de trazer uma covariância definitiva no entendimento da dinâmica dos corpos.
\end{enumerate}
Esses dois questionamentos fundamentaram a ideia geral, gerando novas conclusões de como o Universo funciona segundo a Relatividade.
Como já mencionado na seção anterior, a mecânica newtoniana teve seu sucesso concedido tanto pela sua veracidade, quanto por fazer correlações com a gravitação e prescrever movimentos tanto de corpos na Terra como fora dela, trazendo um avanço científico inigualável para a época. Da mesma forma, a Relatividade Especial que mencionava sobre corpos que viajavam próximo ou na velocidade da luz, sofrendo assim os seus efeitos e gerando uma nova mecânica para referenciais inerciais, era preciso também alargar essa fronteira e se compatibilizar com a gravitação, como reafirma os autores da Ref.~\cite{Peruzzo} em dizer que "a generalização da teoria da Relatividade Especial surgiu da necessidade de compatibilizá-la com a descrição da gravidade". E por que compatibilizar com a gravitação? Qual a necessidade? As respostas dessas perguntas vêm da própria influência do avanço que Maxwell trouxe, implementando de forma aberta o termo \textit{campo}, saindo da visão newtoniana de força como algo localizado e instantâneo.
Os corpos sobre efeitos gravitacionais não seriam mediados por linhas retas e forças localizadas, mas sim como interação de campos gravitacionais. Os autores da ref.~\cite{Peruzzo} explicam um pouco sobre essa interação de campos mostrando intuitivamente que,
\begin{quote}
Quando se larga um objeto nas proximidades da Terra ele cai em direção ao seu centro. A Terra cria ao seu redor um campo gravitacional. Este campo atua sobre qualquer objeto, provocando o seu movimento de queda. Quando um corpo está sob ação exclusiva do campo gravitacional ele experimenta uma aceleração que não depende do tipo de material nem do estado físico do corpo. (pág. 72)
\end{quote}
Isso parece um pouco não tão alarmante, mas quando pensamos na epistemologia da física, existe uma grande diferença entre o conceito de força e conceito de campo. A Relatividade Geral precisava ser compatível a essa nova ideia e explicar além da mecânica newtoniana. É nesse entendimento de interação de campo gravitacional sobre corpos que Einstein propôs o \textit{"Princípio da Equivalência"}, mostrando que corpos sobre efeitos gravitacionais em queda livre, ou seja, referenciais acelerados, não sentiam o seu peso, ou a influência direta da gravitação. Em outras palavras, Einstein fez a correlação ou a equivalência entre massa gravitacional e massa inercial mostrando que elas são proporcionais. O leitor pode elucidar melhor a ideia do princípio da equivalência observando a Fig.~\ref{equivalencia}.
\begin{figure*}[ht]
\centering
\includegraphics[scale=0.07]{equivalenciaC.jpeg}
\caption{A figura mostra um observador dentro de uma nave espacial sem janelas. Se o observador solta um objeto (quadros a e c), ele não irá saber a diferença entre está parado na superfície da Terra (quadro b), onde a aceleração gravitacional é 9,8 m/$s^2$, ou no espaço sendo acelerado (quadro d) para cima a 9,8 m/$s^2$. (Imagem modificada a partir da original disponível publicamente em http://www.if.ufrgs.br/~thaisa/wp-content/uploads/2017/03/Gravitação-e-princípio-da-equivalência.pdf)}
\label{equivalencia}
\end{figure*}
Através da mecânica newtoniana, podemos relacionar a massa inercial, $M_{iner.}$, de um corpo com a sua aceleração, $a$, através da equação
\begin{eqnarray}
M_{iner.} = \frac{F}{a}\, ,
\label{massin}
\end{eqnarray}
onde $F$ é a resultante das forças que atuam no corpo.
Já para corpos em queda sob efeito gravitacional, sabemos que sofrem uma influência correlacionada com a gravidade como sendo o único ente acelerador, assim obtendo
\begin{eqnarray}
M_{grav.} = \frac{F}{g} \\
F = M_{grav.} \times g \, .
\label{force}
\end{eqnarray}
Substituindo a equação (\ref{force}) na equação (\ref{massin}), tem-se
\begin{eqnarray}
a = \frac{M_{grav.}}{M_{iner.}}\times g \, .
\end{eqnarray}
Considerando então o princípio da equivalência, e que num campo gravitacional a aceleração de um corpo independente da sua estrutura ou estado físico, é fácil compreender que $a=g$, e para isso ocorrer
\begin{eqnarray}
\frac{M_{grav.}}{M_{iner.}} = 1 \\
M_{grav.} = M_{iner.} \, .
\end{eqnarray}
Essa foi a porta de entrada da inclusão da gravitação na Relatividade.
Outro ponto que contribuiu para que a Relatividade Geral fosse formulada foi a tentativa de trazer uma covariância às equações que regiam o movimento dos corpos em uma única equação, ou um conjunto de equações que juntas explicariam tudo, mostrando que as leis da física são as mesmas em qualquer referencial e não mais apenas em referenciais inerciais como a Relatividade Especial trazia. Esse foi o avanço considerável entre a Relatividade Especial e a Geral, a covariância de ideias. É preciso também mencionar os efeitos de toda essa idealização; assim como a Relatividade Especial trouxe seus efeitos relativísticos com as transformações de Lorentz, a Relatividade Geral também trouxe fenômenos interessantes, sendo o mais intrigante e revolucionário, a curvatura do espaço-tempo.
A curvatura do espaço-tempo (cf. Fig.~\ref{curvatura}) é outro efeito relativístico que mostra que corpos supermassivos através de relações gravitacionais curvam o espaço-tempo a sua volta, sendo esse, o primeiro ponto da fundamentação do objetivo principal deste trabalho que são as ondas gravitacionais.
\begin{figure}[!h]
\centering
\includegraphics[scale=0.043]{curvatura2C.jpeg}
\caption{Curvatura do espaço-tempo devido à massa do Sol e da Terra. (Imagem disponível publicamente em https://www.ligo.caltech.edu/WA/image/ligo20160211e)}
\label{curvatura}
\end{figure}
A ideia de curvatura do espaço trouxe outro choque na comunidade acadêmica da época. Saindo das concepções da geometria euclidiana, conhecida a mais de dois milênios, e entrando agora em uma nova geometria, dessa vez curvada, chamada de \textit{"Geometria não-Euclidiana"}, desenvolvida de forma independente pelos matemáticos Jamos Bolyay, Nicolai Lobachevsky, Carl Gauss e Bernhard Riemann~\cite{Riemann}, é então necessária para fazer jus a esse efeito relativístico da teoria. Com essa nova concepção geométrica do espaço, finalizava o ponto chave entre a teoria "einsteiniana" e a teoria newtoniana. Pois agora o movimento de planetas não está mais fundamentado no conceito de força gravitacional como ligação direta, mas sim pelo próprio movimento dos corpos que são pré-definidos devido a curvatura do espaço pela a matéria e energia. No caso do nosso sistema, devido ao o Sol, como enfatizado na Ref.~\cite{Peruzzo}, em dizer que "os planetas não giram em torno do Sol por causa de alguma força misteriosa, mas porque esta é a trajetória determinada pela geometria do espaço-tempo", e também segundo o físico John Wheleer em uma carta sobre a Relatividade, menciona que "a matéria-energia diz ao espaço-tempo como se curvar, e o espaço-tempo diz a matéria-energia, como se mover".
Em 1916, Einstein formalizava matematicamente a curvatura do espaço-tempo através de um conjunto de equações de campo, conhecidas como \textit{"equações de Einstein"}, escritas num espaço quadri-dimensional de Riemann na forma~\footnote{Os índices de Lorentz que aparecem na equação possuem os valores $\mu, \nu, \ldots = 1,2,3,4$.}
\begin{eqnarray}
R_{\mu \nu} - \frac{1}{2}g_{\mu \nu}R = \kappa T_{\mu \nu} \, ,
\label{eqeinstein}
\end{eqnarray}
onde $\kappa$ é dado por
\begin{eqnarray}
\kappa = \frac{8\pi G}{c^4},
\end{eqnarray}
sendo $G = 6,672 \times 10^{-11} N \cdot m^2/kg^2$ a constante gravitacional e $c = 2,997 \times 10^8 m/s$ a velocidade da luz no vácuo. Segundo os autores da Ref.~\cite{Peruzzo}, "esta é uma das mais compactas e poderosas equações dentro da Física".
Seguindo a descrição das Refs.~\cite{Cattani2,Maluf}, temos que do lado esquerdo da equação (\ref{eqeinstein}), o termo $R_{\mu \nu}$ representa o \textit{tensor de curvatura} de Ricci definido por
\begin{eqnarray}
R_{\mu \nu} = R_{\nu \mu} = \partial_{\sigma}\Gamma_{\mu \nu}^{\sigma} - \partial_{\nu}\Gamma_{\sigma \mu}^{\sigma} + \Gamma_{\sigma \tau}^{\sigma}\Gamma_{\nu \mu}^{\tau} - \Gamma_{\nu \tau}^{\sigma}\Gamma_{\sigma \mu}^{\tau} \, ,
\label{tensorricci}
\end{eqnarray}
sendo $\Gamma$ os chamados \textit{símbolos de Christoffel} dados por
\begin{eqnarray}
\Gamma_{\mu \nu}^{\sigma} = \frac{1}{2}g^{\sigma \lambda} \left(\partial_{\mu}g_{\nu \lambda} + \partial_{\nu}g_{\mu \lambda} - \partial_{\lambda}g_{\mu \nu} \right) \, .
\end{eqnarray}
O $g_{\mu \nu}$ é um dos termos mais conhecidos no que se refere a matemática relativística e representa o tensor métrico do espaço. Já o escalar $R$ é conhecido como escalar de curvatura ou invariante de curvatura do espaço e é definido como
\begin{eqnarray}
R = g^{\mu \nu} \left( \partial_{\sigma}\Gamma_{\mu \nu}^{\sigma} - \partial_{\nu}\Gamma_{\sigma \mu}^{\sigma} + \Gamma_{\sigma \tau}^{\sigma}\Gamma_{\nu \mu}^{\tau} - \Gamma_{\nu \tau}^{\sigma}\Gamma_{\sigma \mu}^{\tau}\right) \, .
\end{eqnarray}
Finalmente, $T_{\mu \nu}$ refere-se ao tensor energia-momento da matéria. Ele carrega toda a informação de massa, energia e momento de um sistema a ser estudado.
Podemos observar que as equações de campo de Einstein formam um sistema de dez equações de derivadas parciais, não lineares e de segunda ordem, caracterizando a complexidade da matemática utilizada para a fundamentação da teoria da Relatividade Geral, com estruturas e conceitos um pouco mais rebuscados, que até o próprio Einstein se refere a essa "matematização" da sua teoria dizendo que depois que os matemáticos entraram em sua teoria, nem ele a entenderia mais.
Devemos enfatizar que o motivo da apresentação da matemática introdutória da Relatividade Geral neste trabalho não é de caráter descritivo e minucioso, mas apenas em caráter de conhecimento e familiarização da teoria de campo, necessária ao leitor para compreender que as equações básicas que preveem as ondas gravitacionais podem ser obtidas a partir das equações de campo de Einstein. Um aprofundamento na discussão matemática acerca das ondas gravitacionais pode ser encontrado nas Refs.~\cite{Cattani, Cattani2, Maluf, Cattani3, Cattani4}.
\subsection{Contexto histórico e o desenvolvimento das OG}
O conceito de ondas gravitacionais foi proposto em 1916, onde Albert Einstein publicara o seu primeiro artigo sobre a ideia da sua existência como uma das consequências direta do entendimento sobre a teoria da Relatividade Geral. O problema no que se propõe a seguinte afirmativa, \textit{"ondas gravitacionais propostas em 1916"}, é dar a ideia de que as ondas gravitacionais já estavam de fato fundamentadas e prontas para enfrentar as discussões na comunidade científica, no entando, a afirmação não é correta. Assim como a ideia da relatividade, as ondas gravitacionais não eram um conceito tão novo quanto se parece para a época, já sendo discutido desde o século 18 mas encontrando fundamentos teóricos pra sua existência apenas em meados do século 20, surgindo como um resultado inerente ao desenvolvimento da Relatividade Geral de Einstein. Com isso, o conceito das OG surgiu como resposta para algumas questões que a teoria gravitacional newtoniana não era capaz de prever e explicar como, por exemplo, o prolongamento do periélio de Mercúrio.
O problema de Mercúrio sempre foi uma "pedra no calçado" de vários físicos que adentravam aos estudos gravitacionais. Por ser um sistema de dois corpos e Mercúrio o planeta mais próximo do Sol com orbitas de maior excentricidade, exatamente 0,2056, as relações gravitacionais envolvidas nesse sistema são mais atenuantes do que em qualquer outro sistema de dois corpos, daí então a sua complexidade e visibilidade por parte de estudos. Segundo Kennefick~\cite{Kennefick}, em 1908 o físico Henry Poincaré já mencionava a existência de ondas gravitacionais, sob a influência da teoria eletromagnética de Maxwell, como resposta para a discrepância no prolongamento do periélio de Mercúrio em forma de perda energética, afirmando que "(...) a emissão de ondas gravitacionais a partir da órbita deste planeta interno que se deslocava rapidamente estava removendo energia suficiente de seu movimento para aparecer na forma do deslocamento do periélio~\footnote{Versão livre do original, \textit{"That the emission of gravitational waves from the orbit of this quickly moving inner planet was removing sufficient energy from its motion as to show up in the form of the perihelion shift".} (pag. 38)}", fazendo ainda mais uma analogia com cargas elétricas aceleradas que liberam radiação.
Vale mencionar que a utilização do termo de ondas gravitacionais como resposta ao avanço do periélio de Mercúrio foi debatido anos depois e desmistificado por Einstein em seus trabalhos de escolha de coordenadas para o estudo de ondas gravitacionais.
As ondas gravitacionais, também chamadas de radiação de amortecimento ou ondas de aceleração, surgiram inicialmente em dois âmbitos:
\begin{enumerate}
\item Com o propósito de explicar as adversidades nos estudos de Mercúrio e seu periélio, como também explicar qualquer influência gravitacional que se propague pelo espaço, já que a ideia de uma força gravitacional instantânea de Newton estava perdendo sua concepção, dando a ideia de que se ondas gravitacionais se propagam, deveriam assim fazer com velocidade finita, pois nada poderia superar a velocidade da luz;
\item Conseguir fazer uma correlação entre gravidade e eletromagnetismo. A eletricidade e o magnetismo já haviam sido organizadas anos atrás por James Clerk Maxwell, gerando então, o Eletromagnetismo. Um passo imensurável no entendimento das forças que regem o Universo. Einstein também compartilhava dessa ideia de que era possível mensurar todo o nosso conhecimento físico em uma única força que pudesse explicar tudo. Morreu tentando fazer isso; e as ondas gravitacionais, como já mencionado, nada mais são do que uma tentativa de fazer essa união entre eletromagnetismo e gravitação.
\end{enumerate}
Com Maxwell, não veio apenas o Eletromagnetismo ou a quantização da velocidade da luz, mas também adentrou ao meio físico o ideal de campo. Campo como entidade física, mesmo com sua complexidade no quesito entendimento filosófico, pode ser bem aplicado em diversas situações físicas, dando novas explicações de funcionamento. Esse mesmo ideal, veio parar na gravitação, saindo do termo força e entrando no termo campo, e aí onde está a primeira base analógica entre eletromagnetismo e gravitação que já era discutido no ano de 1908~\cite{Kennefick}.
Campos eletromagnéticos podem gerar ondas eletromagnéticas, não poderia então campos gravitacionais gerar ondas gravitacionais? Essa é a pergunta primordial da sua fundamentação e esse também é o primeiro comparativo, a primeira analogia para então fundamentar as ondas gravitacionais e dar uma fixada na Relatividade Geral de Einstein. Durante os anos de formalização das ondas gravitacionais, muitas analogias foram fundamentais para servirem de base consistente no entendimento e visualização da existência de ondas gravitacionais, isto será discutindo com mais detalhes na próxima seção.
Com o avanço do entendimento das ondas gravitacionais, passando por descrenças e crenças, dois problemas aparecem como decisivos para a estabilização da Teoria:
\begin{enumerate}
\item Como essas ondas se propagam?, visando não somente a ideia matemática (como equações de ondas), mas uma forma conceitual;
\item E qual a fonte dessa irradiação gravitacional? Como ela funciona ou deveria funcionar?
\end{enumerate}
O segundo problema apresentado foi um dos mais complexos a ser examinado, pela dificuldade observacional e experimental das ondas gravitacionais na época, o que levou muitas vezes as descrenças e descartes dessa teoria. Esses são os dois pontos cruciais que levaram uma gama de físicos, matemáticos e engenheiros a buscarem entender um pouco mais sobre as resoluções matemáticas de ondas aplicadas às ondas gravitacionais e a entender sobre sistemas binários, como estrelas e buracos negros, fortes concorrentes a serem capazes de formular ondas gravitacionais, focando um pouco na solução de Schwarzschild para as equações de Einstein.
As ondas gravitacionais só foram começar a ser de fato fundamentadas de forma fixa e predominante em 1937, 21 anos depois da sua apresentação, com uma contribuição importante de Robert Oppenheimer que encontrou discrepâncias nas soluções de Leopold Infeld, assistente de Einstein em meados dos anos 1930, trazendo uma solução final para ondas planas e infinitas, necessárias para fazer das OG um fato existente e consequentemente um progresso inigualável na teoria. Fora Oppenheimer, outros físicos importantes se envolveram na construção filosófica, matemática e física do ideal gravitacional, alguns de forma a negar e comprovar a sua não existência, como Max Abraham, considerado como o primeiro cético à teoria, por publicar um trabalho referindo-se às OG que não poderia desempenhar nenhum papel significativo na teoria relativística da gravitação~\cite{Kennefick} e outros a acreditar na teoria da Relatividade e consequentemente nas suas implicações.
O número de opositores à teoria da Relatividade sempre sucumbiu aqueles que a apoiavam, mesmo após anos de estudos e desenvolvimento da teoria, muitos daqueles que eram opositores acabaram por se tonar fontes indispensáveis no desenvolvimento das OG. Alguns dos exemplos são os físicos Karl Schwarzschild, Gunnar Nordström, Leopold Infeld, Wolfgang Pauli, Max Born e vários outros. Um dos grandes opositores da ideia da existência das OG foi o astrofísico Arthur Stanley Eddington, que questionava uma série de problemas que de fato existiam nos primórdios da idealização de Einstein, como a propagação de onda e energia, a "incapacidade" de demonstração experimental para a época e principalmente no que diz respeito a velocidade de propagação da onda proposta por Einstein. Eddington foi tão grande opositor, da ideia de onda gravitacional se propagando mediante corpos massivos no espaço-tempo, que formulou umas das frases mais icônicas e irônicas na época da formulação das OG, em mencionar que as ondas gravitacionais se propagavam na "velocidade do pensamento". Esse questionamento é mostrado em um artigo publicado pelo próprio Eddington~\cite{Eddington} em 1922.
Essa discussão fervorosa, perdurou por um longo tempo, dando a Eddington, segundo o autor da Ref.~\cite{Kennefick}, o patamar de um dos primeiros céticos fervorosos da teoria, gerando uma verdadeira "perseguição" a Einstein. Eddington não estava errado em questionar o desenvolvimento das OG, pelo contrário, se tornava um impulso para que inúmeros problemas com relação a fundamentação da teoria fossem superados um a um, como menciona Kennefick~\cite{Kennefick}. Como já mencionado no decorrer de todo processo construtivo das OG, a maior dificuldade se deu na sua comprovação experimental, processo crucial na validação teórica, onde a menção inicial seria de que o modelo proposto para supostamente irradiar as ondas mencionadas seriam um sistema binários de estrelas, mas depois sendo mencionado a possibilidade de buracos negros também irradiarem, como proposto por Schwarzschild. Entendia-se que por estarem tão distantes em escala astronômica, as ondas propagadas pelo espaço que chegariam até a Terra, seriam de dimensões tão desprezíveis quanto um alfinete em um palheiro, como apresenta Saa~\cite{Saa} reafirmando que "as estimativas iniciais, feitas pelo próprio Einstein, apontavam corretamente que as amplitudes típicas das ondas gravitacionais seriam minúsculas, talvez não detectáveis na prática"; e outros problemas como: métrica de espaço-tempo, tipo de coordenadas fundamentadas, propagação da onda, funcionamento da fonte (sistema binário), que juntos fizeram até do próprio Einstein, cético da sua ideia, chegando a ponto de mencionar inúmeras vezes que as ondas gravitacionais não existiam como mostra uma carta~\cite{Born} em meados de 1936 escrita pelo próprio Einstein para Max Born, dizendo que "(...) cheguei ao interessante resultado de que as ondas gravitacionais não existem, embora tivessem sido assumidas como uma certeza para a primeira aproximação"~\footnote{Versão livre do original, \textit{"I arrived at the interesting result that gravitational waves do not exist, though they had been assumed a certainty to the first approximation".} (pag. 125)}.
Com a métrica utilizada por Einstein e depois de uma reviravolta com o uso de pseudo-tensores e resoluções de equações linearizadas espaço-temporais, três tipos de ondas são supostamente encontradas e que estão inerentes às ondas gravitacionais, as ondas Longitudinais Longitudinais (LL), Longitudinais Transversais (LT) e as Transversais Transversais (TT) que serão mais detalhadas nas próximas seções deste trabalho. A problemática com o tipo de coordenada utilizada para formalizar as ondas gravitacionais tem uma relação direta com os 3 tipos de equações de onda encontradas por Einstein, pois a sua mudança foi o fator responsável por trazer essa variância dos 3 tipos de ondas. Vale a pena frisar um pouco mais sobre a disputa de coordenada usada por Einstein para viabilizar as OG, pois foi um fator importantíssimo para o andamento da teoria e consequentemente sua fortificação~\cite{Kennefick}.
Inicialmente, Einstein apresenta as ondas gravitacionais trazendo consigo, pela primeira vez, as aproximações linearizadas das equações de campo advinda de teorias anteriores, sendo que a escolha de coordenadas iniciais, as coordenadas unimodulares, deixava os cálculos mais simplórios e fáceis de manipular com um fator de métrica definido por $\sqrt{-g}=1$. Na tentativa de usar as mesmas coordenadas adotadas na aproximação pós-newtoniana com uma falsa impressão de que os cálculos presentes seriam simplificados para o estudo das OG, e na esperança de fazer menção da sua teoria gravitacional ser compatível com a newtoniana em algum aspecto, Einstein comete um erro; com o apoio de Schwarzschild, observa uma discrepância para esse tipo de problema gravitacional, onde a coordenada adotada gerava parâmetros matemáticos inconsistentes, sendo essa umas das primeiras provas concretas de quebra da analogia das ondas eletromagnéticas e a gravitação. Em 1916 Einstein comenta esse fator a Schwarzschild através de carta. Meses após a sua convicção de que ondas gravitacionais não poderiam existir por inconsistência matemáticas, ele mudou a sua forma de analisar as propriedades do estudo, utilizando dessa vez não de uma aproximação pós-newtoniana, mas se utilizando de concepções adotadas na Relatividade Especial e sua aproximação linearizada, também chamada de coordenadas isotrópicas, introduzindo o ideal de OG na Relatividade Geral, sobre influência do astrônomo Willem de Sitter, grande influenciador do desenvolvimento das ondas gravitacionais.
A explicação da utilização de fatores linearizados em uma teoria cujo principal componente é a não linearidade das equações, como a Relatividade Geral, se dá em uma abordagem um pouco diferente sobre as OG na teoria geral. Sendo a teoria da Relatividade Geral embasada em uma geometria não euclidiana, ou seja, espaço-tempo curvos devido a corpos massivos, e a radiação gravitacional como de uma amplitude mínima, quase desprezíveis, pode-se adotar, para esse caso, o espaço não como curvo, mas sim planificado já que as curvaturas causadas pelas ondas gravitacionais seriam mínimas, dando então uma boa chance de encontrar equações condizentes pela sua simplicidade. Com a mudança de aproximações da pós-newtoniana para a Relatividade Especial, em 22 de junho de 1916 em uma carta amigável a Sitter, Einstein abandona de vez a coordenada unimodular de fator $\sqrt{-g}=1$, devido a utilização de potenciais retardados trazendo uma nova aproximação a teoria eletromagnética de campo~\cite{Kennefick}.
Em Janeiro de 1918, Einstein encontra e conserta um erro de derivação em seus pseudos-tensores utilizados para o cálculo das energias em suas equações publicadas em um artigo em 1916, gerando então novas formulações quadripolares para as ondas gravitacionais, sendo explicada como a "fórmula de radiação revisada que expressa a quantidade de energia irradiada por uma fonte de ondas gravitacionais"~\footnote{Versão livre do original, \textit{"revised formula that expresses the amount of energy radiated by a source of gravitational waves".} (pag. 71)}~\cite{Kennefick}, com ajuda do físico irlandês Gunnar Nordström que segundo Kennefick~\cite{Kennefick} era considerado como "um dos primeiros pioneiros da teoria da Relatividade, que foi, de fato, o primeiro a desenvolver uma teoria relativista totalmente auto consistente da gravidade, um ano antes da Einstein"~\footnote{Versão livre do original, \textit{"one of the earlier pioneers of relativity theory, who was in fact the first to develop a fully self-consistent relativistic theory of gravity, a year before Einstein's".} (pag. 71)}. Surge de forma incisiva a ideia de formulações quadripolares, que são importantes para o entendimento de fonte das OG.
Com o avanço da teoria e a "crença" de Einstein em uma teoria unificadora, o mesmo leva o estudo das ondas gravitacionais em meados dos anos 1950, a uma tentativa de unificação entre a estrutura quântica e a gravitação, com relação ao seu pensamento e estudo sobre elétrons atômicos, formalizando o ideal, nomeado anos depois de gravitação quântica, sendo também responsável por trabalhos e estruturação das OG.
Mesmo com todo esforço empreendido, avanços e perdas, as OG só foram ter uma estrutura fixada e predominante nas décadas de 1960 e 1970, onde a sociedade tem como aliado o desenvolvimento tecnológico e avanços da engenharia de detectores, necessários para trazer um avanço inigualável tanto na formalização teórica, quanto e principalmente na realização experimental, fazendo dessa teoria algo real e imponente na sociedade científica, abrindo novas portas para o conhecimento.
\subsection{Processos analógicos para o entendimento das OG}
Nesta seção decorreremos sobre a analogia da formalização científica das OG, enfatizando a possibilidade delas serem a porta de entrada para a unificação do eletromagnetismo e gravitação, sendo amplamente presente e fundamental no desenvolvimento da teoria das OG. O processo de analogia empregada em teorias científicas sempre foi um dos mecanismos mais utilizados na caracterização e entendimento da mesma, servindo como terreno fértil tanto para a descoberta quanto para a controvérsia, tendo como objetivos primordiais:
\begin{enumerate}
\item Trazer um embasamento inicial em conceitos já estruturados e definir modelos teóricos viáveis, contribuindo assim para o desenvolvimento da sua formalização;
\item Gerar uma futura unificação de conceitos físicos na tentativa de encontrar padrões para o desenvolvimento da "teoria de tudo".
\end{enumerate}
São incontáveis os processos científicos embasados por analogias iniciais como parâmetro moldador a fim de chegar a uma teoria concreta e fundamentada, como foi o caso da formalização da teoria cinética dos gases, em 1738, e anos mais tarde a tentativa de modelagem do éter luminífero, no séc. XIX.
A analogia não pode ser entendida como uma menção igualitária e simétrica, mas sim como uma comparação entre dois sistemas de ideias. Até hoje existem muitos embates sobre o significado do termo "analogia" e o que de fato ela pode proporcionar ao entendimento de entes físicos, mas é incontestável a sua eficácia na idealização de parâmetros para o estudo do desconhecido e aprimoramento do conhecido.
Segundo Duarte~\cite{Duarte}, "a analogia não pressupõe, portanto, a existência de uma igualdade simétrica, mas antes uma relação que é assimilada a outra relação, com a finalidade de esclarecer, estruturar e avaliar o desconhecido a partir do que se conhece".
Para enfatizarmos ainda mais esse processo, podemos mencionar Thomas Kuhn, um dos mais respeitados filosóficos científicos do séc. XX, é um grande defensor da ideia de analogias presentes na ciência como uma forma de elucidação de ideias e formulação de teorias primitivas, sendo a partir de então mais palpáveis e lapidáveis.
A presença da analogia no campo de estudo das ondas vem percorrendo um caminho longo desde o século IV a.C. com fundamentos de Aristóteles e demais filósofos gregos e romanos sobre o som, que segundo os mesmos, era uma onda que viajava pelo ar, em analogia com ondas formadas na superfície da água em um copo. Passando para o desenvolvimento físico do século XVIII, com trabalhos de Isaac Newton e Chistiaan Huygens, e século XIX com a proposição da luz como uma onda devido a analogia com a propagação do som, chega-se por fim ao século XX com os teóricos relativistas levantando a ideia analógica entre o eletromagnetismo e a gravitação sugerido a presença de ondas em uma teoria da gravitação.
Esse foi o primeiro momento da presença de analogias para embasar a ideia das ondas gravitacionais, levantando indagações que, se o eletromagnetismo tem uma influência de propagação das ondas eletromagnéticas pode então ter a gravitação a influência de ondas gravitacionais? Em caso particular do desenvolvimento das OG a utilização de ideias analógicas teve um caráter maior, não de explicar e entender a teoria, mas sim de correlacionar uma matemática e de prevê-la com base nos avanços da relatividade, se tornando ainda mais necessária devido à falta de comprovação experimental, sendo reafirmada por Kennefick~\cite{Kennefick} em dizer que "começando com sua abordagem, os teóricos da relatividade analisaram várias analogias com o campo eletromagnético enquanto tentavam construir uma teoria das ondas gravitacionais na ausência de evidências experimentais"~\footnote{Versão livre do original, \textit{"Beginning with his approach relativity theorists looked to various analogies with the electromagnetic field as they attempted to construct a theory of gravitational waves in the absence of experimental evidence".} (pag. 71)}, que somente vai ser dada anos depois, principalmente quando se refere a analogia imediata empregada a teoria gravitacional com o eletromagnetismo de Maxwell, já mencionado em seções anteriores. Segundo Infeld~\cite{Infeld}, assistente de Einstein, a existência das ondas gravitacionais pode ser deduzida da Relatividade Geral, e as ondas eletromagnéticas deduzidas da teoria de Maxwell.
Outro ponto importante para a firmação da analogia com o eletromagnetismo se deu pela ideia da velocidade de propagação de uma onda gravitacional que deveria então respeitar intrinsecamente o dito pela teoria eletromagnética em que nada poderia se propagar com velocidade maior do que a luz. Questão debatida mais tarde por Eddington. Vale ressaltar que a ideia da gravidade se propagar como ondas e com velocidades finitas foi o ponto crucial para a reformulação da teoria gravitacional de Newton. O choque com a ideia eletromagnética que até então parecia tão promissora para uma dada unificação, muda quando começa a se tratar da ideia de como deveria funcionar a fonte emissora dessas ondas gravitacionais, gerando ideais monopolares, dipolares e quadripolares.
Em meados do século XIX a menção "ondas gravitacionais" era incrivelmente relacionada ao estudo das oscilações em superfícies da água, dada em razão do cálculo do próprio peso da água, sendo mais tarde o termo utilizado para se atribuir a ideais gravitacionais~\cite{Kennefick}. Abre-se então uma outra ideia analógica com base nas perturbações na superfície da água devido a propagação de ondas, como podemos observar na Fig.~\ref{ondasagua}, usada como uma demonstração mais simplória e didática sobre o funcionamento de OG. Com o desenvolvimento da teoria, essa analogia nos leva ao modelo mais atual da propagação das ondas gravitacionais como podemos observar na Fig.~\ref{og}.
\begin{figure}[!h]
\centering
\includegraphics[scale=0.30]{ondas_agua.jpeg}
\caption{Surgimento de ondas devido a interação de uma gota com a superfície da água. (Imagem disponível publicamente em https://brasilescola.uol.com.br/fisica/a-classificacao-das-ondas.htm)}
\label{ondasagua}
\end{figure}
\begin{figure}[!h]
\centering
\includegraphics[scale=0.025]{ondas_gravitacionaisC.jpeg}
\caption{Representação das ondas gravitacionais devido à fusão de dois buracos negros. (Frame retirado do video de simulação em https://www.ligo.caltech.edu/mit/video/ligo20160615v1)}
\label{og}
\end{figure}
Essa analogia foi uma das mais fundamentais e importantes para o desenvolvimento da teoria, pois vai ser motivo de discussão sobre a utilização de coordenadas isotrópicas por Einstein, já relatadas anteriormente, e principalmente do funcionamento da fonte emissora. A analogia com as perturbações na água tomou outro enfoque quanto à discussão sobre o espaço de propagação das OG, quando Einstein entende a dificuldade da observação experimental das suas ondas, justamente por possuírem uma amplitude muito baixa para serem detectadas, gerando equações de ondas planas, por conterem baixas amplitudes, as discrepâncias e perturbações no espaço-tempo seriam tão mínimas que poderiam ser consideradas como planas. Essa nova contradição, também já relatado em seções anteriores, tende a ser analisada segundo a analogia das ondas na água.
Essa associação foi de suma importância, pois levou à discussão do funcionamento da fonte emissora das ondas gravitacionais, ponto crucial debatido exaustivamente por Einstein para a fundamentação final da teoria, sendo que ao mesmo tempo que discute algo tão primordial para o desenvolvimento das OG. Aponta também um dos primeiros desequilíbrios entre a analogia eletromagnética e gravitacional, para o entusiasmo dos céticos que não aceitavam tal analogia como Arthur Eddington, Nathan Rosen e principalmente Hermann Bondi por questionar a liberação de energia pelo sistema dipolar e quadripolar. Já era de conhecimento que as radiações eletromagnéticas trabalhavam com sistemas dipolares (cf. Fig.~\ref{dipolo}), onde as perturbações são geradas e se movem ao longo de uma linha, possuindo variação em apenas um eixo, não possuindo uma simetria esférica como os monopolos, mas que ainda possui uma simetria axial, gerando a chamada radiação dipolar.
\begin{figure}[!h]
\centering
\includegraphics[scale=0.70]{dipolo.jpeg}
\caption{Representação de uma interação dipolar. (Figura retirada da Ref.~\cite{Kennefick})}
\label{dipolo}
\end{figure}
Um exemplo didático se dá no funcionamento de antenas de rádio que se relacionam por um dado dipolo. Esse tipo de sistema foi em primeira instancia recusado por um apanhado de físicos quando aplicado a sistemas gravitacionais, tanto por ser inaceitável a ideia de uma gravitação repulsiva, já que os corpos oscilariam em apenas um eixo e também por ferir a ideia de conservação, que no caso gravitacional, deveria se dar pela conservação do momento, onde cada massa acelerada deveria influir o mesmo momento, o que acabaria anulando qualquer influência de campo, não liberando, portanto, radiação. Isso gerou uma discussão fervorosa principalmente entre o maior cético da analogia Eletromagnetismo-Gravitação, Hermann Bondi e o maior defensor e pioneiro na detecção de OG, John Weeler e também com demais cientista. Uma discussão que teve seu início em 1914, devido a sistemas de estrelas binárias e se estendeu até 1970 aplicado a sistemas gravitacionais. Entendeu-se então que para sistemas gravitacionais onde massas estariam acelerando e que então deveria liberar energia, ponto em que Bondi foi rígido em questionar, só ocorreria em sistemas quadripolares (cf. Fig.~\ref{quadrupolo}) que se apresenta em um sistema com movimentos em torno de dois eixos separados, logo quatro polos, em simetria, muito utilizados na idealização de sistemas binários, a muito já estudados. A quantidade de polos presentes na geração da onda também explica o fato do porquê de OG terem amplitudes tão baixas "inviabilizando" a sua detecção, mostrando que de fato não poderia se apresentar em sistemas dipolares. A apresentação de sistemas quadripolares para OG deu abertura para Einstein formular suas equações de perda de energia em função do tempo com relação a fonte de emissão.
\begin{figure}[!h]
\centering
\includegraphics[scale=0.60]{quadrupolo.jpeg}
\caption{Representação de uma interação quadripolar. (Figura retirada da Ref.~\cite{Kennefick})}
\label{quadrupolo}
\end{figure}
Mesmo tendo uma de suas primeiras contradições, a analogia Eletromagnetismo-Gravitação sempre foi defendida e apresentou uma série de regularidades que contribuíram para o desenvolvimento das OG, não sendo pelo fato de ter encontrado uma discordância que tal analogia perdeu sua credibilidade~\cite{Kennefick}.
\subsection{Ondas gravitacionais e a detecção}
Segundo o LIGO~\cite{ligo}, "as ondas gravitacionais são "ondinhas" no tecido do espaço-tempo causado por alguns dos processos mais violentos e energéticos do Universo", em outras palavras, ondas gravitacionais são oscilações espaço-temporais ocasionadas por corpos super-massivos que ao se colidirem por perda energética, liberam energia em forma de ondas que curvam o espaço-tempo e se propagam na velocidade da luz. Essa é a forma mais simplória de se mencionar OG para o entendimento mútuo.
Mesmo com todo avanço em cima da teoria ondulatória da gravitação, o maior problema da passagem das OG de "simples" teoria para se tornar algo aplicável e real, foi sempre a sua experimentação. Como já mencionado, essa era a "pedra" que Einstein sempre teve que carregar e que o levou muitas vezes a desacreditar na sua teoria, assim como também, era o argumento que muitos dos céticos utilizavam para desestimular aqueles que tanto se esforçavam para dar vida a crença nas OG. Era compreensivo a falta de preparo tecnológico para a detecção das OG na época, sabendo que as revoluções tecnológicas somente tomaram força apenas na metade do séc. XX, mas mesmo assim se tornou um grande empecilho na fundamentação da teoria.
Essa problemática começa a ter outro rumo a partir da década de 1960 e 1970, com Joseph Weber, físico americano e pioneiro na tentativa de detecção das OG, e seus alunos. Vale lembrar que nessa época as OG já possuíam uma estrutura matemática e física bem construída, logo faltava apenas a sua detecção. Com a iniciativa de Weber, começa-se uma verdadeira corrida tecnológica e científica na construção de dispositivos capazes de detectar as tão esperadas OG. Um período que foi essencial para o desenvolvimento tecnológico na Física.
Outro nome icônico na busca pela detecção das OG de Einstein, é Kip Thorne, que segundo Kennefick, foi um dos pioneiros e um dos maiores impulsionadores na criação e manutenção do LIGO, responsável atualmente pela detecção direta das OG. O autor da Ref.~\cite{Kennefick} menciona algo interessante sobre a trajetória de credibilidade de Thorne, mencionando que em 1981, Thorne entra em uma aposta com um dos maiores críticos experimentais das OG, o astrônomo Jeremiah Ostriker, em que as OG seriam detectadas no final do séc. XX, o que de fato não ocorreu e Thorne perdeu a aposta.
Não desacreditando em seu trabalho, em 1992, o LIGO é implementado como um centro de pesquisa e detecção por Kip Thorne, Ronald Drever, físico escocês do CALTECH (California Institute of Technology), e Rainer Weiss, físico americano do MIT (Massachusets Institute of Technology). Juntos e com o apoio da NFS (National Science Foundation) e de outros laboratórios como o VIRGO Interferometer, constroem um dos mais emblemáticos e promissores dispositivos experimentais de meio bilhão de dólares, com o objetivo de detectar as famosas ondas gravitacionais. Após 100 anos da predição de Einstein da existência das OG e 24 anos de pesquisa e trabalho persistente, no dia 11 de fevereiro de 2016, o LIGO divulga para a mídia mundial a observação direta das OG em um artigo intitulado "Observation of Gravitational Waves from a Binary Black Hole Merger" publicado na \textit{Physical Review Letters} \cite{Abbott} entusiasmando a comunidade científica e trazendo luz para novos campos de estudos como a da Astronomia Gravitacional. A divulgação das detecções ocorreu em 2016, mas as detecções em si ocorreram em duas épocas, a primeira em 14 de setembro de 2015 e a segunda em 26 de dezembro de 2015, trazendo uma segurança a mais na confirmação das ondas gravitacionais.
A detecção que o LIGO conseguiu captar veio de um processo já esperado entre buracos negros há 1,3 milhões de anos-luz da Terra. Tal momento na história do desenvolvimento científico, ofereceu não só a comunidade científica provas da existência das OG como também bases reais da ação e existência de buracos negros. Já era predito que os únicos entes capazes de gerar OG que possam se propagar pelo espaço eram estrelas binárias ou um sistema binário de buracos negros, devido a sua elevada massa, como menciona os autores da Ref.~\cite{Cattani} e já citado na introdução deste trabalho. No caso da detecção, o fenômeno ocorreu entre buracos negros de massas respectivamente iguais a 36 e 29 vezes a massa do Sol passando por 3 estágios: \textit{inspiral}, \textit{merger} (ou \textit{plunge}) e por fim o \textit{ringdown} como esquematizado na Fig.~\ref{bbns}.
\begin{figure}[!h]
\centering
\includegraphics[scale=0.60]{bbns.jpeg}
\caption{Representação dos estágios de um BBN captado pelo LIGO com a respectiva estimativa da amplitude de deformação das OG. (Figura retirada da Ref.~\cite{Abbott})}
\label{bbns}
\end{figure}
Com base na Ref.~\cite{Cattani}, podemos obter uma explicação, mais detalhada, sobre cada estágio do sistema binário apresentado na Fig.~\ref{bbns}. Temos que a fase \textit{Inspiral} é a fase inicial da vida de um sistema binário de buracos negros que oscilam um em relação ao outro, com baixa velocidade e com baixa produção de OG. O tempo de diminuição das órbitas é muito grande devido a pequena força de atração. Com o passar do tempo as órbitas vão se encolhendo, devido a perda energética e consequentemente aumenta a velocidade orbital e a liberação de OG fica mais evidente e ativa. A medida em que se aproximam a amplitude da onda atinge o seu máximo, esse é o segundo estágio, \textit{Merger}, que chega a atingir velocidades extremamente elevadas até o ponto que a perda energética sucumbe o sistema e acabam por se fundir em um só buraco negro atingindo uma espécie de estabilidade, essa é a terceira fase conhecida como \textit{ringdown}. Quando o \textit{ringdown} ocorre, uma gama de energia em forma de OG é liberada de forma violenta. No caso do sistema binário detectado pelo LIGO, o momento de \textit{ringdown} ocorreu em um buraco negro resultante de 62 vezes a massa do Sol, com uma liberação energética em forma de ondas, equivalente a 3 vezes a massa do Sol.
Todo o processo de captação das OG, desde a simulação do BBN até a prova concisa da existência das OG, ocorreu por técnicas de interferômetros de luz instalados em Hanford, Washington (cf. Fig.~\ref{ligo1}), e em Livingston, Louisiana (cf. Fig.~\ref{ligo2}), com um equipamento similar ao interferômetro de Michelson-Morley, produzido em 1887, com espelhos suspensos em sistemas a vácuo em braços de 3 a 4 km de extensão que acabavam por gerar padrões de interferência.
\begin{figure*}[ht]
\begin{minipage}[b]{0.45\linewidth}
\includegraphics[width=\linewidth]{ligo1C.jpeg}
\caption{LIGO - Hanford, Washington DC. (Imagem disponível publicamente em https://www.ligo.caltech.edu/WA/image/ligo20150731d)}
\label{ligo1}
\end{minipage} \hfill
\begin{minipage}[b]{0.45\linewidth}
\includegraphics[width=\linewidth]{ligo2C.jpeg}
\caption{LIGO - Livingston, Louisiana. (Imagem disponível publicamente em https://www.ligo.caltech.edu/WA/image/ligo20150731c)}
\label{ligo2}
\end{minipage}
\end{figure*}
As ondulações gravitacionais ao passarem pelo interferômetro mudam o padrão de interferência, informando que algo passou por aquela região. Como o sistema inteiro estava a vácuo e livre de qualquer influência externa, a mudança do padrão de interferência só poderia ocorrer em duas situações: ou pela mudança da fonte (feixe de luz), ou pela mudança dos braços, no quesito movimentação dos espelhos. Com essa logística, ficava mais claro a identificação das OG. Dados do artigo do LIGO~\cite{Abbott}, publicado em 11 de fevereiro de 2016, mostram que a primeira detecção, identificada por GW150914, chegou até o interferômetro com uma frequência de 35 a 250 Hz e uma amplitude muito baixa de aproximadamente $1,0 \cdot 10^{-21}$ m, como já era de se esperar, amplitudes muito baixas que inviabilizaram por muitos anos a sua detecção. Esse foi um ponto que comprovou que de fato se tratava de OG. A segunda detecção, identificada por GW151226, teve parâmetros semelhantes, com uma frequência que variava de 35 a 450 Hz e uma amplitude de onda de aproximadamente $3,4 \cdot 10^{-22}$ m e que segundo os autores da Ref.~\cite{Cattani}, "esses resultados confirmam que OG finalmente foram detectadas e que elas são geradas pela fusão do sistema BBN"~\footnote{Versão livre do original, \textit{"These results confirm that GW have finally been detected and that they are generated by merging BBH system".} (pag. 7)}. O gráfico da Fig.~\ref{ligo_paper}, demonstra as proporções de amplitudes e frequências captadas pelos dois laboratórios. Os detectores foram calibrados com frequências entre 35 a 350 Hz afim de filtrar o máximo as linhas espectrais observadas e suprimir as grandes flutuações não compatíveis com a calibração do equipamento. Segundo os dados, a onda gravitacional GW150914 chegou primeiro no detector de Louisiana (L1) e após, aproximadamente, alguns milisegundos, chegou ao detector de Hanford (H1), com comprimentos de onda na ordem de gerar os padrões de confirmação.
Os dois parâmetros (L1 e H1) são sobrepostos de forma invertida em termo de 94\%, como é possível ver no primeiro gráfico do lado direito, em L1, para que fosse subtraído as formas das ondas e filtrado os resíduos para melhor análise das curvas da onda, mostrados na terceira linha.
A última linha dos gráficos mostra as ondas sendo compatíveis com a calibração do detector, mantendo sua frequência aumentando com o tempo.
\begin{figure}[h]
\centering
\includegraphics[scale=0.6]{resultados_ligo_og.jpeg}
\caption{Gráficos das amplitudes e frequências das OG detectadas pelo LIGO. (Figura retirada da Ref.~\cite{Abbott})}
\label{ligo_paper}
\end{figure}
\subsection{Ondas gravitacionais direcionadas para o ensino médio}
Após apresentarmos de forma concisa o contexto histórico, físico e matemático do desenvolvimento das OG como teoria, já possuimos a capacidade de entender que tal comprovação é de fato um dos momentos mais importantes no avanço científico e que tem a capacidade de gerar inúmeros frutos de pesquisa e desenvolvimento no entendimento do Universo. Mas as perguntas básicas que fazemos são: de qual forma esse desenvolvimento e avanço pode influenciar o ensino de física nas escolas? Como o professor pode utilizar desses avanços para trazer luz à novas ideias em sala de aula seguindo os parâmetros curriculares escolares?
Antes de discutirmos uma solução para a aplicação do estudo das OG em sala de aula, levando o discente mais próximo da física de fronteira, é preciso entender em que cenário se encontra esse sistema de ensino de física e como o mesmo está sendo passado em sala de aula. Em seu trabalho~\cite{Nascimento}, Nascimento aponta uma ideia de qual cenário o ensino de física se apresenta, quando menciona que "pesquisas no mundo todo têm sugerido que o ensino de Física é via de regra, e salvo honrosas exceções, caótico, pouco frutífero e dicotomizado da realidade de professores e alunos".
Vale a pena discutir essa problemática de ensino, principalmente no quesito ensino de física, pois é na sala de aula que se encontra um dos maiores polos de divulgação científica que funciona basicamente como uma "faca de dois gumes", onde, se utilizado de forma correta, pode-se preparar gerações e gerações a se desenvolverem cientificamente, ou, se utilizado de forma errada pode-se trazer uma visão totalmente desfocada do ensino de física, sendo que infelizmente é o que atualmente mais acontece. Também vale a pena ressaltar que existem uma série de impasses e variáveis que tornam o ensino de física algo totalmente mecânico e desvirtuado, no qual citaremos e discutiremos esses pontos com mais clareza nas próximas seções.
Já é de conhecimento que existe uma diferença entre o desenvolvimento da física e o ensino de física, que infelizmente em muitos casos, parecem não andar de mãos dadas. O que podemos observar é que os avanços da física estão bem à frente do ensino das suas implicações nas salas de aula, e isso é um grande problema, que nos motiva a propor soluções para resolver essa discrepância. O problema reflete principalmente na forma de tornar a ciência acessível à sociedade e consequentemente em desenvolver cientificamente esta sociedade, pois não tendo acesso ao desenvolvimento científico, não há condições de gerar mentes críticas à ciência. Podemos citar algumas afirmações que contribuem para a construção deste esteriótipo, como por exemplo: \textit{"alunos de escolas do ensino básico não possuem condições de aprender temas tão complexos"} ou \textit{"os alunos não irão precisar desse tipo de informação"} e isso acaba refletindo diretamente na ideia de que a "ciência é apenas para cientistas" e que "pessoas leigas não possuem condições de aprender algo um pouco mais avançado e complexo", monopolizando o avanço científico e o excluindo do ensino de física que a muito se encontra desatualizado e repetitivo, dando a visão errada aos discentes de que a física apresentada em sala de aula é uma mera disciplina cuja funcionalidade é a aprovação perante aos sistemas escolares e vestibulares, em geral, sem nenhum raciocínio crítico, inovador e científico, como podemos enfatizar o que os autores da Ref.~\cite{Praxedes} mencionam em dizer que "as pesquisas relacionadas ao ensino de Física demonstram que o ensino atual tem assumido o caráter de preparação para a resolução de exercícios de vestibular".
O ensino de física se encontra defasado no sentido de que boa parte do ano escolar do aluno, o mesmo só possui contato com a física clássica, enquanto observamos o desenvolvimento da física do século XXI, a física que os discentes possuem relação não passa do século XIX, como conclui Pereira e Aguiar~\cite{Pereira} em mencionar que "o ensino de física no nível médio tem se limitado, principalmente a temas da física clássica: mecânica, eletricidade e magnetismo, calor e óptica. Além disso, esse ensino se caracteriza, na maioria das vezes, por aulas teóricas e descritivas, distantes da realidade dos alunos".
Terrazzan~\cite{Adolfo} também menciona sobre essa problemática dizendo que a prática escolar usual exclui tanto o nascimento quanto o entendimento da ciência, pois a grande concentração de tópicos se dá na física desenvolvida, aproximadamente, entre 1600 e 1850.
Vale ressaltar que a menção anterior sobre os discentes terem acesso apenas ao ensino de física clássica, em sua maioria, não desmerece em nenhum caso a sua importância no desenvolvimento científico do aluno.
Segundo Nascimento~\cite{Nascimento}, "a física participa do desenvolvimento científico e tecnológico com importantes contribuições específicas, cujas consequências têm alcance econômico, social e político". Esse sim, é o maior problema que se pode encontrar nas escolas atualmente, onde praticamente o aluno não é estimulado a pensar de forma crítica, a raciocinar de forma científica, mas apenas a "aprender" uma física repetitiva e que por sua vez acaba se tornando um fardo para o aluno. Em outras palavras, muitas vezes o conteúdo visto pelo discente em sala de aula não possui uma ligação com a sua realidade fora dela, sendo reafirmado por Moreira~\cite{Moreira} em mencionar que "o ensino da Física na educação contemporânea estimula a aprendizagem mecânica de conteúdos desatualizados".
Outro problema que será discutido na próxima subseção é a presença da Física Moderna e Contemporânea (FMC) em sala de aula, que é praticamente inexistente, mesmo estando presente nas bases curriculares nacionais, os PCN's. A explicação da escassez da presença da FMC nas escolas é bastante simples, a escola, em sua maioria, não atua mais na formação de novos conhecimentos para o desenvolvimento do aluno, acompanhando o desenvolvimento social, mas atua como um repetidor de ideias sem inovação e desenvolvimento científico do alunado, tendo como base regedora os próprios vestibulares, como menciona o educador Rubem Alves ao afirmar que são os vestibulares que definem as práticas escolares.
Entendendo o real cenário no qual o ensino de física está imerso e todas as suas problemáticas, agora pode-se retornar a pergunta: Como o professor pode se utilizar do avanço científico das OG em sala de aula, dando ao aluno contato a uma física interessante e nova?
Assim como os cientistas e pesquisadores que se empolgaram com a comprovação das OG, assim também deveria se sentir um professor de física em saber que velhos conceitos, já presentes em sala de aula, podem ser renovados e novos apresentados aos seus alunos. Conceitos estes que possuem uma relação direta com o achado das OG, no qual mencionamos:
\begin{itemize}
\item O efeito ondulatório da luz, no quesito propagação construtiva e destrutiva de ondas, fazendo uma menção ao importante experimento de Michelson - Morley, datado como um dos mais memoráveis experimento da física;
\item A abertura ao conhecimento da Relatividade Geral e Restrita de Einstein;
\item A gravidade sobre corpos massivos e suas reais influências no tecido espaço-temporal, conceito este que fica vago no ensino comum abordado em sala de aula, resultando em que o discente ainda tem a ideia de espaço e tempo absoluto da mecânica de Newton;
\item O próprio conhecimento sobre o espaço-tempo;
\item Gerar então novas visões adentrando a um novo universo de conhecimento embasado pela física moderna.
\end{itemize}
São inúmeras as formas que a comprovação das OG podem ser apresentadas ao aluno pelo professor, principalmente ao mostrar que através desses novos conceitos pode-se entender mais a fundo o Universo em que conhecemos, mostrando além daquilo que somente as ondas eletromagnéticas podiam, trazendo então o aluno para uma área interessante da física, tornando o aprendizado mais significativo e assim tirando a visão errônea que a física só serve para uma determinada prova ou vestibular, mas que ela é um grande empreendimento humano, como abordado na Ref.~\cite{Rosella}.
Para melhorar o ensino da física em sala de aula é preciso de uma vigorosa renovação e conceitos interessantes como o de OG, principalmente com relação aos conteúdos que o aluno já possui contato. Esse é um passo fundamental para mostrar ao discente que o desenvolvimento da física ainda consegue surpreender e modificar o pensamento humano. Encontrando essa correlação, entre conceitos novos e aquilo que os discentes veem em sala, traz uma nova visão real da atuação da física, mostrando que a mesma não se limita apenas às atividades escolares, como muitos discente pensam. Essa correlação mostra ao aluno o que de fato a física é, uma ciência que tem como capacidade primordial mudar visões sobre o universo a sua volta se tornando aplicável e real.
É compreensivo gerar a concepção de que independentemente das comprovações das OG de forma direta, os conceitos de ondulação, gravitação e os demais apresentados já seriam repassados para o aluno em sala de aula, mas é sabido entender que o professor, que de fato acredita no trabalho da ciência e que ela pode ser acessível a qualquer pessoa, pode ver esse momento da física contemporânea como um impulsionador para ministrar esses conteúdos de forma empolgante e realista, pois estão envolvidas em um recente avanço da física, compartilhando do seu entusiasmo pela ciência com seus alunos e assim gerando um aprendizado significativo. Todo esse contexto é endossado pela afirmação de Moreira~\cite{Moreira} em dizer que o "Ensino de Física não é uma questão de encher um cérebro de conhecimentos, mas de desenvolver esse cérebro em Física".
A escola ainda se apresenta como o maior palco de divulgação científica e a ideia da inclusão não só de conceitos como as de OG mas de qualquer assunto referente a FMC, dá nova luz ao conhecimento do aluno, podendo até influenciar nas escolhas profissionais dos mesmos, como menciona os autores da Ref.~\cite{Renner} em enfatizar a presença de tais conteúdos em sala de aula podem sim influenciar jovens a procura de carreiras científicas, pois constituem, potencialmente, os futuros pesquisadores e professores de física.
\subsubsection{Problemáticas do ensino de Física Moderna e Contemporânea nas escolas}
Abordaremos nesta subseção a problemática da inserção da FMC nas escolas, apontando possíveis motivos da não inclusão dessa temática e como resolver essa curricularização, afim de trazer uma maior compreensão e resolução do cenário em que o ensino de física está imerso.
O cenário atual do ensino de física no País é de quase total estagnação quando olhamos para a grade curricular, onde ano após ano os mesmos assuntos e as mesmas aulas são ministradas, sem nenhum tipo de inovação do conhecimento apresentado em sala de aula, o que acaba por refletir de forma direta de como os discentes veem a disciplina. Sabendo disso, gera-se uma pergunta que acaba por embasar a nossa abordagem: Quais são as dificuldades encontradas no cenário do ensino de física que inviabilizam a manutenção do ensino e a fortificação do ensino de física moderna e contemporânea nas escolas?
Antes de responder a pergunta, precisa-se entender primordialmente qual a importância da presença da FMC nas escolas, pois sabendo da sua importância fica mais claro discutir sobre sua falta perante o ensino de física. A Ref.~\cite{Renner} ressalva sobre a inserção de tópicos relacionados à FMC no Ensino Médio ser de grande relevância, podendo proporcionar aos discentes o entendimento do mundo atual, tornado os conceitos mais significativos.
Logo, entende-se que a presença da FMC nas escolas traz ao aluno luz sobre novas fronteiras de conhecimento e cultura. Além disso, um contato direto com uma física mais interessante, despertando então no discente mais afinidade e consequentemente um melhor envolvimento com a disciplina. Agostin~\cite{Agostin} menciona essa importância da FMC para o discente ao dizer que a cultura científica deve fazer parte da cultura do educando. Isso é possível se a inserção dos conceitos da Física Moderna e Contemporânea estiver associado a um processo de aplicação da cultura do educando.
Compreendendo a importância da FMC e tudo que ela pode proporcionar ao aluno, podemos agora apontar as principais causas da sua inconsistência em sala de aula e principalmente como tentar resolvê-las. O primeiro ponto crucial da problemática da presença da FMC em bases curriculares, vem dos próprios vestibulares que não possuem a estimativa de abordar tais temas em suas provas e bases, mesmo tendo o propósito em comum de abordar questões do cotidiano e de contextualizar problemas físicos, como o ENEM (Exame Nacional do Ensino Médio). Não existe nenhuma menção de física moderna, tanto analisando editais recentes em seus conteúdos programáticos disponibilizados pelo INEP (Instituto Nacional de Estudos e Pesquisas Educacionais Anísio Teixeira), quanto analisando as suas competências e habilidades da prova, o que se parece meio contraditório em se tratando do maior sistema de avaliação de conhecimento do país, pois a base regedora a educação brasileira, os Parâmetros Curriculares Nacionais (PCN) menciona a importância do contato do aluno com os conteúdos atualizados e recentes, colocando assim o discente frente a inovações e avanços no conhecimento científico. Infelizmente, isso na prática, não é o que acontece.
Com base na visão apresentada, qual a relação das bases regedoras dos vestibulares na falha da inserção do ensino de FMC nas escolas? A resposta é simplória. Como mencionado anteriormente, as escolas, internamente, são direcionadas pelos vestibulares. Assim que é posto como conteúdo direcionado para tal exame de avaliação, as escolas, em sua maioria, adotam tal regimento focando na preparação e aprovação ao final da jornada escolar do aluno, não dando espaço para professores, na maioria das vezes, trabalharem assuntos fora dessa grade curricular, sendo esse então uma das maiores problemas encontrados que barram o avanço do conhecimento em sala de aula.
Outro ponto crucial na implementação da FMC no sistema escolar, vem muitas vezes por parte do professor, tanto no quesito de má preparação do professor, quanto no quesito ausência de formação na área, o que é mais comum do que se imagina, quanto na carência de sua formação nesses respectivos assuntos, como relatividade, ondas gravitacionais, física de partículas e muitas outras temáticas contemporâneas do ensino de física. Agostin~\cite{Agostin} menciona essa problemática em assegurar que alguns professores não se sentem seguros em lecionar conteúdos de Física Moderna e Contemporânea devido a uma formação inadequada.
Essa deficiência na formação acaba por se tornar uma grande barreira entre o professor e o aluno, sendo o professor uma espécie de canal de informação cujo fluxo é direcionado aos alunos; sem esse fluxo direcionado de forma correta, não há informação precisa. É lógico de mencionar que mesmo com essa problemática apresentada, a má formação docente, também entra em cena como um influente aspecto, o desestímulo do profissional professor que encara situações complicadas e exaustivas a cada dia de trabalho, com pouca valorização, fazendo muitas vezes com que o mesmo perca o interesse de renovar o seu conteúdo em sala de aula e em levar novas ideias para a discussão.
Apontando tais problemáticas de uma forma bem breve e direta, pode-se pensar em uma solução na tentativa de minimizar esse afastamento da FMC das escolas e preparar o campo escolar para a futura incursão da FMC nos currículos escolares. É indiscutível o fato de que é necessário uma renovação rápida no ensino de física a fim de trazer um aprendizado mais significativo, saindo da inércia em que a física entrou dentro da sala de aula. A maior renovação deve vir por parte, principalmente, dos sistemas avaliativos que dão ao aluno ingresso nas Universidades, pois sendo eles, em sua maioria, os regentes daquilo que é apresentado nas escolas, fazendo valer o que os PCN defendem e adotando mais conceitos de FMC em seus testes, no objetivo de avaliar não somente a capacidade conteudista dos alunos, como tem feito atualmente, mas sim de avaliar como anda o aluno perante aos avanços científicos atuais, o avaliando pela capacidade de se contextualizar perante tais avanços. Isso traria um aprendizado mais significativo e consequentemente mais interesse dos alunos nessa área científica. No mesmo segmento, os vestibulares adotando temas como os de FMC em seus testes, as escolas acabariam por tentar se adequar a essa nova investida dos vestibulares e passariam a dar mais espaço ao ensino de FMC em seus estabelecimentos, visando uma melhor preparação dos seus alunos. Consequentemente, com a mudança das temáticas dos vestibulares e as escolas se adaptando a elas, o professor teria uma maior liberdade para compartilhar com seus alunos tais avanços científicos em sala de aula e investindo mais em sua preparação pessoal e profissional, gerando então um efeito em cadeia.
Claro que toda essa proposta iria levar algum tempo para ter mais clareza na sua atuação, mesmo com inúmeras pesquisas que buscam ajudar na renovação do ensino como apresenta Menezes~\cite{Menezes} em dizer que,
\begin{quote}
É claro que precisa ser cautelosa a sinalização para a inclusão desses novos conteúdos, seja pelos desafios didáticos que implica, encontrando professores despreparados e os textos escolares desguarnecidos, seja porque as próprias universidades, ainda por algum tempo, continuarão a solicitar os velhos conteúdos em seus vestibulares. Será preciso algum tempo para que a mensagem seja, primeiro, compreendida e, mais tarde, aceita. (pág. 7)
\end{quote}
É indiscutível a presença da FMC nas escolas, pois prepara seus alunos para a vida, a sociedade e principalmente para os avanços tecnológicos. Com base na exposição dessa problemática, vamos apresentar na seção seguinte uma proposta metodológica para a inserção da FMC nos conteúdos de física, tomando como base o conteúdo de OG.
\section{Metodologia e aplicação}
Para o desenvolvimento da pesquisa usamos uma metodologia de caráter empírico e avaliativo que foi empregada na obtenção de dados necessários para a discussão dos objetivos do trabalho. Com isso, estabelecemos 3 estágios para o seu desenvolvimento:
\begin{enumerate}
\item Apresentação em sala de aula do tema ondas gravitacionais e a discussão sobre sua importância e envolvimento de tal avanço com o currículo escolar dos estudantes presentes;
\item Apresentação do experimento de Michelson-Morley caseiro em sala de aula;
\item Avaliação/Questionário de caráter objetivo e com a intenção de captar dados daquilo que foi compreendido pelos alunos presentes, que responderam a questões do tipo:
\begin{itemize}
\item Você se acha capaz de aprender assuntos que advenham da física moderna como ondas gravitacionais?
\item O que você conseguiu absorver/aprender da aula de introdução sobre ondas gravitacionais?
\item Acredita que o assunto de ondas gravitacionais abordado em sala de aula tem alguma relação direta com conteúdos que você já viu nos anos anteriores?
\item O que você acha da presença de conteúdos da física moderna e contemporânea acrescidos ao currículo escolar? Pode trazer algum benefício ao aprendizado do aluno? Se sim, especifique.
\item A apresentação do experimento de Michelson-Morley melhorou o seu entendimento sobre as ondas gravitacionais e sua detecção?
\item Encontrou alguma dificuldade durante toda a aula de apresentação e demonstração do experimento?
\end{itemize}
\end{enumerate}
\subsection{Construção do interferômetro de Michelson-Morley}
Como uma das propostas desse trabalho, a construção e apresentação do experimento de Michelson - Morley é usado para dar um embasamento da ideia de funcionamento dos interferômetros responsáveis pela comprovação das ondas gravitacionais, pelo LIGO, dando ao aluno um contato mais visual e real do seu funcionamento, já que o assunto de ondas gravitacionais é algo um pouco abstrato e que precisa de mais aprofundamento. A construção do experimento tem também a importante missão da inserção da física experimental em sala de aula, mostrando que a sua presença sempre foi uma excelente ferramenta para sair da inércia do ensino de física e trazer mais luz ao conhecimento apresentado, despertando sempre a curiosidade e o lado investigativo do aluno.
O experimento do interferômetro de Michelson - Morley é um dos mais importantes experimentos já realizados na física, sendo responsável basicamente pelo transpassar de uma física clássica para uma física moderna, trazendo conceitos importantes e quebras de paradigmas que influenciaram diretamente e completamente os passos seguintes do conhecimento físico científico. O seu principal motivo de formulação foi a tentativa de entender mais a fundo o funcionamento da luz e as suas particularidades, já que a comunidade científica aplaudia e se vangloriava com os avanços de Maxwell principalmente pela dada unificação entre a eletricidade e o magnetismo.
O experimento, fundamentado por Albert Michelson e Edward Morley, em 1887, acabou por ser conhecido por um fator fundamental na movimentação da sociedade entre a física clássica e a física moderna, acerca do entendimento do Éter luminífero, propriedade física criada a fim de fundamentar em qual meio a luz deveria se propagar, em analogia com o som, além de fundamentar muitos ideais newtonianos aqui já comentados. Como é de conhecimento, o resultado do experimento foi negativo, descartando a ideia do Éter como propriedade presente no que chamamos de espaço-tempo; um outro resultado do experimento foi a confirmação, já predita por Maxwell, da constância da velocidade luz.
É de imaginar o quanto esses resultados influenciaram no entendimento "progressivo" da física, mudando as concepções físicas estabelecidas, dando espaço para o desenvolvimento da relatividade. Einstein menciona que para desenvolver sua teoria da Relatividade não teve a necessidade de usar nenhum dado advindo de Michelson-Morley, mas que se o soubesse na época da formulação, com certeza iria mencionar o grande feito dos dois cientistas.
A ideia de interferômetro volta à tona tanto na década de 1970, quando foi posto o início para o desenvolvimento tecnológico de equipamentos capazes de detectar as ondas gravitacionais, quanto agora no século XXI, em 2015, quanto a primeira onda gravitacional foi detectada diretamente. Muitos equipamentos foram desenvolvidos com o decorrer dos anos, em diversos países, inclusive no Brasil, com o experimento Mário Schenberg~\cite{Souza} que atualmente está em posse do INPE (Instituto Nacional de Pesquisas Espaciais), com a finalidade de detecção das tão esperadas ondas de Einstein. Mas, entre todas as tecnologias e equipamentos desenvolvidos, os interferômetros tomaram a posse do equipamento capaz de realizar tal feito. Daí a importância que esse trabalho teve em levar um protótipo do interferômetro de Michelson-Morley para a sala de aula, em decorrência da sua importância atual e na tentativa de elucidar as ideias dos alunos sobre a formalização das ondas gravitacionais.
O experimento em sala de aula é desafiador e complicado de ser elaborado, pois possui uma série de variáveis que precisam ser minimizadas, como por exemplo as vibrações presentes no ambiente de execução que podem gerar mudanças no padrão de interferência das ondas, para então ter-se a efetivação do experimento com a geração do seu padrão de interferência, sendo esse um dos maiores empecilhos da sua utilização em sala de aula por parte dos professores de física. Devido a alta sensibilidade do experimento, utilizamos materiais simples em sua fabricação como:
\begin{itemize}
\item Base metálica de 70,0 cm de comprimento por 50,0 cm de largura;
\item 2 espelhos refletores, cada um com 9,0 cm de lado;
\item 1 divisor de feixes de vidro cúbico espesso de 9 cm de lado e 0,50 cm de espessura (podendo ser utilizado outros materiais como acrílico espesso, mas no caso do experimento para a execução desse trabalho foi usado o vidro);
\item 1 laser pointer de 8000 mW de potência, 532 nm de comprimento de onda, utilizado como fonte de luz;
\item 1 anteparo branco de papel.
\end{itemize}
Cada componente do aparato experimental, desde os espelhos, divisor do feixe e a fonte de luz foram montados sobre bases. Os espelhos e a fonte de luz foram colocados em uma base de madeira, e para a base do divisor de feixe foi utilizado o material de isopor a fim de minimizar as vibrações do meio. Com o mesmo motivo de minimizar as vibrações e entendendo que a fonte é um dos mecanismos mais importantes para a execução do experimento, a fonte de luz foi coberta por um material esponjoso e colocado sobre uma estrutura previamente definida para auxiliar no direcionamento do feixe de luz (cf. Fig.~\ref{aparato1}).
\begin{figure}[h]
\centering
\includegraphics[scale=0.80]{aparato1.jpeg}
\caption{Interferômetro de Michelson-Morley construído com materiais de baixo custo.}
\label{aparato1}
\end{figure}
Outros materiais também poderiam ter sido utilizados para complementar o experimento, como por exemplo, a massa de modelar. A mesma poderia ser colocada abaixo da estrutura dos espelhos e também da base que sustenta os componentes com a finalidade de minimizar o efeito de vibração sobre o experimento. Também pode ser usado uma lente focalizadora convergente na saída dos feixes para melhor definição do padrão de interferência. Ambos os materiais não foram necessários para a execução positiva do experimento, sendo, portanto, possível fazer a observação dos padrões de interferência de forma nítida e clara sem o auxílio dos mesmos. Ressaltamos que um dos fatores importantes que levou ao bom funcionamento do experimento foi justamente a potência do laser utilizado. Foram realizados alguns testes com outros tipos de lasers de potências menores e os resultados foram insatisfatórios devido a pouca nitidez e as vezes nenhum tipo de padrão de interferência possível de se visualizar.
Observamos que a maior dificuldade encontrada na montagem do experimento se deu na calibragem do mesmo. Para o seu bom funcionamento, todas as medidas de separação entre divisor-espelhos e divisor-fonte foram feitas cuidadosamente para que os feixes fizessem os mesmos caminhos ópticos e gerassem no anteparo um padrão contínuo e observável. Como podemos observar na Fig.~\ref{aparato2} a separação entre o centro do divisor e os espelhos foi de 17,0 cm e a separação dos espelhos até a base de sustentação do divisor foi de 13,0 cm, assegurando assim que o feixe percorresse o mesmo caminho ótico tanto para o espelho 1, quanto para o espelho 2. A distância entre a base da fonte de luz e a base do divisor foi de 13,0 cm e de 17,0 cm até o centro da base do divisor de feixes, mantendo uma regularidade no caminho ótico do feixe desde a sua saída da fonte até a sua propagação no anteparo. Essa regularidade de caminho ótico se mostrou importantíssimo para a execução de forma positiva do experimento, sendo que em testes anteriores, os padrões de interferência não se efetivam ou se apresentavam com pouca nitidez e difícil visualização.
\begin{figure}[h]
\centering
\includegraphics[scale=0.65]{aparato2.jpeg}
\caption{Medidas para a construção do interferômetro de Michelson-Morley caseiro.}
\label{aparato2}
\end{figure}
Depois de regular o caminho óptico e a calibração estrutural do experimento gerou-se então padrões limpos e nítidos de interferência como também a sua observação de variação do padrão quando movimentado um dos espelhos, variando o caminho ótico e simbolizando como paralelamente ocorreu no interferômetro do LIGO quando a onda gravitacional se propagou pelos espelhos, mudando-os e alterando o caminho ótico, gerando padrões também alterados. A Fig.~\ref{franjas} mostra o resultado dos padrões de interferências encontrados com o interferômetro caseiro.
Para findar a parte de especificações do experimento, todo o aparato proposto acima, foi posto sobre uma base de metal acolchoada embaixo para minimizar mais ainda as vibrações do meio.
\begin{figure}[h]
\centering
\includegraphics[scale=0.08]{interferencia.jpeg}
\caption{Padrão de interferência encontrado em testes do interferômetro caseiro.}
\label{franjas}
\end{figure}
Toda a construção do projeto do interferômetro caseiro saiu em torno de 20 reais, sendo que a maioria dos componentes utilizados foram reaproveitados e podem ser encontrados com muita facilidade. Isso mostra que é um experimento de alta excelência, com importâncias significativas, mas com muito baixo custo, sendo acessível a qualquer profissional da área que tenha a idealização de melhorar o seu ensino em sala de aula, levando os alunos a terem contato com algo mais palpável e visual. O maior problema que se encontra com esse tipo de experimento é a sua calibração e utilização, pois como se trata de um experimento muito sensível, o ambiente em si acaba interferindo muito na sua execução, o que dificulta a realização desse experimento por parte dos professores que muitas vezes não tem tempo algum para utilizarem em sala de aula.
\subsection{Projeto em sala de aula}
O segundo passo de execução e conclusão dessa pesquisa foi ministrar os conceitos teóricos de OG em sala de aula, apresentando o interferômetro caseiro e dando aos alunos conhecimentos renovados e interessantes, principalmente fazendo uma correlação com os conteúdos que os mesmos possuem em sala de aula.
O local escolhido para a prática do projeto foi uma escola particular da cidade de Picos (PI), sendo aplicado em turmas de 2º e 3º ano, justamente pela capacidade de conteúdos já vistos pelos mesmos e envolvendo alunos com diferentes níveis de conhecimento de física, ficando então mais viável apresentar o projeto. O total de alunos participantes do projeto foi de 128 alunos, separados em 3 salas diferentes, que tiveram contato tanto com a ideia de ondas gravitacionais como também com o funcionamento do interferômetro, gerando ao final uma série de questionamentos e interesses. O projeto foi apresentado em três etapas:
\begin{enumerate}
\item A primeira etapa se deu na apresentação do embasamento teórico de ondas gravitacionais. Discussão sobre a importância dessa comprovação na física moderna e a sua relação com os conteúdos já vistos pelos alunos, trazendo o ideal apresentado para algo mais próximo da convivência dos alunos. Uma aula expositiva de 30 a 40 minutos, cujo principal objetivo era fornece conhecimentos necessários e básicos para o entendimento prévio das ondas gravitacionais e consequentemente do funcionamento do interferômetro.
\item A segunda etapa se efetuou com a apresentação do interferômetro caseiro para os alunos a fim de fundamentar o funcionamento dos laboratórios do LIGO.
\item A terceira e última etapa foi formulada com a aplicação de um questionário simples e objetivo com os questionamentos apresentados no início desta seção.
\end{enumerate}
Um importante relato que devemos mencionar, como fruto da aplicação do projeto em sala de aula, foi o interesse que os alunos tiveram ao se deparem com uma física totalmente fora da convivência deles, mesmo que aparentasse ser um conteúdo bem complexo e dificultoso, por um momento os alunos que tiveram contato com o projeto, deixaram um pouco de lado essa barreira que muitas das vezes parece ser intransponível quando fala-se em ensino de física e se atentaram a novidade apresentada ali, levantando questionamentos de suma importância para o acréscimo desta pesquisa. Isso mostra que de fato o ensino de física nas escolas precisa urgentemente de uma renovação curricular, como já mencionado anteriormente.
Ressaltamos que alguns problemas foram encontrados quanto a apresentação em sala de aula, pois sendo um experimento sensível e que necessita de um local com baixa luminosidade para assim concretizar a visualização das franjas de interferência, algumas das salas não contavam com essa baixa luminosidade, o que atrapalhou um pouco a execução em sala de aula, mas na tentativa de suprir essa falta, testes com o interferômetro foram feitos anteriormente à apresentação e por seguinte mostrados aos alunos presentes em sala. Tal empecilho não influenciou em nenhum quesito na opinião dos alunos dado nos questionários apresentados. Nas Figs.~\ref{aula1}-\ref{aula4} pode-se acompanhar sobre a apresentação do projeto em sala de aula.
\begin{figure*}[!ht]
\begin{minipage}[b]{0.47\linewidth}
\includegraphics[width=\linewidth]{aula1.jpeg}
\caption{Aula teórica sobre ondas gravitacionais.}
\label{aula1}
\end{minipage} \hfill
\begin{minipage}[b]{0.47\linewidth}
\includegraphics[width=\linewidth]{aula2.jpeg}
\caption{Apresentação do protótipo do interferômetro caseiro.}
\label{aula2}
\end{minipage}
\end{figure*}
\begin{figure*}[!ht]
\begin{minipage}[b]{0.47\linewidth}
\includegraphics[width=\linewidth]{aula3.jpeg}
\caption{Amostra Experimental do Interferômetro.}
\label{aula3}
\end{minipage} \hfill
\begin{minipage}[b]{0.43\linewidth}
\includegraphics[width=\linewidth]{aula4.jpeg}
\caption{Franjas de interferência encontradas na apresentação do projeto.}
\label{aula4}
\end{minipage}
\end{figure*}
\section{Resultados e discussão}
Após todo um processo de desenvolvimento do protótipo do interferômetro caseiro de Michelson-Morley e apresentação do projeto em sala de aula, onde levamos para a sala o desenvolvimento da física moderna através da temática de ondas gravitacionais, coletamos dados através de um questionário para discutirmos acerca das ideias debatidas neste trabalho e que nessa seção discutiremos sobre a presença das ondas gravitacionais no ensino de física e quais os seus benefícios perante aos discentes.
Os alunos envolvidos no processo de coleta de dados se depararam, após uma breve discussão e apresentação do conceito de ondas gravitacionais, com questões que acabaram por fazê-los raciocinar e darem respostas que mostram de fato como o aluno vê o ensino de física perante o mesmo, colocando declarações que aqui serão mencionadas a fim de embasar mais ainda as ideias apresentadas neste trabalho. Um dos questionamentos fundamentais dessa pesquisa, desde o início de sua formulação, foi de saber se os alunos que estão em séries do Ensino Médio, com currículos escolares preenchidos com o conteúdo da física convencional, poderiam ter certa capacidade de se familiarizarem com conceitos de física moderna e contemporânea em sua trajetória de conhecimento, pois não adianta fazer uma renovação do currículo escolar quanto ao ensino de física, acrescentando ideais de física moderna e contemporânea, que já entendemos ser de grande importância para o desenvolvimento científico dos alunos, sem ao menos entender se os mesmos são capazes de lhe dar com essas novas ideias e trabalhar em cima das mesmas. Com base no que foi apresentado em sala de aula e com os dados coletados a partir dos alunos, que foram instruídos a serem os mais verdadeiros e coerentes em suas respostas, observou-se que dentre os 128 entrevistados, 115 acreditam que são capazes de aprender e lhe dar com conteúdo de física moderna e contemporânea, sobre a prerrogativa de que esse tipo de conteúdo gera mais \textit{"interesse, estímulo e curiosidade para aprender física"} nas palavras de um dos alunos entrevistados, fazendo jus ao que foi mencionado anteriormente.
Dos 128 entrevistados, apenas 4 acreditam que não são capazes de lhe dar com os ideais da física moderna e contemporânea com a prerrogativa de acharem complexo e distante daquilo que conhecem, mantendo a barreira da dificuldade presente. Como podemos observar no gráfico da Fig.~\ref{g1}, quase 90\% dos entrevistados acreditam ser apto em discutir conceito físicos mais modernos, enquanto 3,1\% não acreditam nessa possibilidade. Já 6,25\% dos entrevistados se recusaram a responder esse questionamento.
\begin{figure}[h]
\centering
\includegraphics[scale=0.4]{grafico1.jpeg}
\caption{No gráfico estão relacionados, em termos porcentuais, a capacidade de aprendizado do aluno em temas de Física Moderna e Contemporânea.}
\label{g1}
\end{figure}
Esses dados são de grande importância para a inclusão de conceitos de física moderna e contemporânea em sala de aula, servindo como indicativo para a sua presença perante os discentes, quebrando o estereótipo de que pessoas leigas, alunos leigos a esse tipo de desenvolvimento científico não possuem capacidade de assimilá-lo e compreendê-lo mesmo que de forma superficial.
Outro ponto chave deste trabalho era mostrar que o ideal de ondas gravitacionais está presente naquilo que os alunos já conhecem em sala de aula, mostrando que existe uma forma do professor, preocupado com o desenvolvimento científico dos seus alunos e não apenas nas suas aprovações, introduzir avanços científicos como os de ondas gravitacionais no currículo escolar, se entusiasmando juntamente com seus alunos com os avanços da ciência. Esse é outro indicativo bem defendido nesse trabalho, dando uma abertura a mais para a inclusão desses ideais. Com base no que foi debatido em aula e nos dados colhidos, observou-se que cerca de 74,2\% dos entrevistados conseguem ver algum tipo de relação com aquilo que aprendem ou aprenderam em sala de aula com o avanço da comprovação direta das ondas gravitacionais como podemos observar no gráfico da Fig.~\ref{g2}.
\begin{figure}[h]
\centering
\includegraphics[scale=0.40]{grafico2.jpeg}
\caption{No gráfico mostramos a correlação, em termos porcentuais, entre o conceito de ondas gravitacionais e assuntos já vistos em sala de aula pelos alunos.}
\label{g2}
\end{figure}
Considerando ainda o gráfico da Fig.~\ref{g2}, quase 18\% dos avaliados mencionaram que não conseguem fazer uma correlação com um avanço recente da observação das ondas gravitacionais e os conteúdos vistos em sala. Para critério de complementação, quase 8\% dos entrevistados declinaram em responder esse questionamento. A conclusão que se pode chegar com esse segundo dado é que existem formas tanto do professor quanto do aluno em desenvolverem ideias de física moderna e contemporânea sem sair da grade curricular, servindo como porta de entrada para futura inserção da FMC em sala de aula.
Seguindo com a análise dos dados, como segunda etapa do projeto, foi apresentado o protótipo do experimento de interferômetro de Michelson-Morley como uma analogia ao funcionamento os laboratórios do LIGO, a fim de trazer o avanço gravitacional para mais próximo do aluno. Mesmo parecendo muito distante da realidade, mas com base no experimento apresentado em sala de aula, dos 128 alunos entrevistados, quase a sua totalidade, 122 alunos (95,30\%), viram que a apresentação do experimento de Michelson-Morley ajudou consideravelmente no entendimento mais a fundo do desenvolvimento e processo da comprovação das ondas gravitacionais como podemos observar no gráfico da Fig.~\ref{g3}. Para questão de complementação, apenas 3,10\% dos alunos não observaram melhoria no entendimento do assunto de ondas gravitacionais com o auxílio do experimento, enquanto 1,5\% não quiseram opinar sobre esse questionamento. Esse resultado corrobora com o que já foi mencionado em seções anteriores deste trabalho e em outras pesquisas que defendem de forma indiscutível a presença de experimentos em sala de aula para enriquecer o ensino de física.
\begin{figure}[h]
\centering
\includegraphics[scale=0.40]{grafico3.jpeg}
\caption{No gráfico mostramos, em termos porcentuais, a aplicação do experimento de interferômetro de Michelson-Morley como facilitador no entendimento sobre as ondas gravitacionais.}
\label{g3}
\end{figure}
Discutiremos agora o que os avaliados acham do acréscimo de assuntos de física moderna e contemporânea à sua grade curricular escolar e como ela pode ser útil no seu desenvolvimento. De antemão, pode-se imaginar uma certa relutância da parte dos alunos em aumentar a sua carga horária de estudos em física ou modificá-la, acrescentando assuntos que os mesmos mal possuem contato, mas com base nos dados obtidos na pesquisa, de uma forma contrária do que se imaginava, houve uma aceitabilidade positiva por parte dos discentes nessa questão de acréscimo de conhecimento, mostrando o interesse pelos estudos e contatos com a física contemporânea. Dos 128 dados obtidos, cerca de 75\% acreditam e apoiam a inserção desse tipo de abordagem física em sala de aula, como podemos observar no gráfico da Fig.~\ref{g4}. Esse é um dado bem significativo e positivo para a presença da FMC em sala de aula, levantando mais uma vez questões da mesmice e ultrapassada física apresentada em ambiente escolar com uma certa desaprovação expressada pelos próprios discentes avaliados.
Vale mencionar alguns dos comentários dos alunos avaliados que se expressavam em dizer que acham \textit{"muito importante"} e acreditam na ideia do incremento da física moderna e contemporânea em sala e que estão \textit{"presos a descobertas físicas passadas e acabam alienados a questões relacionadas a física moderna, que caso, estudada em sala de aula, traria muitos benefícios"}. Outro aluno menciona que os conteúdos da escola em ensino de física são \textit{"retrógrados e que necessitam de uma renovação"}, fazendo jus à proposta do trabalho. Outros avaliados mencionam que \textit{"o estudo da física moderna é imprescindível para que os estudantes sejam capazes, além de compreender fenômenos, de ter mais visibilidade sobre o que o estudo da física pode proporcionar de avanços nas mais diversas áreas"}, além também de mencionar a correlação entre o apresentado no projeto e aquilo que os mesmos tem contato em sala de aula em mencionar que \textit{"é uma ideia bastante relacionada a outras, como gravitação e óptica, o que gera uma maior absorção desses conteúdos"}. Todas as declarações aqui mencionadas reforça o que foi defendido no trabalho e mostrando que de fato é necessário uma renovação do ensino de física, dando aos alunos contato com as evoluções e revoluções científicas, mas que também os próprios discentes aparentam desejar essa mudança e renovação.
\begin{figure}[h]
\centering
\includegraphics[scale=0.4]{grafico4.jpeg}
\caption{No gráfico mostramos, em termos porcentuais, a opinião dos discentes acerca da presença da física moderna no currículo escolar.}
\label{g4}
\end{figure}
Ainda com base no gráfico da Fig.~\ref{g4}, apenas 10\% acreditam não achar necessária essa mudança por defenderem a ideia de que tal temática deve ser direcionada apenas a aqueles que cursam ensino superior na disciplina, ou seja, em física, mantendo o estereótipo inicial e 15\% dos entrevistados não quiseram participar dessa avaliação.
Para findar a análise e discussão de dados, durante todo o processo de apresentação do projeto em ambiente escolar, apenas 13,2\% dos 128 alunos avaliados encontraram algum tipo de dificuldade, seja ela experimental ou até mesmo de entendimento e raciocínio do conteúdo de ondas gravitacionais. Em contrapartida, quase 80\% dos avaliados não encontraram uma dificuldade para expressar como podemos observar no gráfico da Fig.~\ref{g5}. Apenas 6,25\% não participaram de tal questionamento.
\begin{figure}[h]
\centering
\includegraphics[scale=0.4]{grafico5.jpeg}
\caption{No gráfico mostramos, em termos porcentuais, a análise de dificuldades de compreensão por parte dos alunos com o tema apresentado.}
\label{g5}
\end{figure}
Após todo o processo de análise e discussão dos dados obtidos, temos bons indícios para implementar a presença da FMC em sala de aula, principalmente pelas opiniões por parte dos alunos que observaram essa necessidade. A física moderna e contemporânea tem muito a acrescentar no crescimento científico dos alunos, os tornando mais abertos ao desenvolvimento e gerando mais qualidade no ensino e no aprendizado, como os próprios entrevistados abordaram durante a aplicação do projeto. Talvez o "efeito dominó" volte a ser aplicado nesse ponto, onde a partir do momento em que os alunos tiverem interesse nessa área, os professores talvez se preocupem mais em se prepararem para apresentar e levar a seus alunos um conhecimento mais abrangente, onde futuramente sendo temas de sistemas avaliativos e como consequência a física moderna e contemporânea estará estabelecida em ambiente escolar, acompanhando o avanço científico. Foi mostrado também que a ideia de ondas gravitacionais em sala de aula, o que parece meio complexo e longe de suas realidades, se tornou algo compreensivo e de grande interesse, levantando questionamentos e trazendo de volta para o aluno aquela vontade de conhecer o funcionamento da física e o mundo que ela explica. Agostin~\cite{Agostin} menciona de uma forma bem geral tudo apresentado nessa seção em dizer que,
\begin{quote}
(...) os alunos têm maturidade para aprender sobre essa temática e indicam que para que a mudança de fato ocorra em sala de aula é preciso dar condições e subsídios para que os professores tenham conhecimento sobre os assuntos, sintam-se confiantes para ensinar e possam assim contribuir para a renovação curricular de Física solicitada nos documentos oficiais. (pág. 5)
\end{quote}
\section{Conclusão}
Com base nos dados apresentados e discutidos observa-se a grande necessidade de renovação em que o currículo escolar do ensino de física precisa passar, sendo almejado não só por professores e pesquisadores nessa área, mas pelos próprios alunos que muitas vezes se sentem alienados por ficarem restrito a apenas um ensino ultrapassado, com didáticas ultrapassadas; alguns dos discente não se importam com tal ideal, justamente por já estarem desestimulados e desconhecidos de que o ensino de física atual continua a contribuir ainda mais para a sua completa rejeição dessa nova abordagem. Os próprios discentes sentem essa necessidade e veem na física moderna e contemporânea uma luz para superar essa barreira da dificuldade em física. O objetivo final desse trabalho foi mostrar que pessoas que não possuem nenhum contato com ciência de fronteira, possuem capacidade e anseio em aprender sobre coisas novas, conhecimentos revolucionários que trazem a sensação de que a física ainda está viva, pois infelizmente no ensino ela aparente está estagnada. O estereótipo inicial apresentado por esse trabalho deve ser quebrado. Cabe aos professores começarem a ter a audácia de desenvolver os alunos cientificamente, mostrando o outro lado da ciência e influenciando em suas escolhas futuras.
Ondas gravitacionais é um marco no século XXI, um marco de desenvolvimento científico e que precisa ser apresentado nas salas de aulas, pois como mencionado anteriormente, lá se encontra o maior polo de divulgação científica e precisa-se aproveitar tal oportunidade, não falando apenas em ondas gravitacionais, mas em assuntos como física de partículas, física nuclear, supercondutores, nanotecnologia e outros mais que devem ser incrementados ao ensino, trazendo nova luz ao conhecimento e seguindo o que já está previsto nas leis que regem a educação do país.
Todo e qualquer ser pensante possui capacidade de entender, compreender e aplicar evoluções e revolução na física, sendo que não só a comunidade científica deva se vangloriar com os avanços que estão a porta da sociedade e com os que virão, mas também o ensino deveria se alegrar e acompanhar tal momento em que a sociedade passa, no quesito desenvolvimento da física. Talvez essa seja a porta de entrada para melhorar o entendimento científico dos alunos e começar a não se preocupar mais com quantidade, mas sim dessa vez, com qualidade. Indícios para isso, esse trabalho mostra que há, precisando apenas por em prática tal idealização e começar a fazer a diferença no ensino de física brasileiro.
Desenvolver pesquisas físicas, acrescendo mais ainda ao nosso entendimento de Universo é de suma importância, mas resolver problemáticas da divulgação científica através do ensino aparenta ser uma problemática bem mais alarmante no Brasil, sendo que ainda, mesmo a longo prazo, pode trazer inúmeros frutos e avanços.
\section*{Agradecimentos}
Os autores agradecem ao Colégio São Lucas, Picos (PI), e ao Instituto Federal de Educação, Ciência e Tecnologia do Piauí - IFPI, \textit{Campus} Picos, pelo suporte e colaboração para a realização da pesquisa; e aos Professores Pedro José Feitosa Alves Júnior e Maria Girlandia de Sousa pela leitura crítica e sugestões para a melhoria da escrita do artigo.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,910 |
Racing on TV 11/11-11/13
Discussion Starter • #1 • Nov 9, 2011
FRIDAY, NOVEMBER 11 (REMEMBRANCE DAY – CANADA)
8:00A-9:30 SPEED
Formula 1 PRACTICE #2, Etihad Airways Abu Dhabi Grand Prix, Yas Marina Circuit, Abu Dhabi, UAE, HD, L
1:30P-2:55 ESPN2
NASCAR Sprint Cup PRACTICE, Kobalt Tools 500, Phoenix International Raceway, HD, L
NASCAR Sprint Cup FINAL PRACTICE, Kobalt Tools 500, Phoenix International Raceway, HD, L
Formula 1 QUALIFYING, Etihad Airways Abu Dhabi Grand Prix, Yas Marina Circuit, Abu Dhabi, UAE, HD, L
12:00n-1:30P SPEED
NASCAR Nationwide Series QUALIUFYING, WypAll* 200, Phoenix International Raceway, HD, L
1:30P-3:00 SPEED
NASCAR Sprint Cup QUALIFYING, Kobalt Tools 500, Phoenix International Raceway, HD, L
NASCAR Nationwide Series COUNTDOWN, WypAll* 200, Phoenix International Raceway, HD, L
NASCAR Nationwide Series WypAll* 200, Phoenix International Raceway, HD, L (expect green at 3:45P)
NASCAR K&N Pro Series West, Casino Arizona 125, Phoenix International Raceway, HD, L
12:15A-2:00 ESPN2
NHRA Full Throttle drag series QUALIFYING, Automobile Club of Southern California Finals, Pomona, CA, HD, SDD
GP2 Championship Series at the Abu Dhabi Grand Prix, Abu Dhabi. UAE, Nov 12-13/11, N
7:30A-10:00 SPEED
Formula 1 Etihad Airways Abu Dhabi Grand Prix, Yas Marina Circuit, Abu Dhabi, UAE, HD, L
2:00P-3:00 ESPN
NASCAR Sprint Cup COUNTDOWN, Kobalt Tools 500, Phoenix International Raceway, HD, L
NASCAR Sprint Cup Kobalt Tools 500, Phoenix International Raceway, HD, L (expect green at 3:15P)
2011 Porsche Rennsport Reunion IV, Laguna Seca, Monterey, CA, Oct 14-16/11, HD, N
7:00P-10:00 ESPN2
NHRA Full Throttle drag series ELIMINATIONS, Automobile Club of Southern California Finals, Pomona, CA, HD, SDD
rickaren Nov 9, 2011 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,727 |
\section{Introduction}
Throughout this paper, $\mk$ is an algebraically closed field of characteristic zero, for example $\mc$. Let $\mk^*=\mk\setminus\{0\}$ and $q\in\mk^*$ is not a root of unity.
Assume that $\sg$ is an indecomposable Lie algebra of dimension $3$, then it is one of the following:
\begin{itemize}
\item{The three dimensional simple Lie algebra $\frak{sl}_2$.}
\item{The three dimensional Heisenberg Lie algebra.}
\item{$\frak{b}_\lambda={\rm span}\{h, x, y\}$ such that $[h,x]=x, [h,y]=\lambda y, [x,y]=0$ for some $\lambda\in\mk^*$.}
\end{itemize}
They are very important in the representation theory of Lie algebras. The simple modules over $\frak{sl}_2$ and the simple modules over Heisenberg Lie algebra have been completely classified in \cite{B}.
If $\lambda$ is not rational, the classification of simple $\frak{b}_\lambda$-modules is not yet done. When $\lambda$ is rational, $\frak{b}_\lambda$ is isomorphic to some $\frak{b}_{m,n}$, which is the three dimensional indecomposable Lie algebra with basis $\{h,x,y\}$ and brackets
\beqs [h,x]=mx, [h,y]=ny, [x,y]=0,\eeqs
for some nonzero integers $m,n$. The simple modules over $\frak{b}_{m,n}$ have been classified, and the classification has a little difference according to ${\rm sgn}(mn)$.
In this paper, we consider the Heisenberg double of quantum groups obtained from the quantized universal enveloping algebra of $\frak{b}_{m,n}$.
\begin{defi}The Hopf algebra $\oq(\frak{b}_{m,n})$ is generated by the elements $a,a^{-1},b,c$ subject to the following relations
\beqs ab=q^nba,\;ac=q^{m}ca,\;bc=cb,\;aa^{-1}=a^{-1}a=1.\eeqs
Its comultiplication $\Delta$, counit $\varepsilon$, antipode $S$ are defined by
\beqs &&\Delta(a)=a\otimes a,\; \varepsilon(a)=1,\; S(a)=a^{-1},\\
&&\Delta(b)=b\otimes a^{-n}+a^n\otimes b,\; \varepsilon(b)=0,\; S(b)=-q^{-n^2}b,\\
&&\Delta(c)=c\otimes a^m+a^{-m}\otimes c,\; \varepsilon(c)=0,\; S(c)=-q^{m^2}c.\eeqs
\end{defi}
\begin{defi}The Hopf algebra $\ou(\frak{b}_{m,n})$ is generated by the elements $K,K^{-1},E,F$ subject to the following relations
\beqs KE=q^{2m}EK,\;KF=q^{-2n}FK,\;EF=FE,\;KK^{-1}=K^{-1}K=1.\eeqs
Its comultiplication $\Delta$, counit $\varepsilon$, antipode $S$ are defined by
\beqs &&\Delta(K)=K\otimes K,\; \varepsilon(K)=1,\; S(K)=K^{-1},\\
&&\Delta(E)=E\otimes K^{m}+1\otimes E,\; \varepsilon(E)=0,\; S(E)=-EK^{-m},\\
&&\Delta(F)=F\otimes 1+K^{-n}\otimes F,\; \varepsilon(F)=0,\; S(F)=-K^{n}F.\eeqs
\end{defi}
Note that $\oq(\frak{b}_{m,n})$ is a quantized analogue of $U(\frak{b}_{m,n})$, at the same time $\ou(\frak{b}_{m,n})$ is a quantized analogue of $U(\frak{b}_{m,-n})$. In particular, $\oq(\frak{b}_{1,1})$ is the quantum Euclidean group and $\frak{b}_{1,-1}$ is the Euclidean Lie algebra. Thus we call $\oq(\frak{b}_{m,n})$ the generalized quantum Euclidean group and call $\frak{b}_{m,-n}$ the generalized Euclidean Lie algebra.
\begin{prop}$\ou(\frak{b}_{m,-n})$ is isomorphic to a Hopf subalgebra of $\oq(\frak{b}_{m,n})$.
\end{prop}
\begin{proof}It is easy to verify that the following map defines an embedding of Hopf algebras:
\beqs K\mapsto a^2,\; E\mapsto a^mc,\; F\mapsto ba^{n}.\eeqs
\end{proof}
There is a unique non-degenerate dual pair $\langle\cdot,\cdot\rangle:\ou(\frak{b}_{m,n})\times\oq(\frak{b}_{m,n})\rightarrow\mk$ determined by non-vanishing pairs:
\beqs \langle K, a\rangle={q}^{-1}, \langle K, a^{-1}\rangle=q, \langle E,c\rangle=1,\langle F,b\rangle=1.\eeqs
{\it Note that there are two different non-degenerate dual pairs $\langle\cdot,\cdot\rangle:\oq(\frak{b}_{m,-n})\times\oq(\frak{b}_{m,n})\rightarrow\mk$.
}
This dual pair makes $\oq(\frak{b}_{m,n})$ to be a left $\ou(\frak{b}_{m,n})$-module algebra with the action defined by
\beqs u\cdot x=\sum_{x}x_{(1)}\langle u,x_{(2)}\rangle,\;\forall u\in\ou(\frak{b}_{m,n}), x\in\oq(\frak{b}_{m,n}).\eeqs
Explicitly, the action takes the following form
\beqs &&K\cdot a=q^{-1}a,\;K\cdot b=q^nb,\;K\cdot c=q^{-m}c,\\
&&E\cdot a=0,\;E\cdot b=0,\;E\cdot c=a^{-m},\\
&&F\cdot a=0,\;F\cdot b=a^n,\;F\cdot c=0.\eeqs
We define the {\it Heisenberg double of the generalized quantum Euclidean group}, which is the smash product algebra
\beqs \od(\frak{b}_{m,n})=\oq(\frak{b}_{m,n})\rtimes\ou(\frak{b}_{m,n}).\eeqs
In this paper we are concerned with the Heisenberg double $\od(\frak{b}_{m,n})$ and its representation theory.
\begin{defi}The Heisenberg double $\od(\frak{b}_{m,n})$ of the generalized quantum Euclidean group is the unital algebra generated by the elements $a, a^{-1}, b, c, K, E, F$ subject to the following relations
\beqs&&ab=q^nba,\;ac=q^{m}ca,\;bc=cb,\;aa^{-1}=a^{-1}a=1,\\
&&KE=q^{2m}EK,\;KF=q^{-2n}FK,\;EF=FE,\;KK^{-1}=K^{-1}K=1,\\
&&Ka=q^{-1}aK,\;Kb=q^nbK,\;Kc=q^{-m}cK,\\
&&Ea=aE,\;Eb=bE,\;Ec=cE+a^{-m}K^m,\\
&&Fa=q^naF,\;Fb=q^{-n^2}bF+a^n,\;Fc=q^{mn}cF.\eeqs
\end{defi}
The centrally extended Heisenberg double of $SL_2$ and the Heisenberg double $\od(\frak{b}_{1,1})$ of the quantum Euclidean group were studied by Tao (see \cite{Tao, Tao2}). For the general construction of the Heisenberg double of a Hopf algebra, one is referred to \cite{Lu}.
\section{The weight modules}
Because the map $\xi_K: x\rightarrow KxK^{-1}$ (resp. $\xi_a: x\rightarrow axa^{-1}$) is diagonal, it is possible to study the $K$-weight (resp. $a$-weight) modules over $\od(\frak{b}_{m,n})$.
\begin{defi}A $\od(\frak{b}_{m,n})$-module $V$ is called a $K$-weight module provided that $V=\oplus_{\lambda\in\mk^*}V_\lambda$ where $V_\lambda=\{v\in V:Kv=\lambda v\}$. Denote by ${\rm supp}_K(V)=\{\lambda\in\mk^*|V_\lambda\not=0\}$ the set of all $K$-weights of $V$.
\end{defi}
\begin{defi}A $\od(\frak{b}_{m,n})$-module $V$ is called an $a$-weight module provided that $V=\oplus_{\mu\in\mk^*}V^\mu$ where $V^\mu=\{v\in V:av=\mu v\}$. Denote by ${\rm supp}_a(V)=\{\mu\in\mk^*|V^\mu\not=0\}$ the set of all $a$-weights of $V$.
\end{defi}
Let $\od(\frak{b}_{m,n})^+$ be the polynomial algebra $\mk[E,b]$, let $\od(\frak{b}_{m,n})^0$ be the quantum torus $\mk[K^{\pm1},a^{\pm1}]$ and let $\od(\frak{b}_{m,n})^-$ be the quantum polynomial algebra $\mk[F,c]$. Then as algebra, $\od(\frak{b}_{m,n})$ has a triangular decomposition
\beqs \od(\frak{b}_{m,n})=\od(\frak{b}_{m,n})^-\od(\frak{b}_{m,n})^0\od(\frak{b}_{m,n})^+.\eeqs
Let $b'=a^nbK^{-n}, c'=a^{-m}cK^{-m}, E'=a^{2m}E, F'=q^{-n^2}a^{-2n}FK^n$. Then $\{a^{\pm1}, K^{\pm1}, b',c',E',F'\}$ is also a generating set of $\od(\frak{b}_{m,n})$. In particular, we have
\beqs &&Kb'=b'K,\; Kc'=c'K,\; KE'=E'K,\; KF'=F'K,\\
&&ab'=b'a,\; ac'=c'a,\; aE'=E'a,\; aF'=F'a,\\
&&b'c'=q^{2mn}c'b', \; E'b'=q^{2mn}b'E',\; F'b'=q^{-2n^2}b'F'+1, \\
&&E'c'=q^{2m^2}c'E'+1,\; F'c'=q^{-2mn}c'F',\;E'F'=q^{-2mn}F'E'. \eeqs
Let $S$ be the subalgebra $\mk[b',c',E',F']$, then we have the following isomorphism of algebras
\beqs \od(\frak{b}_{m,n})&\cong&\od(\frak{b}_{m,n})^0\otimes S.\eeqs
\begin{lemma}\label{S-mod}The $S$ has no finite dimensional modules.
\end{lemma}
\begin{proof}Note that $S$ has two subalgebras $S_1=\mk[E',c']$ and $S_2=\mk[F',b']$, both of them are generalized Weyl algebras. It is known that a generalized Weyl algebra has no finite dimensional modules.
\end{proof}
Our first main result is the following theorem.
\begin{theo}\label{weight} (i) Let $V$ be a simple $K$-weight $\od(\frak{b}_{m,n})$-module. Then ${\rm supp}_K(V)=\{q^i\lambda|i\in\mz\}$ for some $\lambda$ and any $K$-weight space of $V$ is a simple $S$-module. In particular, any $K$-weight space of $V$ is infinite dimensional.
(ii) Let $W$ be a simple $a$-weight $\od(\frak{b}_{m,n})$-module. Then ${\rm supp}_a(W)=\{q^i\mu|i\in\mz\}$ for some $\mu$ and any $a$-weight space of $W$ is a simple $S$-module. In particular, any $a$-weight space of $W$ is infinite dimensional.
\end{theo}
\begin{proof} We only prove part (i), the proof for part (ii) is very similar.
Let $V$ be a simple $K$-weight module with a weight $\lambda\in{\rm supp}_K(V)$. Because $a, a^{-1}$ are invertible and $KaK^{-1}=q^{-1}a$, we have
\beqs aV_\mu\subseteq V_{q^{-1}\lambda},\;a^{-1}V_\mu\subseteq V_{q\lambda}.\eeqs
By induction, it holds ${\rm supp}_K(V)\supseteq\{q^i\lambda|i\in\mz\}$. Because $[K,S]=0$, it implies
\beqs S\cdot V_{q^i\lambda}\subseteq V_{q^i\lambda}.\eeqs
So ${\rm supp}_K(V)=\{q^i\lambda|i\in\mz\}$ and any weight space is an $S$-module. If $V_{q^{i_0}\lambda}$ contains a proper submodule $V'$ over $S$, then
\beqs \sum_{i\in\mz}a^{i}V'\eeqs
is a proper $K$-weight submodule over $\od(\frak{b}_{m,n})$. Thus any weight space is a simple $S$-module. By Lemma \ref{S-mod}, any $K$-weight space of $V$ is infinite dimensional.
\end{proof}
\section{Some simple $S$-modules}
In this section, we construct some classes of simple $S$-modules. In particular, all of these modules have GKdim $2$.
\begin{prop}
Let $J_1(\sigma,\tau)$ be the left $S$-ideal generated by $b'-\sigma, c'-\tau$ for all $\sigma,\tau\in\mk$ such that $\sigma\tau=0$. Then $S/J_1(\sigma,\tau)$ is a simple $S$-module of GKdim $2$.
\end{prop}
\begin{proof}
It is obvious that $S/J_1(\sigma,\tau)\cong\mk[E',F']v$ with $b'v=\sigma v, c'v=\tau v$.
If $\sigma=0$, for any $x=\sum_{i=0}\varphi_i(E')(F')^i\not=0$, we have
\beqs b'xv=\sum_{i=1}^I\varphi_i(q^{-2mn}E')c_i(F')^{i-1}v\eeqs
for some nonzero constants $c_i, i\geq 1$. Induction on $I$, we may obtain a nonzero element $\varphi(E')v$. It is known that $\mk[E']v$ is a simple $S_1$-module, so this lemma holds.
If $\tau=0$, the proof is similar.
\end{proof}
\begin{prop}
Let $J_2(\sigma,\tau)$ be the left $S$-ideal generated by $b'-\sigma, E'-\tau$ for all $\sigma,\tau\in\mk$ such that $\sigma\tau=0$. Then $S/J_2(\sigma,\tau)$ is a simple $S$-module of GKdim $2$.
\end{prop}
\begin{proof}
First we have $S/J_2(\sigma,\tau)\cong\mk[c',F']v$ with $b'v=\sigma v, E'v=\tau v$.
If $\sigma=0$, for any $x=\sum_{i=0}\varphi_i(c')(F')^i\not=0$, we have
\beqs b'xv=\sum_{i=1}^I\varphi_i(q^{2mn}c')c_i(F')^{i-1}v\eeqs
for some nonzero constants $c_i, i\geq 1$. Induction on $I$, we may obtain a nonzero element $\varphi(c')v$. Because $\mk[c']v$ is also a simple $S_1$-module, so this lemma holds.
If $\tau=0$, the proof is similar.
\end{proof}
Similar to above, we state the following propositions without proof.
\begin{prop}
Let $J_3(\sigma,\tau)$ be the left $S$-ideal generated by $F'-\sigma, c'-\tau$ for all $\sigma,\tau\in\mk$ such that $\sigma\tau=0$. Then $S/J_3(\sigma,\tau)$ is a simple $S$-module of GKdim $2$.
\end{prop}
\begin{prop}
Let $J_4(\sigma,\tau)$ be the left $S$-ideal generated by $F'-\sigma, E'-\tau$ for all $\sigma,\tau\in\mk$ such that $\sigma\tau=0$. Then $S/J_4(\sigma,\tau)$ is a simple $S$-module of GKdim $2$.
\end{prop}
From above propositions, we obtain various simple $K$-weight modules (resp. $a$-weight modules) of GKdim $3$:
\beqs \sum_{i\in\mz}a^iS/J_k(\sigma,\tau),\quad\left(\hbox{resp.}\sum_{i\in\mz}K^iS/J_k(\sigma,\tau)\right)\quad k=1,2,3,4.\eeqs
In particular, when $m=n=1$, the $\od(\frak{b}_{m,n})$-modules
\beqs \sum_{i\in\mz}a^iS/J_k(0,0),\quad\left(\hbox{resp.}\sum_{i\in\mz}K^iS/J_k(0,0)\right)\quad k=1,2,3,4.\eeqs
cover those modules constructed in \cite{Tao2}.
\section{The prime and primitive spectra of $S$}
\def\pp{\frak{p}}
Let $\pp$ be a proper ideal of a ring $R$. Then for all ideals $\frak{i},\frak{j}$, if $\frak{ij}\subseteq\pp$ then either $\frak{i}\subseteq\pp$ or $\frak{j}\subseteq\pp$. In particular, if $R/\pp$ is a domain, the ideal $\pp$ must be prime. Let ${\rm Spec}(S)$ be the set of all prime ideals of $S$.
Define symbols
\beqs\phi_1=E'c'-c'E',\;\phi_2=F'b'-b'F'.\eeqs
\begin{lemma}
\beqs &&\phi_1\phi_2=\phi_2\phi_1,\;\phi_1F'=F'\phi_1,\;\phi_1b'=b'\phi_1,\;E'\phi_2=\phi_2E',\;c'\phi_2=\phi_2c',\\
&&\phi_1E'=q^{-2m^2}E'\phi_1,\;\phi_1c'=q^{2m^2}c'\phi_1,\;F'\phi_2=q^{-2n^2}\phi_2F',\;b'\phi_2=q^{2n^2}\phi_2b'.
\eeqs
\end{lemma}
\begin{proof}It follows by directly computing.
\end{proof}
Assume $d=(m,n)$. Set $(0)=\{0\}, I_1=S\phi_1, I_2=S\phi_2, I_3=I_1+I_2$.
If $mn>0$, we set
\beqs J_1(z)=S(\phi_1^{|n|/d}-zb'^{|m|/d})+S\phi_2, \quad J_2(z)=S\phi_1+S(\phi_2^{|m|/d}-zc'^{|n|/d}).\eeqs
If $mn<0$, we set
\beqs J_1(z)=S(\phi_1^{|n|/d}-zF'^{|m|/d})+S\phi_2, \quad J_2(z)=S\phi_1+S(\phi_2^{|m|/d}-zE'^{|n|/d}).\eeqs
\begin{prop}The following statements hold.
\item 1. Both $S/I_1$ and $S/I_2$ are domains.
\item 2. $S/I_3$ is simple.
\item 3. Both $S/J_1(z)$ and $S/J_2(z)$ are domains.
\end{prop}
\begin{proof} 1. In the quotient algebra $S/S\phi_1$, we have $E'c'=c'E'$, then $E'c'=q^{2m^2}c'E'+1$ implies $E'c'\in\mk^*$. Consequently,
\beqs S/I_1\cong\mk[E',E'^{-1}][F',b']\cong\mk[c',c'^{-1}][F',b'],\eeqs
which is a domain. In a similar way, $S/I_2$ also is a domain.
2. The quotient algebra $S/I_3$ is isomorphic to the quantum torus $\mk[E'^{\pm1},F'^{\pm1}]$, which is simple.
3. $S/J_1(z)$ is isomorphic to a finite extension of $S_1$. Explicitly,
\beqs S/J_1(z)\cong S_1+S_1\sqrt[|m|]{\phi_1^{|n|}}+S_1\sqrt[|m|]{\phi_1^{2|n|}}+\cdots+S_1\sqrt[|m|]{\phi_1^{(|m|/d-1)|n|}},\eeqs
which is a domain. In special, when $m=\pm n$, $S/J_1(z)\cong S_1$ is simple. The proof for $S/J_2(z)$ is very similar.
\end{proof}
\begin{lemma}
Let $\Omega=\{zb'^ic'^j|z\in\mk^*,i,j\in\mathbb{N}\}$. If $\pp$ is a prime ideal of $S$, then $\Omega\cap\pp=\emptyset$.
\end{lemma}
\begin{proof}
If $zb'^ic'^j\in\pp$, we have $b'^ic'^j\in\pp$. When $i>0$,
\beqs F'b'^ic'^j-q^{-2mnj-2n^2i}b'^ic'^jF'\in\mk^*b'^{i-1}c'^j,\eeqs
thus $b'^{i-1}c'^j\in\pp$. By induction, we infer that $c'^j\in\pp$. Similarly by $E'c'=q^{2m^2}c'E'+1$, we obtain $1\in\pp$ and $\pp=S$, a contradiction.
\end{proof}
\begin{theo}
The prime spectrum of the algebra $S$ is given below,
\beqs{\rm Spec}(S)&=&\{(0), I_1, I_2, I_3\}\cup\{J_1(z)|z\in\mk^*\}\cup\{J_2(z)|z\in\mk^*\}.\eeqs
All the containments of the prime ideals of $S$ are shown in the following diagram
\vskip3mm
\centerline{
\xymatrix{\{J_1(z)|z\in\mk^*\}\ar@{-}[rd]&&I_3\ar@{-}[rd]\ar@{-}[ld]&&\{J_1(z)|z\in\mk^*\}\ar@{-}[ld]\\
&I_1\ar@{-}[rd]&&I_2\ar@{-}[ld]&\\
&&(0)&&}
}
\end{theo}
\begin{proof}We only prove for $mn>0$.
By Lemma 6.3, the spectrum of $S$ is homeomorphic to the spectrum of its Ore extension $S\Omega^{-1}$. Now we consider the Ore extension
$\mathbb{S}=S\Omega_1^{-1}$ with Ore set
\beqs \Omega_1=\{zb'^ic'^j\phi_1^k\phi_2^l|z\in\mk^*,i,j,k,l\in\mathbb{N}\}.\eeqs
In particular, $\mathbb{S}$ is the localization of $S\Omega^{-1}$ obtained by inverting the elements $\phi_1,\phi_2$.
The algebra $\mathbb{S}$ is a quantum torus with the structural matrix
\beqs Q=\left[\begin{array}{cccc}1&q^{2m^2}&1&1\\q^{-2m^2}&1&q^{-2mn}&1\\1&q^{2mn}&1&q^{2n^2}\\1&1&q^{-2n^2}&1\end{array}\right],\eeqs
associated to the variables $\phi_1,c',b',\phi_2$.
Let $\pp_1$ be a prime ideal of $\mathbb{S}$ and given a nonzero element $x\in\pp_1$ such that
\beqs x=\sum_{i,j,k,l}z_{i,j,k,l\mz}b'^ic'^j\phi_1^k\phi_2^l,\eeqs
with finitely many nonzero coefficients. Because
\beqs \phi_1 x-q^{2m^2j_0}x\phi_1=\sum_{i,j,k,l\in\mz}(1-q^{2m^2(j_0-j)})z_{i,j,k,l}b'^ic'^j\phi_1^k\phi_2^l,\eeqs
we can choose $j_0$ such that $z_{i,j_0,k,l}$ for some $i,k,l$. Either $z_{i,j,k,l}=0$ for all $j\not=j_0$ or we obtain a nonzero element with less nonzero coefficients.
Consider the powers $i,k,l$ in the same way and by induction on the number of nonzero coefficients, we can find a monomial $zb'^ic'^j\phi_1^k\phi_2^l\in\pp_1$. Therefore $1\in\pp_1$ and it is impossible. This implies $\mathbb{S}$ is simple.
Consequently, for any nonzero prime ideal $\pp$ of $S$ (equivalent to consider the prime ideal $\pp\Omega^{-1}$ of $S\Omega^{-1}$), either $I_1\subseteq\pp$ or $\phi_2\subseteq\pp$.
When $I_3\in\pp$, since $S/I_3$ is isomorphic to a quantum torus, which is simple, we obtain $\pp=I_3$.
Assume $I_1\subseteq\pp\not=I_3$. Because $S\Omega^{-1}/I_1\Omega^{-1}\cong \mk[b',b'^{-1},c',c'^{-1},\phi_2]$,
there exists an irreducible polynomial
\beqs y=\sum_{i,j\in\mz,k\in\mathbb{N}}z_{i,j,k}b'^ic'^j\phi_2^k\in\pp\Omega^{-1}.\eeqs
Similar to above approach, by considering the number of nonzero coefficients of
\beqs\phi_2y-q^{-2n^2i_0}y\phi_2,\eeqs
we may assume $z_{i,j,k}=0$ except $i=i_0$ for some $i_0$. Multiple by $b'^{-i_0}$, we obtain a nonzero irreducible element
\beqs y_1=\sum_{j\in\mz,k\in\mathbb{N}}z_{j,k}c'^j\phi_2^k\in\pp\Omega^{-1},\eeqs
and hence some
\beqs y_2=\sum_{j=0}^rf_{j}(c')\phi_2^j\in\pp,\eeqs
with $r>0$ and $f_0\not=0$. Because
\beqs b'^iy_2=\sum_{j=0}^rq^{2n^2ij}f_{j}(q^{2mni}c')\phi_2^jb'^i,\eeqs
it implies
\beqs \sum_{j=0}^rq^{2n^2ij}f_{j}(q^{2mni}c')\phi_2^j\in\pp,\eeqs
for all $i\in\mathbb{N}.$ Therefore, we can assume
\beqs y_2=\sum_{j=0}^rz_jc'^{i_j}\phi_2^j\in\pp,\eeqs
such that $nj-mi_j$ is a constant. Such irreducible element of the polynomial ring $\mk[c',\phi_2]$ has to be
$\phi_2^{|m|/d}-zc'^{|n|/d}$ for some nonzero constant $z$. So $J_1(z)\subseteq\pp$. Because $S/J_1(z)$ is simple, we have $\pp=J_1(z)$.
The proof for $I_2\subseteq\pp\not=I_3$ is similar. \end{proof}
\begin{theo}The prime spectrum of the algebra $\od(\frak{b}_{m,n})$ is given below,
\beqs{\rm Spec}(S)=\{(0),\od(\frak{b}_{m,n})^0I_1,\od(\frak{b}_{m,n})^0I_2, \od(\frak{b}_{m,n})^0I_3\}\cup\{\od(\frak{b}_{m,n})^0J_1(z),\od(\frak{b}_{m,n})^0J_2(z)|z\in\mk^*\}.\eeqs
All the containments of the prime ideals of $S$ are shown in the following diagram
\vskip3mm
\centerline{
\xymatrix{\{\od(\frak{b}_{m,n})^0J_1(z)|z\in\mk^*\}\ar@{-}[d]&\od(\frak{b}_{m,n})^0I_3\ar@{-}[rd]\ar@{-}[ld]&\{\od(\frak{b}_{m,n})^0J_1(z)|z\in\mk^*\}\ar@{-}[d]\\
\od(\frak{b}_{m,n})^0I_1\ar@{-}[rd]&&\od(\frak{b}_{m,n})^0I_2\ar@{-}[ld]&\\
&(0)&}
}
\end{theo}
\begin{proof}Because $\od(\frak{b}_{m,n})^0$ is simple, $\od(\frak{b}_{m,n})^0\cap\pp=0$ for any prime ideal of $\od(\frak{b}_{m,n})$. Assume $\pp$ is a prime ideal of $\od(\frak{b}_{m,n})$. Given a nonzero element
\beqs x=\sum_{i,j\in\mz}x_{i,j}K^ia^j\in\pp\eeqs
for finitely many nonzero elements $x_{i,j}\in S$. Then
\beqs K^ra^sxa^{-s}K^{-r}=\sum_{i,j\in\mz}q^{is-jr}x_{i,j}K^ia^j\in\pp.\eeqs
So it is easy to see that $x_{i,j}\in\pp$ for all $i,j$. Hence $\pp=\od(\frak{b}_{m,n})(\pp\cap S)$. The proof is finished.
\end{proof}
For $m=n=1$, this agrees \cite[Theorem 3.6]{Tao2}.
\section{The automorphism groups}
In this section, we investigate the automorphisms of algebras $\oq(\frak{b}_{m,n})$, $\ou(\frak{b}_{m,n})$ and $\od(\frak{b}_{m,n})$.
\begin{theo}
\item 1. For $m=\pm n$, let $\tau\in{\rm Aut}\oq(\frak{b}_{m,n})$ be defined by
\beqs\tau&=&\left\{\begin{array}{ll}a\mapsto a, b\mapsto c, c\mapsto b,&m=n,\\a\mapsto a^{-1}, b\mapsto c, c\mapsto b,&m=-n.\end{array}\right.\eeqs
Then $\{{\rm id},\tau\}\cong\mz_2$.
\item 2. For any $i\in\mz$, let $\xi_i\in{\rm Aut}\oq(\frak{b}_{m,n})$ be defined by
\beqs\xi_i: a\mapsto a, b\mapsto a^{\frac{in}{(m,n)}}b, c\mapsto a^{\frac{im}{(m,n)}}c.\eeqs
Then $\{\xi_i|i\in\mz\}\cong\mz$.
\item 3. For all $z,z_1,z_2\in\mk^*$, let $\zeta_{z,z_1,z_2}\in{\rm Aut}\oq(\frak{b}_{m,n})$ be defined by
\beqs\zeta_{z,z_1,z_2}: a\mapsto za, b\mapsto z_1b, c\mapsto z_2c.\eeqs
Then $\{\zeta_{z,z_1,z_2}|z,z_1,z_2\in\mk^*\}\cong(\mk^*)^3$.
\item4. \beqs{\rm Aut}\oq(\frak{b}_{m,n})&\cong&\left\{\begin{array}{ll}(\mk^*)^3\rtimes(\mz\times\mz_2),&m=\pm n,\\(\mk^*)^3\rtimes\mz,&m\not=\pm n.\end{array}\right.\eeqs
\end{theo}
\begin{proof}It is clear that the statements 1-3 hold. Moreover, the subgroup $G$ generated by $\tau, \xi_i(i\in\mz), \zeta_{z,z_1,z_2}(z,z_1,z_2\in\mk^*)$ is isomorphic to $(\mk^*)^3\rtimes(\mz\times\mz_2)$ and
the subgroup $G_1$ generated by $\xi_i(i\in\mz), \zeta_{z,z_1,z_2}(z,z_1,z_2\in\mk^*)$ is isomorphic to $(\mk^*)^3\rtimes\mz$.
We prove statement 4. Assume $\rho\in {\rm Aut}\oq(\frak{b}_{m,n})$. Obviously, the group $\{za^i|z\in\mk^+,i\in\mz\}=\mk^*\times\langle a\rangle$ is the set of all invertible elements in $\oq(\frak{b}_{m,n})$, which can be generated by
$\mk^*$ and $a$. So this group also can be generated by $\mk^*$ and $\rho(a)$. This implies that $\rho(a)=za^{\pm1}$ for some $z\in\mk^*$.
(i) If $m=n$, $\oq(\frak{b}_{m,n})$ has a decomposition of $a$-weight spaces
\beqs \oq(\frak{b}_{m,n})&=&\bigoplus_{i=0}^\infty \oq(\frak{b}_{m,n})_{q^{im}},\eeqs
under the action $x\mapsto axa^{-1}$, where
\beqs \oq(\frak{b}_{m,n})_{q^{im}}&=&\bigoplus_{r=0}^i\mk[a,a^{-1}]b^{i-r}c^{r}.\eeqs
So either $\rho(b)=xb, \rho(c)=yc$ for some $x,y\in\mk[a,a^{-1}]$ or $\rho(b)=x'c, \rho(c)=y'b$ for some $x',y'\in\mk[a,a^{-1}]$,
and in this case $\rho(a)=za$. Moreover, the elements $x,y,x',y'$ are invertible. By the identity $\rho(b)\rho(c)=\rho(c)\rho(b)$, we also infer that $xy^{-1},x'y'^{-1}\in\mk^*$. Explicitly, there exists $z,z_1,z_2\in\mk^*$ and $i\in\mz$ such that either
\beqs \rho(a)=za,\;\rho(b)=z_1a^ib,\;\rho(c)=z_2a^{i}c,\eeqs
or
\beqs \rho(a)=za,\;\rho(b)=z_1a^ic,\;\rho(c)=z_2a^{i}b.\eeqs
Then $\rho\in G$, the statement holds.
(ii) If $m=-n$, similar to (i), there exists $z,z_1,z_2\in\mk^*$ and $i\in\mz$ such that either
\beqs \rho(a)=za,\;\rho(b)=z_1a^ib,\;\rho(c)=z_2a^{-i}c,\eeqs
or
\beqs \rho(a)=za^{-1},\;\rho(b)=z_1a^{-i}c,\;\rho(c)=z_2a^{i}b.\eeqs
Then $\rho\in G$, the statement holds.
(iii) If $m\not=\pm n$, we have $\rho(b)\in\mk[a,a^{-1}]b$, $\rho(c)\in\mk[a,a^{-1}]c$. Then similar to above, there exists $z,z_1,z_2\in\mk^*$ and $i\in\mz$ such that either
\beqs \rho(a)=za,\;\rho(b)=z_1a^{\frac{in}{(m,n)}}b,\;\rho(c)=z_2a^{\frac{im}{(m,n)}}c.\eeqs
Then $\rho\in G_1$, the statement holds.
\end{proof}
\begin{theo}
\beqs{\rm Aut}\ou(\frak{b}_{m,n})&\cong&\left\{\begin{array}{ll}(\mk^*)^3\rtimes(\mz\times\mz_2),&m=\pm n,\\(\mk^*)^3\rtimes\mz,&m\not=\pm n.\end{array}\right.\eeqs
\end{theo}
\begin{proof}It is straightforward by the isomorphism of algebras
\beqs \ou (\frak{b}_{m,n})\cong\oq(\frak{b}_{2m,-2n}).\eeqs
\end{proof}
\begin{theo}\label{aut}
\item 1. For any $z_1,z_2\in\mk^*$, let $\zeta_{z_1,z_2}\in {\rm Aut}\od(\frak{b}_{m,n})$ be defined by
\beqs K\mapsto z_1K, a\mapsto z_2a, \rho|_S=\id_S.\eeqs
Then $\{\zeta_{z_1,z_2}|z_1,z_2\in\mk^*\}\cong(\mk^*)^2$.
\item 2. For any $A=(A_{i,j})\in SL_2(\mz)$, let $\rho_A\in {\rm Aut}\od(\frak{b}_{m,n})$ be defined by
\beqs K\mapsto K^{A_{1,1}}a^{A_{2,1}}, a\mapsto K^{A_{1,2}}a^{A_{2,2}},\rho|_S=\id_S.\eeqs
The subgroup generated by $\zeta_{z_1,z_2}(z_1,z_2\in\mk^*), \rho_A, (A\in SL_2(\mz))$ is isomorphic to $(\mk^*)^2\rtimes SL_2(\mz)$.
\item 3. For any $z_3,z_4\in\mk^*$, let $\xi_{z_3,z_4}\in {\rm Aut}\od(\frak{b}_{m,n})$ be defined by
\beqs K\mapsto K, a\mapsto a, E'\mapsto z_3E', F'\mapsto z_4F', c'\mapsto z_3^{-1}c', b\mapsto z_4^{-1}b'.\eeqs
Then $\{\xi_{z_3,z_4}|z_3,z_4\in\mk^*\}\cong(\mk^*)^2$.
\item 4.\beqs{\rm Aut}\od(\frak{b}_{m,n})&\cong&((\mk^*)^2\rtimes SL_2(\mz))\times (\mk^*)^2.\eeqs
\end{theo}
\begin{proof}The statements 1 and 3 are clear.
It is also obvious that the map $\rho_A$ is injective. By the definition, one can verify that $\rho_A\circ\rho_B=\rho_{AB}\circ\zeta_{z_1,z_2}$ for some $z_1,z_2\in\mk^*$. This implies $\rho_A$ is an isomorphism since
$\rho_A\circ\rho_{A^{-1}}\circ\zeta_{z_1^{-1},z_2^{-1}}={\rm id}$. Moreover, the subgroup generated by $\zeta_{z_1,z_2}(z_1,z_2\in\mk^*), \rho_A (A\in SL_2(\mz))$ is isomorphic to $(\mk^*)^2\rtimes SL_2(\mz)$, this proves statement 2.
Obviously, the subgroup $G$ generated by $\zeta_{z_1,z_2}(z_1,z_2\in\mk^*), \rho_A (A\in SL_2(\mz)), \xi_{z_3,z_4}(z_3,z_4\in\mk^*)$ is isomorphic to $((\mk^*)^2\rtimes SL_2(\mz))\times (\mk^*)^2$.
We prove statement 4. Assume $\rho\in {\rm Aut}\oq(\frak{b}_{m,n})$.
Clearly, the group $\{zK^ia^j|z\in\mk^*,i,j\in\mz\}$ is the set of all invertible elements in $\od(\frak{b}_{m,n})$. So $\rho(K)=z_1K^ia^j, \rho(a)=z_2K^ra^s$ for some $z_1,z_2\in\mk^*$ and $i,j,r,s\in\mz$. Moreover,
$\rho(K)\rho(a)=q^{-1}\rho(a)\rho(K)$ implies
\beqs\det\left(\begin{array}{cc}i&r\\j&s\end{array}\right)=1.\eeqs
So $\rho|_{\od(\frak{b}_{m,n})^0}\in {\rm Aut}\od(\frak{b}_{m,n})^0$ and
\beqs \rho|_{\od(\frak{b}_{m,n})^0}=\rho_A\circ\zeta_{z_1,z_2},\; A=\left(\begin{array}{cc}i&r\\j&s\end{array}\right).\eeqs
Since $\rho(\od(\frak{b}_{m,n})^0)=\od(\frak{b}_{m,n})^0$, we also have $\rho(S)=S$ by the fact that $S$ is the centralizer of $\od(\frak{b}_{m,n})^0$. Next we consider the automorphisms of $S$.
Because $\rho$ maps prime ideals to prime ideals, it must holds
\beqs\{\rho(\phi_1),\rho(\phi_2)\}=\{x\phi_1,y\phi_2\}\eeqs
for some invertible elements $x,y$, so $x,y\in\mk^*$. Up to an automorphism $\zeta_{z_3,z_4}$, we may assume $x=y=1$.
When $\rho(\phi_1)=\phi_1, \rho(\phi_2)=\phi_2$. Because $\rho(c')\rho(\phi_1)=q^{-2m^2}\rho(\phi_1)\rho(c')$ and $\rho(E')\rho(\phi_1)=q^{2m^2}\rho(\phi_1)\rho(E')$, we have
\beqs\rho(c')=f_1(\phi_1,b',F')c',\; \rho(E')=E'f_2(\phi_1,b',F')\eeqs
and
\beqs\mk^*\phi_1+\mk\ni\rho(c')\rho(E')=f_1(\phi_1,b',F')c'E'f_2(\phi_1,b',F'),\eeqs
this implies $f_1(\phi_1,b',F')f_2(\phi_1,b',F')$ is a constant. Moreover, $\rho(c')\rho(E')=c'E'$ forces
\beqs \rho(c')=zc', \rho(E')=z^{-1}E'\eeqs
for some $z\in\mk^*$. Similarly, $\rho(b')=z'c', \rho(E')=z'^{-1}E'$ for some $z'\in\mk^*$.
When $\rho(\phi_1)=\phi_2, \rho(\phi_2)=\phi_1$. The proof is similar. Hence
\beqs \{\rho|_S \mid \rho\in\od(\frak{b}_{m,n})\}=\{\xi_{z_3,z_4}|_S\mid z_3,z_4\in\mk^*\}={\rm Aut}(S)\cong(\mk^*)^2.\eeqs
The proof is finished.
\end{proof}
\begin{remark}The structure of the automorphism group of $\od(\frak{b}_{m,n})$ is independent on the choice of $m,n$. When $m=n=1$, Theorem \ref{aut} corrects the result of \cite[Theorem 4.5]{Tao2}, in which the automorphism group is $(\mk^*)^4\rtimes \mz$.
\end{remark}
\section*{Acknowledgments}
The author gratefully acknowledge partial financial supports from the National Natural Science Foundation of China (11871249, 12171155).
\def\refname{\centerline{\bf REFERENCES}}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,534 |
package ch.raffael.contracts.processor.cel.ast;
import java.util.List;
import com.google.common.base.Objects;
import com.google.common.collect.ImmutableList;
import ch.raffael.contracts.NotNull;
import ch.raffael.contracts.processor.cel.Position;
/**
* @author <a href="mailto:herzog@raffael.ch">Raffael Herzog</a>
*/
public final class ConditionalOp extends AstNode {
private final AstNode condition;
private final AstNode onTrue;
private final AstNode onFalse;
ConditionalOp(@NotNull Position position, @NotNull AstNode condition, @NotNull AstNode onTrue, @NotNull AstNode onFalse) {
super(position);
this.condition = condition;
this.onTrue = onTrue;
this.onFalse = onFalse;
}
@Override
protected void toString(Objects.ToStringHelper toString) {
// FIXME: Not implemented
super.toString(toString);
}
@Override
public boolean equals(Object obj) {
if ( !super.equals(obj) ) {
return false;
}
ConditionalOp that = (ConditionalOp)obj;
return condition.equals(that.condition)
&& (onTrue.equals(that.onTrue)
&& onFalse.equals(that.onFalse));
}
@Override
public int hashCode() {
int hash = super.hashCode();
hash = appendHash(hash, condition);
hash = appendHash(hash, onTrue);
hash = appendHash(hash, onFalse);
return hash;
}
@NotNull
@Override
protected List<AstNode> children() {
return ImmutableList.of(condition, onTrue, onFalse);
}
@Override
protected void doAccept(AstVisitor visitor) {
visitor.visit(this);
}
@NotNull
public AstNode getCondition() {
return condition;
}
@NotNull
public AstNode getOnTrue() {
return onTrue;
}
@NotNull
public AstNode getOnFalse() {
return onFalse;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,060 |
Live on St. Patrick's Day from Boston, MA é um álbum ao vivo da banda de punk rock Dropkick Murphys. Foi gravado ao longo de três shows no Ballroom Avalon em, como o nome indica, Boston, Massachusetts, e foi lançado em 10 de setembro de 2002.
Faixas
"Intro" - 0:57
"For Boston" (T.J. Hurley) - 1:27
"Boys on the Docks" - 2:26
"Road of the Righteous" - 2:38
"Upstarts & Broken Hearts" - 2:49
"The Gauntlet" - 2:57
"Rocky Road to Dublin" (Tradicional) - 2:36
"Heroes From Our Past" - 3:50
"Finnegan's Wake" (Tradicional) - 2:15
"Which Side Are You On?" (Florence Reece) - 2:31
"A Few Good Men" - 3:12
"Curse of a Fallen Soul" - 3:16
"The Torch" - 3:48
"Gang's All Here" - 4:52
"Forever" - 3:35
"Spicy McHaggis Jig" - 3:23
"John Law" - 1:30
"Wild Rover" (Tradicional) - 3:24
"Fortunate Son" (John Fogerty) - 3:23
"Nutty (Bruin's Theme)" - 1:38
"Good Rats" - 4:10
"Amazing Grace" (John Newton) - 2:28
"Alcohol" (Gang Green) - 1:54
"Barroom Hero" - 2:43
"Dirty Water" (Ed Cobb) - 3:20
"Bloody Pig Pile" - 3:15
Álbuns de Dropkick Murphys
Álbuns ao vivo de 2002 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 856 |
FATE'S STAR
Elizabeth Vaughan
Description:
Five years before the events in Warprize and Destiny's Star...
Her family dead, her home destroyed, all she has left are her wits and her songs...
When the flames of civil war rage across the Kingdom of Palins, Warna of Farentell has no choice but to flee to the neighboring Barony of Tassinic. The daughter of a wealthy merchant, raised to run a noble house in the hope of a good marriage, she watches her future burn with the rest of her homeland.
Elven Lord of a human Barony, betrayed and attacked by those he thought to trust...
Verice of Tassinic has suffered the wounds of war, knowing loss and betrayal at the hands of those he trusted most. He buries himself in work and duty, behind emotional walls as high as those of his castle, rather than risk more pain. While dealing with a kingdom in political and economic turmoil, he 'rescues' Warna only to discover that the helpless human woman is anything but. Before he knows it, she is deep within the defenses of his heart, forcing him to confront his grief, his distrust, and the scars of his past...and maybe even steal his heart in the process.
Praise for The Chronicles of The Warlands
"Over the course of the series, Vaughan has built a fantasy world that is believable, relatable and filled with well-loved characters."—Not a Book Snob on the Warlands Chronicles
"This is a wonderful series with engaging characters that grow and develop with each book."—Sharynn Blood, reviewer
"Warsong is a thrilling, romantic, and epic read filled with beloved characters and daring deeds."—Vicki Stiefel, reviewer
"Vaughan's brawny barbarian romance recreates the delicious feeling of adventure and the thrill of exploring mysterious cultures created by Robert E. Howard in his Conan books and makes for a satisfying escapist read with its enjoyable romance between a plucky, near-naked heroine and a truly heroic hero."—Booklist on Warprize
"Ms. Vaughan has written a wonderful fantasy...The story is well-written and fast paced. Run to the bookstore and pick up this novel. You won't be disappointed by the touching relationship that grows between the Warlord and his Warprize."—A Romance Review on Warprize
"A classic read for me right up there with Linda Howard's MacKenzie's series or Nora Roberts' The Donovan's Legacy series or Anne McCaffrey's Tower and Hive series. If those three are favorites...enjoy this one too!"—Kindle Customer on Warprize
"Full of daring, nobility, and great surprises!"—Leigh Anne Jensen, on Warprize
FATE'S STAR
ELIZABETH VAUGHAN
TABLE OF CONTENTS
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
Chapter 19
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Chapter 24
Chapter 25
Chapter 26
Chapter 27
Chapter 28
Chapter 29
Chapter 30
Chapter 31
Chapter 32
Chapter 33
Chapter 34
Chapter 35
Chapter 36
Chapter 37
Chapter 38
Chapter 39
Chapter 40
Chapter 41
Chapter 42
Chapter 43
Chapter 44
Chapter 45
Chapter 46
Chapter 47
Chapter 48
Chapter 49
Chapter 50
Chapter 51
Chapter 52
Chapter 53
Chapter 54
Chapter 55
Chapter 56
Chapter 57
Chapter 58
Chapter 59
Chapter 60
Chapter 61
Chapter 62
Chapter 63
Chapter 64
Chapter 65
Chapter 66
Chapter 67
Epilogue
About the Author
Acknowledgments
Works by the Author
The events in this book occur about five years before the events in Warprize and Dagger-Star.
To my beloved dead,
gone before,
unseen and unknowing,
yet knowing and seeing,
who wait for me beyond the snows,
within the stars.
Chapter One
Lord High Baron Verice leaned against the cool stone of the window sill and fought the cold inner rage that burned in his heart. He stared down into the gardens below as the men in the room behind him spoke of war.
"You're certain?" Captain Narthing asked in hushed tones.
"Yes," Pernard's voice quavered. "The Barony of Farentell has fallen." Verice heard the weariness in his friend's voice; he shared his pain and grief.
Someone in the garden below was humming a tune that Verice didn't recognize. A faella's voice, someone with a lighter heart than his at the moment. He wished them well of it, for it would not last long.
The breeze caught a strand of his silver hair, and pulled it out of the window. Verice tucked it back behind his pointed ear and took in the scent of flowers and green growing things. Hard to think on death and war when such beauty lay just outside these walls.
But that was his duty and the reason for his visit to Pernard's manor.
Verice turned his head back toward the room. "What of King Everard and his family? Any word?"
Pernard, Captain Narthing and the others stood around the map table. They all shook their heads in the negative.
"None," Pernard whispered.
"All these months," Verice sighed, looking back over the garden. "If they'd escaped, they'd have gotten word to me somehow." Deep within, pain welled. A short life, made even shorter by violent death. Verice took a slow breath and closed his eyes.
"Life is fleeting, life is pain,
What need then to dance in the rain?"
The verse floated up from the garden on the gentle breeze. Verice frowned, trying to spot the singer. Odd, such bitter words sung to such a joyous tune.
Rather like life itself.
He straightened, shoulders back, his hand on his sword hilt and turned to face his people. All of his men, including himself, were armored in black leather and chain with weapons ready to serve. Pernard and his people were garbed in everyday attire, robes over tunics and trous. Verice wondered how long they would have the luxury of regular clothing. "Review the situation for us, Captain."
"Lord High Baron Verice of Tassinic, Lord Mayor Pernard of Anera," Captain Narthing tended to use full titles in meetings such as this. He stood at the head of the map table as Pernard's elven and half-elven warriors crowded around. "It's been confirmed by sources within Edenrich, and by the reports of our scouts that have penetrated the border. The Barony of Farentell has fallen to the forces of the Usurper and the Baroness of the Black Hills."
Dark mutters followed that statement.
"They have laid waste to the land, burning towns and villages," Narthing said. "The people have been killed, taken as slaves, or—" Narthing paused, then continued. "There are rumors that the Baroness is creating odium."
"Ancestors," one of the warriors breathed. "Undead?"
"We've only rumors," Narthing said firmly.
"That would explain the small number of refugees," another mentioned.
"And what refugees crossed over our border are for the most part hardened scum, or very desperate humans. They are causing difficulties all over Tassinic, stretching our City Watches," Narthing said. "But the worst of that tide is probably past," he added.
"There are exceptions," Pernard protested.
Narthing's voice didn't hold much apology. "We will deal with the humans fairly, until they prove otherwise. Interestingly enough, some of those fleeing are speaking of a prophecy of a Chosen One, that will restore Palins."
Verice snorted. Ancestors spare him that.
Narthing continued, "But for right now, with so many maels in the regular army, the watches are spread thin. Lord Pernard, your lands share borders with Farentell and Summerford. Let's see to the placement of your forces to the best advantage, eh?"
Verice stayed silent. Narthing excelled at this; Verice's services weren't needed at the moment. He already knew the ugliness of the reports that he was sharing.
"The Kingdom of Palins seems intent on tearing itself to ribbons," Pernard spoke. "What do we know of the other baronies?"
"Lord Mayor," Narthing said. "Of the eight High Baronies of Palins, six remain intact. To the best of our knowledge, Athelbryght has also fallen. If I may," Narthing pulled out a large map of Tassinic, and spread it out over the table. "So far," he said. "There have been skirmishes along our border, but nothing more than that. And they've usually withdrawn as soon as we arrive to confront them." Narthing made no gesture toward Tassinic's other border, the one with the Elven Kingdom of Valltera. Verice approved. These people had enough worries for the moment.
"They are testing us," a warrior growled.
"We thought them bandits, at first." Pernard pulled forth a smaller map of his town and the surrounding farms. "So far, only two farmsteads have been attacked. The families there managed to flee, and they report seeing the banner of the Black Hills on the attackers."
"I am ordering that you pull everyone in your district within the walls," Verice said. He held up a hand to fend off protests. "We can replace buildings, breed new herds. It's the maels and faellas I value above all else."
"We've stout town walls, thanks to your foresight, m'lord." Pernard said. "It's the farmers you must convince."
"I'll speak to them." Verice gave the mael a wry look. "And use more than words if there's a need. Any so stubborn as to stay on his land is welcome to, but I will demand that the faellas and children be brought to safety."
Verice kept the meeting brief, making sure they understood the important points. Actual details would be worked out later. For now, it was enough that they knew his plans to defend Tassinic.
After enough time for questions, he called the meeting to a close and dismissed them. "We'll reconvene shortly," he commanded. "With the guildmasters and farmers and any others that wish to attend."
They bowed, and streamed out, talking in quiet undertones. He didn't need to hear what they said; there was a lighter note to their voices.
Satisfied, he turned back to the window for a moment. The singer was still in the garden, humming, again. The sound was sweet.
"Lord Verice, perhaps you'd like to take some refreshment with me before the next meeting?" Pernard came to stand beside him. "There's something I'd wish to discuss privately, if you don't mind. Some kav, perhaps?"
"My thanks, Pernard." Verice gestured out the window. "Perhaps we could stroll in your garden for a bit?"
"You would do me an honor," Pernard smiled. "The cuttings you provided have done very well. My roses are particularly lovely this year. And, may I ask, how do yours fare?"
Verice's heart froze. "I've no idea," he clipped out the words. "I haven't stepped foot in the gardens since—" he cut himself off, trying to control his anger.
"Forgive me, m'lord," Pernard apologized with a tilt of his head. "I'll have the kav brought to you."
Verice gave a swift nod and strode from the room. He stalked the corridors, his thoughts grim.
Damn the Regent. Damn Elanore. Everard had been a rare human, with a sense of honor as strong as his own. He'd sworn fealty to the man, gone down on his knees to do it, a thing unheard of. An elf swearing allegiance to a human king. But Verice had known that Everard had been worthy of his oaths.
Human lives were so short compared to his own. Even worse, it seemed that Everard had been cut down by treachery within his own castle, by his own kind.
Verice growled under his breath. Now here he was, an elven High Baron in a human kingdom, with civil war on one border, and the elven Court on another. Somewhere, his ancestors were mocking him.
He stepped out into the garden, into the bright sun, and caught his breath. The area was walled in, and not large, compared with his gardens back home. But Pernard was clever in his use of the space he had, and the effect was lovely.
An apple tree stood to one side, providing shade over a bench. Verice remembered when Pernard had planted the seedling. To the other side, a small path wound around a series of thick rose briars, made to look as if they'd overgrown the area, but in fact were carefully trimmed. Verice took a deep breath, and forced himself to tread slowly and enjoy the serenity that the colors and scents brought. He'd just steal a few moments before—
"Life is fleeting, life is pain.
What need then to dance in the rain?
What need then to sleep in the night,
safe in the arms of my lover held tight?"
Verice looked around, curious. The song was soft and low, clearly not intended for another's ears. He didn't know the words, but the tune was sweet, and the voice...he walked forward.
"What need to love or laugh or sing,
or bind you with my wedding ring?"
He spotted a small foot peeking from under a tattered skirt, sheltered by the roses. It was fair, although bare and dirty. A faella, he guessed, although he couldn't see her ears. She knelt, half-hidden under one of the bushes.
He continued, barely breathing, not wanting to startle her, but wanting to see her face.
"Close or far, low or high, I shall love you ere I—"
There was a gasp, a flash of movement.
Verice paused in mid-step. "Forgive me, lady. I didn't mean to—"
The rose bush trembled and petals fell to the ground as the faella jumped up, and darted past him. He had a glimpse of tattered skirt, tunic and head scarf all of faded dull color as she fled. She was headed for the apple tree.
The warrior in him rose and gave chase, his long legs eating up the gap between them. She'd grabbed for the lowest limb and pulled herself up, rose petals falling from her skirt. He reached up, capturing her ankle.
She looked down, her brown eyes wide. Her scarf caught in the branches, and her blonde hair tumbled down around her.
Ancestors, this was no elven lass. His singer was human.
The very idea made Verice pause, slightly stunned. Humans were rare in Tassinic, despite it being a Barony of a human kingdom. She was pure human, from the looks of her ears. Her brown eyes were large and startled, with flecks of gold in their lovely depths.
"Who are you?" he demanded as she tried to kick her leg free. He held her easily, her skin warm against his hand.
She froze, her lips parted...and then her stomach growled loudly. She flushed and dropped her gaze, golden lashes against her cheek.
Verice felt the loss.
A clatter came from the garden entrance. Two servants were wheeling in a cart, Pernard right behind. Verice turned slightly to call to him.
The woman kicked out, slipped from his hand, and vanished up the tree and over the wall.
Verice barked out a laugh, more at himself than anything else.
"M'lord," Pernard called. "What do you think of my—is something wrong, m'lord?"
"There was a human here, under the rose bushes. A woman." Verice turned to frowned at his old friend. "So much for the security of your walls."
"Ah." Pernard relaxed, settling on a bench and pouring kav. The servants bowed themselves away. "All's well, m'lord. We have sheltered some of the humans that fled Farentell. There are not many, mostly women and children. It was to be a temporary measure, but with the news you bring, I fear we will have to make more permanent arrangements. I was hesitant to mention it, because—"
Verice frowned as he sat on the bench next to him. "My preferences are known, Pernard, but I've never permitted humans to be treated unfairly."
"I know, m'lord," Pernard offered a mug to Verice before pouring his own. "But with the recent attacks..." His voice trailed off. "I wasn't certain how to approach you with the problem."
"Well, give Narthing the details, and we'll make such provisions as we can," Verice said. "I'm not inclined to encourage more of them to come here, but I'll send no innocents back into that conflict." Verice sipped the kav. "What Narthing didn't tell your people is that there has been a buildup of troops along the border with Valltera."
Pernard sucked in a breath. "Why?"
"I don't know," Verice said. "I've let my contacts lapse within King Barathiel's Court, and my diplomatic inquires have been responded to with vague diplomatic answers."
Pernard shook his head. "We don't need this right now."
Verice snorted his agreement. "You said you had something else to discuss..."
Pernard nodded, staring down at the mug in his hands. "M'lord," he said slowly, not lifting his gaze. "It's been months since the attack. Some of your other advisors and staff have asked me to talk to you about the castle and the keep."
"No," Verice said.
Pernard lifted his head, and Verice had to look away from the pity he saw there. "Verice—"
"No," Verice said, and this time he let the venom show in his voice. "My orders stand."
"You cannot continue in this manner," Pernard argued.
"Do not think to presume upon our friendship," Verice warned.
Pernard went silent.
"As to this assembly," Verice said, trying to return to a reasonable tone. "How many of the farmers have you managed to gather, and who is likely to give me the most resistance?"
Pernard took the hint. "All of them have gathered, and I fear they are all resistant. They're a stubborn folk." He glanced at Verice. "Much like their Lord High Baron."
Pernard was correct. The gathering with the angry and terrified farmers was as tense and difficult as Verice anticipated. But halfway through the questions and arguments, Verice found himself thinking about her. About the woman in the garden.
Pure humans were rare in his lands, and not permitted within his castle. Did that growling sound mean she was hungry? He frowned at the thought, causing the onion farmer in front of him to sputter and lose track of his speech. Annoyed with himself, Verice used the moment to cut through their protests and order that they take shelter within the town walls.
While Narthing was summarizing the scouting reports in detail, Verice found himself thinking about her again. Pernard was surely generous with food; it was in his friend's nature. So, why was she hungry? She hadn't picked the flowers, just sheltered there, singing.
Annoyed with himself, he forced his attention back to Narthing's words and the damned maps.
Later, while inspecting the town walls and examining the defenses, the flapping of a flag caused to him to blink, and the sight of tumbling gold hair flashed before his eyes.
He growled under his breath, causing the warriors around him to glance around for the source of his irritation. Even more annoyed with himself, Verice walked on.
Finally, the day turning to evening, he stood next to his horse, ready to depart.
"Send reports regularly," Verice said to Pernard. "Let me know if those farmers give you trouble. If I have to, I will return with more men, and—"
"Not necessary, Lord High Baron," Pernard said. "On behalf of my district, I offer our thanks for your care and watchfulness."
"Just see to them all, Pernard," Verice said. "And have a care for yourself, old friend."
"I'd remind you that sauce for the goose works for the gander, m'lord," Pernard said softly. "Have a care yourself."
Verice nodded, and put his foot in the stirrup. His horse shifted, and he gripped the saddle to mount—
—and caught the scent of roses from the garden.
He settled back to the ground with a thump, startling both horse and the warriors around him.
"M'lord?" Pernard raised an eyebrow as Verice turned.
"Take me to those humans."
Chapter Two
Warna slapped another swaddling cloth into the tub of hot soapy water. Whatever else, she'd not go back into that garden, no matter how lovely the flowers were. The fear of being discovered was a lesson well learned, she thought as she started scrubbing.
As a child, she'd dreamed of elves and the Kingdom of Valltera, listened to stories about them and their magic. The reality was colder and harsher than she cared to think on. Although Tassinic was filled with more half-elven than anything else, not that she could tell the difference.
Children's voices rose, reciting their numbers. They were gathered together with their mothers, laughing at silly rhymes. Warna's fears eased as she scrubbed another cloth. So nice to hear, instead of weeping and tears. So nice to be worrying about laundry, rather than hiding in the forests and listening for the tramp of soldiers.
Warna grimaced as she reached into the hot soapy water and pulled out yet another swaddling cloth. Caring for the children had its pleasant moments, but this was not one of them. Still, it had to be done.
She scrubbed the cloth as clean as she was able, then added it to the rinse water. Lord of Light be thanked, at least they had hot water and soap. Amazing how grateful one was for the basics when you'd lost everything.
Warna glanced around the cobblestoned yard. She'd already covered every available surface with clean laundry, and she still had more to dry. Thankfully, the sun was shining.
She'd fled her home with naught but the clothes she wore. She'd spent months alone, hiding in ditches and the woods. It had only been in the last few weeks that she'd met up with others fleeing the devastation. They hadn't been certain they'd be welcome in Tassinic, but the people of Anera had offered them such shelter as they had, cleaning out one of the barrack's barns. They'd bedded them down in the lofts with plenty of straw and blankets.
It was supposed to be a temporary solution, or so it had been explained. But the conflict had followed them, and now Anrea had to see to itself.
The barracks were still filled with warriors, but they were gone most of the day. They'd shelter, food, and the basics, thank the Lord of Light and Lady of Laughter. The children were warm and safe for now. They'd learn their numbers, eat their suppers, and sleep in safety. And dirty yet another load of nappies for her to scrub.
She'd been brought in to this group, all the refugees sheltered together, but she'd had no time to get to know anyone well. The desperate needs of the children and the drive to survive banded them together for a time. There'd been safety in numbers, for both her life and her virtue. Warna shuddered. Others had suffered far more than she.
She slapped another nappy into the water. Her efforts let their mothers see to their children in these precious few moments of peace. If the day ever came that she'd children of her own, she'd teach them their numbers, and see to their tears, and hire someone else to do the wash.
A pang to her heart reminded that the chances of that were gone. It was all gone: her family, her life, her future. Her brothers had all gone off to fight when the High Baron of Farentell had called upon them. Her mother dead of a fever months before that. Father, Grandfather...
Grief washed through her like a wave. Warna closed her eyes for a moment letting tears well, feeling the anguish deep in her bones until it subsided, leaving her empty, tired, and numb.
She wiped away her tears, and forced herself back to dirty cloths, hot water, and soap. Better to not think about that. Better to think about...her song.
Warna started humming as she swirled the cloths through the water. She was still trying to fit roses into the verse, but it wasn't working. She couldn't get the words quite right.
"Life is sour, life's unfair,
Death takes us all without a care.
What need then to enjoy the rose?
What need then to..."
She let the tune trail off, trying to puzzle out the next stanza. What would work? What rhymed with rose?
Well, toes, but honestly...
Her rhyming distracted her, made the chore go faster. She'd need to dump the water soon. The few men who had managed to escape with them were working at whatever odd tasks their benefactors needed done. She'd get a few to aid her when the time came.
There was a stir behind her as horsemen entered the yard. She spared a glance over her shoulder to see elven warriors ride in, lofty and stern. They all sat tall and proud in their matching silver armor upon majestic black horses. She turned back to her laundry. The warriors weren't cruel, but they weren't exactly friendly. Best to stay out of their way.
That elf in the garden, for example. Warna shivered at the memory. He'd been so big, and so feral, in black leather armor, his sword at his side. His silver-white hair and silver-blue eyes had made him seem like something from one of her children's books.
His grip on her ankle had been terrifying, and he'd looked so fierce.
Oh, no. She wasn't going to sneak back into the garden no matter how large and lovely the flowers were. It wasn't worth—
A loud, deep voice spoke in elven, directly behind her.
Startled, Warna twisted to find that very warrior glaring down at her. Her heart threatened to beat out of her chest.
The elven warrior loomed over her, all black leather, silver chain, and swords. "Pardon, I spoke without thought." His glare didn't diminish, but his words were stilted, as if he was trying to remember the common tongue. "I asked how you fared." His frown deepened, and he gestured to the tubs behind her. "Why are you doing that?"
"It needs to be done," Warna replied without thinking, trying to remember to breathe.
Those silver eyebrows furrowed together as he glanced behind him. More of the warriors were approaching, with human males. "Did you get something to eat?"
Warna cringed at the memory of her growling stomach. "Yes, of course. There's bread, cheese, eggs, and milk. I just hadn't eaten. I wanted to spend a few minutes with the—" She cut her words off.
"That is well," the warrior said. "I was concerned. The noises..." he gestured at her belly
Thoroughly mortified, she dropped her gaze. "Thank you."
"Did you finish it?" he asked abruptly.
"Finish what?" she was confused by the question. "Finish my breakfast?"
"Your song," he dropped his voice, asking quietly.
Warna lifted her gaze then, looking to see if she was being mocked. But his expression was open, his eyes seemed sincere. "No," she said slowly, reaching up to tuck a stray curl behind one ear. "I can hear it in my head, but I can't find the words. It's..."
"Frustrating," he said.
She nodded.
He glanced around, his frown returning. "Who sees to you?"
"What?" She frowned back at him.
"Where are your kin?" he demanded.
Warna froze. Her throat closed and the pain just swelled in her heart.
"Where are your protectors?" The elf demanded, as if repeating the question would make her understand.
Grief gave way to fury. Warna turned her back on him, picked up a soiled swaddling cloth, slapped it into the tub, and started to scrub. "My lord, might I ask what business is that of yours?"
"What?" The elf came around to stare at her, his voice as cold and hard as his eyes.
Behind her came the tramp of boots, the sounds of warriors and the human males gathering. "Lord High Baron Verice," one of them stammered, and they all started talking.
Warna sucked in a breath, and kept her head down, eyes on her task. Of course, the lord of the land, a High Baron. Warna dropped the cloth into the tub, and swallowed hard. She was so damned tired, the pain his words had caused still sat in her throat, and come to find out she'd insulted a high baron. All she'd meant to do was steal a few moments in the flowers.
Somewhere, the Lady of Laughter was surely mocking her.
She glanced around. The Lord High Baron stood there, arms crossed over his chest, looking forbidding and angry. Everyone around him seemed to be talking at once, in both elven and common tongue.
She shuddered. She'd made this mess. It would be up to her to bear the consequences and see it right. Quickly, before she lost what she had left of her nerve.
She dried her hands on her skirt, slipped through the crowd, and knelt before the elf. With any luck he'd just lop off her fool head and be done with it.
The men around her stepped away, leaving her in a space and on her own. The babble mounted, but the Lord High Baron's hard voice cut through it all. "Get off your knees, woman."
Warna wasn't that stupid. "I offered insult out of ignorance, Lord High Baron. I beg forgiveness."
"Insult?" one of the men's voices squeaked. "She insulted him?"
"Stand up," Verice ordered.
The babbling escalated.
Warna studied the boots of everyone who was standing around her. She stared at the shiny black leather boots of the elf she'd offended. She'd hate to die without finishing her song. Maybe flower would work instead of rose. Flower, bower, power, shower. Cherish every hour?
A long thin hand appeared in front of her face, open and demanding. "Off your knees," the High Baron commanded impatiently.
Warna lifted her head. He towered over her, glaring down. Harsh. Arrogant. Elven to the core.
Not much else she could do in the face of his anger. She obeyed.
"Silence," Lord Verice ordered as she rose to her feet. His command cut through the talk around them. "Who are her kin? Her family?"
An older human spoke up. "Warna? She's got none."
"Warna." The Lord High Baron's eyes flickered over her, and left Warna cold. She lowered her gaze respectfully, her hands clenched in her skirts. She'd drawn his attention, and she swallowed hard against her growing fear.
"Warna is under my protection now," Verice stated firmly.
Warna stopped breathing. The implications of that were frightening. The Lord High Baron's men were exchanging glances that seemed at once confused, and resigned.
"You are all under my protection," Verice continued. "Now, about your concerns..."
The storm of protest shifted to fears as everyone started talking at once.
All Warna could make out was the roar of her heart, cold in her chest.
It wasn't the first time someone had expressed such an interest in her, and she was capable of dealing with unwanted attentions easily. But this elf had power and authority over them all, and he was not to be denied. She darted a glance around the crowd and caught the eye of one of the older women.
She jerked her head to the edge of the crowd. Relief flooded through Warna. The men might see her as a bargaining chip, but the women would help her.
Warna eased a step back, letting a man squeeze into her spot. They were crowding around the Lord, all talking at once. She kept her eyes down, trying to become invisible. No one seemed to notice.
One of the women tucked a kerchief into her hand. Warna ducked her head, and donned it. She'd be less noticeable with her hair covered. She slipped around one man, and then another, working her way to the edge of the crowd. She kept moving, keeping her head down. If she could get to the barn, she could hide in the hay lofts, burrowed down into the straw. With any luck, the Lord High Baron would—
She thumped against someone, who stepped directly into her path. She looked up.
Lord High Baron Verice was standing there, a grim scowl on his face. He wrapped his arm around her and pulled her in tight.
She sucked in a breath, surprised at the feel of his body against hers. She brought her hands up on his chest, trying to push him away.
He leaned in, his face close to hers, his silver-blue eyes bright. "Sleep," he whispered, his voice seeming to echo in her mind and ears.
The exhaustion caught her in mid-breath, and pulled her into oblivion.
Captain Narthing watched in horror as Lord Verice kidnaped the human woman, using his magic to render her helpless. Verice swung the unconscious woman into his arms, and arrogantly faced the humans before him.
"Ancestors above us," Narthing breathed as he gripped his sword. For all that the humans were elder males and females, they could still attack Lord Verice if they had such a mind. "I've never seen him do anything like this."
Pernard stood next to him. "Have you ever known Lord Verice to act without honor?"
Narthing didn't take his gaze off the crowd. "No, Lord Pernard, but what is he thinking?"
Pernard shook his head. "I'm not sure he is," the older elf said softly.
"You are now under my direct authority and protection," Lord Verice radiated power as he addressed the crowd. "Farentell has fallen, its High Baron killed by the Usurper. You are welcome here, if you are willing to swear fealty to me as your High Baron. Or, if you wish, free to journey on with our aid and blessing. Discuss it amongst yourselves, and then apply to Pernard with your decision."
"Is there anyone who lays claim to this woman?" Lord Verice continued, his tone daring anyone to contradict him.
Narthing held his breath.
No one did.
"You will excuse me. I must be about the business of the land." With that, Lord Verice spun on his heel and headed toward the waiting horses, the woman still in his arms.
Chapter Three
Warna awoke slowly as the mists of sleep left her mind.
Horseback. She was on horseback, cradled in someone's arms, her head on his shoulder. Her skin felt tingly, an uncomfortable sensation that was fading quickly. She stayed limp, her eyes closed.
Where was she?
The sounds around her were of warriors dismounting, muted voices combined with the ringing of horses's hooves on stone.
"Narthing," a voice rumbled in her ear. "assist me, if you would."
The High Baron, it had to be. Panic flooded through her. He'd used magic on her; what other ways did he have to enslave a soul? She jerked up, out of his arms, and half-fell, half-slid to the ground. Verice cursed above her as his horse shied.
One look showed her a courtyard, buildings of smooth white marble, and across the way, an open door. She didn't know where she was, didn't recognize a building or a face, but that doorway called to her. A place to hide, with any luck at all.
"Lord of Light, aid me," Warna prayed as she ran.
Shouts rose behind her as she darted through the door. It was dark and cool within. She could make out a long, carpeted hall, and stairs.
Up. She fled up, running for all she was worth. Fleeing soldiers and slavers in the past had given her strength she hadn't known she'd possessed, as well as an instinct for survival. She'd not lasted this long to be just to be taken so easily. It was better to die.
Her heart in her throat, she ran up the stairs and down a long hall. If she could find the barracks, the barn, or even that rose garden, she could get over the wall and disappear. She'd not risk the others; if she got out, she'd keep going, back into the forests, hiding and moving by night.
The hall kept going, but she found another set of stairs, and then another. She wasn't really thinking in her panic. She could hear cries of pursuit far behind, but the dark and dusty halls themselves were silent and still, the only light from distant windows.
Finally, she saw great doors, and a white marble balcony beyond, gleaming in the sun. The stone was cold beneath her bare feet. She ran out, catching herself on the balustrade, looking for the garden—
—only to see castle walls, and beyond them, an enormous city stretching out before her. This wasn't Anera. Where in the name of all the Gods was she?
Cries behind her. She spun, and ran back to the door. There was no other way off the balcony, she'd be caught if—
Warriors filled the doorway. Warna slid to a stop, her heart in her throat. Only one way to freedom. Better death than a slave.
"Lord of Light, forgive me." Warna drew in a huge gulping breath as she sprinted for the balustrade, reaching out for the cold marble, feeling it under her fingers. The blue sky waited just beyond. Over, up, and free. "Lady of Laughter, open your arms and welcome my spirit—"
"Warna!"
Her name, screamed, as if torn from a soul. Warna hesitated, looked back into silver-blue eyes—
And cursed herself as she embraced oblivion once again.
"We seem to have a misunderstanding." That deep, reserved voice woke her again.
Warna blinked at the suddenness of her awareness. One moment on the edge of the balcony, now...
Facing Verice, she was seated in a wooden chair, surrounded by armed guards.
She swallowed hard, dizzy. Odd to be alive after she'd faced her death. She took a breath, and then another as her heart raced.
The white marble halls were gone; instead they were in a room with wooden walls and floors, and shuttered windows. Chests lined the walls, and there was a table covered in maps in the center of the room.
"—not my intent to—"
Lord High Baron Verice was standing before her, his arms crossed over his chest, talking, apparently to her. At least, he was looking at her and speaking. Warna gripped the seat of the chair, looked away and trembled within. There was no escape now, none that she could see. Two guards by the door, and another at the window of this small room.
"—want you to understand that I meant no—"
He was talking. Warna was fairly certain his words were supposed to mean something, but she couldn't seem to make them out. She frowned at him, puzzled. He was angry, this elven lord. He was gesturing, and talking and—
"—name?" Verice frowned at her, fierce and cold.
The silence let Warna understand he was asking for her name. She looked around at the guards again and wondered just exactly how many they thought it would take to kill her.
One was probably more than enough.
The Lord High Baron sighed, and the sound made Warna focus on him. "In the camp, they said your name was Warna. Warna of Farentell?" he said again, this time softly.
"Yes. Of Farentell," she gathered her courage and rose to her feet. "I will not be your slave."
The Lord High Baron bristled. "That was never my intent. Here in Tassinic, there is no slavery, despite whatever madness may have infested the rest of the Kingdom." He lifted his chin in a graceful, arrogant gesture. "You are alone, and clearly in need of protection. I extend my safeguards to you, as a ward within my household."
Confused, exhausted, Warna blurted out her first thought, "Why?"
"What do you mean, why?" Verice demanded, irritated beyond words. "You are alone, with no male relatives to see to your safety."
"Lots of the women in camp are alone," Warna said. She looked tired, standing before him, pointing out the obvious. "They're not being singled out for—"
"They are also under my protection," Verice snapped. "You are a maiden, are you not?"
The fiery blush over her cheeks was a sign he'd offended. "Unwed, I mean," Verice said impatiently.
"I'm fairly certain there are other unwed women among those that fled," Warna argued.
"Not with your gift of music," Verice countered, certain of victory. "That gift should be cherished and protected, and I'll see to it."
She crossed her arms over her chest, her eyes down but her face filled with doubt. "My music?"
"Your songs," Verice took in a deep breath. Was the woman thick? "Your songs. They are—"
"That's just something I do for myself," Warna said. "I'm not that good."
"You are," Verice insisted. "You are too harsh on yourself. I will see you and your gifts protected, even over your protests."
"Why?" she asked again in that maddening, all-too-reasonable tone. Again, she seemed to be staring off to the side, not looking him in the eye.
"Is there some reason you won't look at me?" Verice growled.
"Yes," she snapped back. "I'll not be charmed or bedazzled by your tricks."
A sudden feeling of shame flooded through him, catching him off guard. "It was necessary," Verice said. He caught himself before he continued to justify his actions to this human.
She didn't look up.
"I'll pledge not to use magic upon you if you will pledge to remain under my protection. I do not know your sense of honor; humans rarely seem to have one. But I—"
She bristled, standing stiff and staring him in the eye. "My word is as good as yours," she retorted. "But I'll not give that promise."
"Then I shall take what steps are necessary," Verice stated. "You will remain here."
"Why?" she demanded again.
Verice stood, and drew himself up to tower over her. "Because I say so," he gritted through his teeth. "And as I am the Lord High Baron of this land, my word is law."
Those brown eyes studied him with skepticism.
"Narthing, see to her needs," Verice commanded, determined to end the conversation by leaving the room.
"I don't even know where I am," she complained as he strode past. "This isn't Anera, is it?"
"No," Verice paused. "This is Octara, my capital. You have the freedom of the castle and its grounds, but understand, lady, you are not to venture outside its walls. Is that clear?"
Her gaze dropped, her lashes dark against her skin. She executed a perfect curtsey, sinking to the floor with grace. "Yes, Lord Verice."
He didn't trust that for a moment.
Narthing stared at the human woman in dismay. His Lord had commanded, and it was his to obey, but what in the name of all his Ancestors was he to do with her?
She stood there staring at him, waiting. His men were all staring at him too.
She'd given them all heart attacks, fleeing into the castle that was supposed to be sealed, running for her life and what she thought was her honor. Narthing admired her; he'd been just behind Verice and seen her determination to face death over degradation. It had been a close thing.
It was the sight of her bare feet that did it. She'd been just like any new recruit showing up at the gate with naught but the clothes on his back, and a willingness to serve.
Well, from the look in her eye the willingness wasn't there, but all else was the same.
"Welcome to Octara, Lady Warna," Narthing started with assurance. "We'll need to get you settled, and then—"
"Where is Octara?" she demanded. "How far are we from Anera?"
"About four days ride," Narthing said.
"Four days? I've been unconscious for four days?" she asked, her voice climbing higher.
"Nay," Narthing said. "Lord Verice opened a portal."
Her eyes were wide at that. Narthing had heard that very few humans were gifted with powers.
"He's been inspecting his border towns and seeing to the defenses. But we're based here in Octara, the capital of Tassinic. Now then—" he almost called her recruit. "What say we get you a wash and a meal, and then some sleep. Tomorrow's soon enough to show you around and answer any questions."
"I'd rather—" She stopped suddenly. Narthing's ear twitched as he caught the faint sound of a grumbling in her stomach. The lady smiled wryly. "Food would be good."
"This way." Narthing gestured toward the door, signaling two men to bring up the rear. He'd noted that she hadn't promised to stay, and she was too fleet of foot for him.
He escorted her out of the High Baron's office, and down to the barracks dining hall. The cooks there were setting another dinner shift, and he gestured Warna to a corner table. As the serving lads seated her and served kav, he gave soft orders to the others to see to her housing.
He'd talk to Constable Ricard. They'd shift maels and rooms around a bit tonight, give her a private chamber. Tomorrow they'd make more permanent arrangements.
From the stares of the men, word had already gotten around. Curiosity, more than anything, about the human woman Lord Verice had brought within the castle walls. Tongues would be wagging, that was certain. There's no worse gossip than a bunch of hardened warriors.
She made an odd picture, that was true enough. A slim, lovely human woman, with golden hair, seated in a roomful of armed and armored elven warriors. Narthing shook his head as he settled himself across from her. What was his lord thinking?
She gave him a nod as he settled and poured a mug of kav for himself. She was lacing hers with cream and honey, he saw. He preferred his black.
"The fare is plain, lady, but good and plentiful." Narthing leaned back as the lads brought platters with baked spiced fish and turnip cakes. A basket of bread and a crock of soft white cheese also appeared, along with a clatter of plates and silverware.
He saw an unwilling smile on her face as the lads banged the plates down before them.
Not condescending either, not like he expected.
But she was puzzled. "Why aren't we in the castle, Captain?" She reached for the bread. "One of your rank would normally dine at the High Baron's seat, at least in Farentell."
"Here as well, lady," Narthing said. "But the castle's abandoned, by Lord Verice's command. Left to the Ancestors."
"Why?" she asked.
"I'll leave that for Lord Verice to say," Narthing said firmly. "Tuck in, lady. While it's hot and within reach."
Thankfully, she did just that. Narthing breathed a sigh of relief. If the Ancestors were kind, she'd not press the issue. He'd see her safe in a bunk and then be off to his own.
Tomorrow was Lord Verice's problem.
Chapter Four
Verice waited until after midnight to begin his casting.
He'd planned the spell the moment he found a long golden hair caught in his armor. A simple matter, really, but it was a casting he hadn't done in some time. It would involve the protections he'd built into the castle walls, but that was a minor complication.
He dug a silver bowl out from one of his chests, and set it on the table next to the pitcher of crisp, cold well water he'd drawn himself. Clearing off the maps and markers from the table, he set them carefully to the side.
He stripped off his chest armor, setting it on its rack, and hung his swords and daggers with care. Sometime soon he'd need a day to see to them. That wasn't a task he cared to have anyone else do, but he might not have a choice.
He stripped to the waist and pulled the ties from his braid, letting his hair flow free down his back. Kicking off his boots, he pulled off the thick socks he wore underneath. The rough wooden floor felt cool under his feet.
He took a moment to stretch, trying to loosen the muscles in his back. Tight and tense from a long day in the saddle, casting portals, dealing with his people and their fears. Just this one last little chore and then he'd sleep, if the nightmares would let him.
With the door and shutters closed and bolted, the room was dark, but his concentration was assured. With a wave of his hand he lit one small candle.
All was in readiness.
He stood listening for a moment more, for the silence of the warriors sleeping in the barracks, for the tramp of the night guard along the walls. He touched the web of protection that he'd set around his castle, even into the city itself. Those protections cost, in his time and energy, but it was well worth the price. This particular casting would add to the burden, but it must be done.
He started the chant, the words flowing soft and formal from his lips. The bowl began to glow as he poured in the water. Carefully he wrapped the hair around his fingers, and touched the water's surface. "Warna," he breathed.
The water shimmered, then grew still and obeyed.
She was sleeping, in one of the loft chambers it looked like. The small window was unshuttered, allowing the moonlight to spill within. Her bed was a simple bunk, filled with old camp blankets, and pillows.
Her hair was spread around her head, her lips parted slightly. She breathed evenly, and regularly, deep in some sweet dream, he hoped.
She shifted then and the blanket slipped down to reveal a bare shoulder. It was then he saw her clothing neatly folded over a chair, her slippers tucked beneath, and understood that she was naked underneath the bedding. He hesitated, wondering just for a moment what she'd look like, bare and sweet in the moonlight.
And chastised himself with his next thought. She was a vulnerable innocent, and a gifted one. Defenseless in a world full of treachery and deceit. Someone worthy and deserving of protection. His protection.
The grief rose, catching him unaware, like a bolt of pure pain through his heart. He'd failed to protect so many of his own.
She shifted then, rolling to her side, hugging a pillow. The blanket shifted further, and he could see the curve of her shoulder. Guilt flooded over him, adding to his pain. Honor demanded he finish his task, and be done. Not be some kind of disgusting voyeur.
If he really wished to protect her, he should send her away. He nodded in agreement to his thought. That would be best. Send her to safety somewhere else, or even into one of the other baronies.
He started to dismiss the spell, and paused as he looked down. A lovely woman, yes, but she was fairly fast on her feet. She'd slipped from his hands quickly enough, almost getting trampled by his horse. How had she slipped through the mage-warded doors, and how had that particular door come to be open? He thought about how she'd fled before him, terrified. She'd frightened the very breath from him as she'd run toward the balcony—
He paused as the image played out before his eyes.
It would take time to arrange a safe location. Perhaps, in the meantime, he should make sure...
Without giving himself a chance to think, he focused his will again. The bowl glowed, and now he took the fine strand of hair and let it fall to the surface of the water. As he chanted, the glow extended to Warna, outlining her against the blankets and pillows.
"This far," Verice whispered. "And no farther." He closed his eyes, seeing the castle and its walls. "Here, but not beyond. Within, but not without. As I will, so guarded and warded be."
The bowl flared bright, then the power faded, leaving only the empty bowl behind.
There. The geas was cast. He could release it temporarily, or dismiss it, at any time, whenever he made the arrangements for her safety. His work was done. Now he could seek his rest.
He threw the bowl back in the chest, replaced the maps and markers, and then opened the shutters. Moonlight poured in and over his bed. Verice stripped, and settled in. The casting had left him weary; with any luck he would sleep.
As he drifted off, a vision appeared in his mind's eye, of a sleeping Warna and the curve of her shoulder.
He slept deeply, untouched by nightmares.
Chapter Five
Captain Narthing looked down from a window to the courtyard below. Lord Verice was out there at sword-practice, attacking the pells like a man possessed. Which wasn't that unusual, but he seemed to have more energy than normal.
"He's been out there all morning?" He glanced at Constable Ricard.
"Aye sir, since before dawn." Ricard looked slightly smug.
Lord Verice's decision concerning the castle had placed a hardship on them. It required the Castle Watch, under the constable's command, and Narthing's men, the Army of Tassinic, to house together. For the most part, they'd managed to work through the inevitable tensions. But they each enjoyed a silent rivalry with the other, especially when it came to dealing with Lord Verice.
Narthing sighed, and stepped away from the window. "Looks like it's going to be one of those days, Constable." He finished buckling on his sword-belt.
"That it does, Captain."
"And the Lady Warna?" Narthing asked.
"At breakfast, sir."
They both went down to get their own meals, knowing full well they needed to eat before the Lord High Baron was done. Narthing was drinking the last of his kav when Lord Verice strode into the dining hall, slapping his gloves against his thigh with impatience. "Narthing, what's keeping you," he demanded as he stopped at the end of the table.
"Just finishing, m'lord," Narthing replied calmly. Ricard dabbed at his eggs with his last bit of bread. Thankfully, the Lord High Baron wasn't one of those that stood on ceremony at meals.
"We're due at Izteria," Verice growled.
"At mid-morning," Narthing said. He glanced at his Lord. "Of course, it's always a good plan to arrive before one is expected, m'lord. See what the real state of readiness is."
"Just so," Verice agreed. "And where's Warna? She wasn't in her chamber."
Down the long row of warriors, a golden head leaned forward. "Here, m'lord."
"What in the name of the Ancestors are you doing there?" Verice barked.
There was dead silence in the hall. Warna's brown eyes flashed for an instant, and then she lifted her chin. "Eating breakfast, m'lord."
The response was respectful enough, even if the tone was not. Narthing raised an eyebrow as the room held its collective breath.
"From this point forward, you take your meals with me when I am in residence," Verice commanded.
"As you say, m'lord," Warna leaned back, disappearing into the line of warriors.
"Constable, you have command," Verice said.
Ricard rose crisply. "Aye, m'lord."
Narthing stood, gesturing for the men to follow.
"We'll return tonight," Verice announced. "At sunset." He spun on his heel, then paused. "Oh, and, Constable, see to our guest. She needs outfitting."
"M'lord?" Ricard had a look of pure horror.
"Yes, Constable," Narthing said under his breath, unable to resist a satisfied smile. "It looks like it's going to be one of those days."
Warna sighed as the High Baron stepped out of the hall and gave the men around her a questioning look. "Is he always so grim in the mornings?"
She'd felt uncomfortable coming into a dining hall full of warriors, but by the time they'd seen her settled at a table and served, she felt more at ease. They reminded her of her brothers, rushing to introduce themselves, and talking too fast over their food.
"Grim most of the time, lady." Erenfet, the warrior on her left rolled his eyes. "Quite the temper, he has."
"He's a good lord to us all, though," Aeric, one of the castle guards on her right chimed in. "Treats all his people, elven, half-elven, and human with a fair hand. Even if he don't normally let your kind within his walls."
"Gwenwyth tea, lady?" Oines, the warrior across the table, held up a pot and poured. The tea had a scent, like flowers on a hot day.
"Eh, that's not for her," Aeric said, catching the cup before Warna could take it. "Your pardon, lady, but me mum was full human, and while she liked the taste, it gave her the flux something fierce."
"You've half-elven?" Warna asked, studying his features. She looked around at the others, not wanting to be rude, but curious.
"Sure enough," Aeric grinned. "So's all of us. Erenfet, pull back your hair, let her see."
Erenfet was in mid-bite, but he obliged, tucking his gray hair back behind his ear.
It wasn't just the ears. Both men had pointed ones, but there was a softness in Aeric's face, his jaw and cheekbones weren't quite as sharp. Erenfet's face was sharper, a lot like the Lord High Baron, but not quite as compelling as—
"Pure elves tend more toward silver-gray hair, straight as an arrow," Aeric said. "Half-elves, well, ya got a full range of colors."
"I saw elves pass through our town once or twice," Warna said, although as she thought about it, she wouldn't have known the difference.
"Tassinic as a whole is a mixture, lady," Erenfet said. "Halves, quarters, whatnot. Not that it matters."
"Even for pure humans?" Warna asked.
There was a hesitation, then Erenfet responded. "No, lady. Lord Verice's law is fair to all."
Something flashed in Aeric's eyes, but all he did was pick up the pitcher of kav, and offer to pour for Warna.
She nodded. "That's good to know, about the tea," Warna said. "Is there anything else I need be careful of?"
"Some of the elven healing herbs don't set well with human folk," Aeric said. "But the healers hereabout know what's what. Nothing that will flat out kill ya, lady. Just make ya want to die."
"Best to be aware, then. My thanks." Warna smiled.
A bell rang in the courtyard, and the warriors all stood, taking a last bite, or a last drink. "Time to serve," Aeric said as he rose, giving Warna a grin.
With that, they all filed out, leaving Warna in an empty room, nursing her mug of kav.
Well. It appeared that she was on her own. She rose from her bench, and went into the back. The serving lads and cooks were scrubbing dishes and pots. The looks of horror at her suggestion that she help them convinced her it would be better to move on.
Which left her free to explore. And maybe find a way to escape.
Not that she had a place to escape to, mind. But one thing at a time. She needed to know her way around.
She stepped outside slowly, waiting to see if there was any exclamation, or protest. But no one seemed to take more than a notice of her presence.
She stood in a large cobblestone courtyard, the barracks behind her. She hesitated, then settled on a bench beside the door to take a moment and stare.
The courtyard was huge, and it circled the keep, which rose in the center of the castle walls. The sight of it took her breath away, all smooth white marble, rising straight up. The lower part was solid stone, built to withstand a siege. Above soared tall, arched windows with colored glass panes. It seemed to her more like a cathedral than a castle.
The beauty did not stop there. The castle walls were white as well, fitted smooth stone, with hanging lanterns spaced along the walls. Various buildings were built into the walls as well, to serve the needs of the keep. The smaller buildings were also white marble with slate roofs. Even the stables, to her surprise.
There were warriors scattered about, some practicing their weapons, or drilling in the yard. Aeric seemed to be talking to a group carrying pole arms. Others stood guard on the walls. The barracks area felt very formal somehow. There was a farrier shoeing a horse, and sounds coming from the smithy, both buildings built up against the walls. But there was an odd feeling of order. A place for everything and everything in its place.
Which made her feel even more uncomfortable.
"Pardon me, miss." Constable Ricard strolled up, looking quite aggrieved.
"Constable," Warna said.
"Miss." The constable looked like he thought she was out-of-place as well. "Miss, I'm not—"
"Constable, I'm a merchant's daughter. I'm not expecting silks and lace," Warna reassured him. "Tunic and trous are fine, for now."
A relieved look passed over the man's face. "If you'd come with me, then."
He led her to a small door and ushered her inside.
The office they entered was crammed with shelves filled with scrolls, going as high as the ceiling with barely enough room to pass between. The constable had to shuffle around her to shut the door, so tight was the squeeze.
Two heads appeared, one younger, the other old and tired. After a quick glance the heads went back down over their work, even as the older one spoke. "Constable, what's the need?"
"A new recruit, Quartermaster." Ricard gave Warna a wink. "Need some gear."
"Name?" The question was barked out impatiently.
Ricard gestured to Warna.
"Warna of Farentell," Warna said, letting the constable have his fun. Sure enough, he grinned as the two heads popped back up, startled.
"Recruit?" sputtered the older man.
"Recruit?" Ricard laughed. "I said guest, sure enough. A guest of Lord Verice."
There was a rustle of papers, and a wizened old man came around a corner, slipping between the shelves easily. Behind him, a lanky elf craned for a sight of her.
"A lovely one at that," the older one said, and bowed. "Welcome, lady. I am Farnor, Quartermaster for the Army of Tassinic. How may I be of assistance?"
In no time, Warna had a small chest of the basics, and new shoes besides. The Quartermaster had trouble with standard gray tunics and trous, for all were meant for maels. They either threatened to split at the breast or the hip, or hung on her like sacks. But he'd a small sewing kit that he added to the pile with a shrug. "Seems to me this is only temporary," he said. "We've no real supplies for a lady like yourself."
"It's enough to get her started," Ricard said. "I'll help ya carry it, miss."
But Warna had other ideas as they left. "Where's the washhouse?"
Constable Ricard was standing guard when she emerged from the bathhouse, washed and changed. "Feel better then, miss?"
"Yes, thank you," Warna smiled.
"I've duties to be about, then." Ricard said. "The noon bell will ring for the meal, and the Lord said you'd dine with him this eve."
"Thank you, Constable." Warna settled on a bench in the sun to dry her hair. "I'll try not to be a trouble."
"Much appreciated, miss," Ricard gave her a nod, and walked off.
Aeric was still drilling his men. Apparently marching in formation with pole arms was more of a challenge than she imagined. But after a while they stopped and formed opposing lines.
"All right then," Aeric barked. "Front lines, take up sword and shield. Second line, halberds."
Warna watched while they practiced. She'd never really seen anyone use a halberd before. It did seem effective, as the men behind jabbed at the attackers over the shoulders of the front line. But it seemed to her that you'd really have to trust the man behind you to know what he was doing with that heavy pole.
Her attention wandered. As nice as it was in the sun, she felt the need to move, and explore.
She took the bundle of her clothing and her comb up to the small loft chamber she'd been assigned to, and left it there. Tunic and trous felt odd, but they'd do until she could get more suitable clothing. She figured that, to some extent, that was Lord Verice's problem, not hers.
She felt odd. Empty. As if there was something she should be doing.
Warna shook herself, and headed back outside. The least she could do was walk around and learn more about the castle.
The courtyard continued on, surrounding the keep at its center. Warna started to walk, thinking to circle the entire keep. She wanted to see the other buildings, designed to supply the keep with its needs. A laundry, an outside kitchen, storage of foodstuffs, perhaps a brewery.
But once she started around, there was an odd stillness. An emptiness.
Warna frowned, but kept going, curious. The sounds behind her faded as she walked the cobblestone yard as it curled around the white marble building in the center. Here the buildings stood silent and vacant.
She thought about the quartermaster, all crammed into those rooms with barely an inch to spare. Why not use the space available? As the daughter of an ambitious merchant, she'd been trained to marry a noble, and in the running of a noble holding. Not one as large as this place, but still. Narthing had said that the keep was not being used, which made no sense at all.
Unless its Lord had turned his back on all but war.
Warna frowned as she walked farther around. A castle's purpose was not just living quarters of its Lord. It was also a symbol of power, a key defensive position, a storehouse of supplies in case of siege. To empty it out? Abandon it? That made no sense.
There were guards on the outer walls, and one or two acknowledged her with a wave of their hand. They didn't seem to find it amiss that she was wandering this way.
She got dizzy, walking along, gazing up at the tall white marble towers and arched windows. She'd never seen anything like this in Farentell, not that she'd ever traveled far. She'd heard tales, of course, but to actually see it was quite another thing.
At the rear of the building, there was a large circular window. She shaded her eyes, and retreated a few paces, trying to make it out. It was dark, and she couldn't see any color. She narrowed her eyes. Was it broken out?
She continued on, filled with questions.
She was almost back around to the practice yard when she spotted the open doorway in the wall of the keep. The room beyond was dark and still. She stepped closer, peering in, seeing nothing but darkness.
Was it the same door? She thought maybe it was.
The guards were paying her no mind, and no one seemed worried as to where she was or what she was doing...
What had Lord Verice said? 'You have the freedom of the castle and its grounds—'
Warna slipped inside the door and stood silent, letting her eyes adjust, listening for sounds of protest or pursuit.
The only sound was her own heartbeat in her ears.
She stepped farther in, looking around. This wasn't the door she'd bolted through. To the best of her memory, that had led to a hall. This one opened on to a huge kitchen, with two huge hearths and long tables for the work.
But what stopped her were the dishes set out, as if for supper, and the kettles hanging over cold hearths. Dust-covered spoons in bowls, and cloths tossed on the tables, as if just thrown by someone in haste. Something had happened here, something in mid-meal.
Fascinated, Warna stepped further in, but the sunlight only went so far. The deeper darkness beyond the next door pulled at her.
She checked the mantel, finding a small copper lamp, the kind used to keep a flame handy for lighting fires. She found flint and steel, and tinder besides, neat as a pin, as if waiting to be used.
She struck a spark, adjusted the wick, took up the tiny light and ventured further into the darkness.
The archway led to a long hall, stretching out to her left and right. Warna paused, hesitating for a moment. The idea of getting lost in a huge keep with a tiny lamp did not appeal to her at all.
But curiosity gnawed at her.
She noticed the dust, thick on the floor. The hallway was white marble, with a heavy carpet down the center. She took a few steps, leaving a clear trail. She could use that to guide her.
She lifted the lamp higher, trying to peer down the hall. There were doorways off to the sides, and there'd be stairs at some point. The lower levels would be dark, but a few floors up those glorious windows would let in the sun.
So, she'd treat it like a maze. Always follow the right wall, leave a trail in the dust, and head up at the first chance.
That odd feeling was back, a cold lump in her chest. She bit her lip for a moment and then it hit her, bringing a well of grief.
It had been so long since she'd done anything for pleasure.
Since losing her family, her home, all that she'd done was concentrate on survival. Doing what had to be done. This felt wrong, somehow.
"Sorrow comes of its own accord. Joy has to be invited," her grandfather's voice whispered in her ear.
Warna turned, lamp in her left hand, her right on the wall. She scuffed an arrow with her foot in the dust, and then started off, heart beating in anticipation.
"We'll run the patrol along the river here," Verice pointed on the map. "I know you say that the water's high, but I don't trust to that alone. I know it thins our forces, but—"
His chest vibrated as his mage-wards broke. Someone was in the keep. Verice lifted his head, focusing on—
"True enough, Lord, but with message birds, the early warning will make all the difference," Narthing stepped in and continued talking, covering for Verice.
Verice blocked out the people around him, and concentrated. Was it an enemy, a member of his force? His anger built as he focused; his orders had been clear. No one was to enter the keep for any reason, and he'd see the offender punish—
It was Warna.
Chapter Six
Warna wandered down the hall in amazement.
This was clearly a working area of the castle, with various rooms off the long hall. The first few doors she came to were ajar, and swung open at her touch. They all showed signs of a hasty departure, chairs overturned, scrolls left on desks, fireplaces unswept.
The dust was thick, as were the cobwebs. She stifled a cough, trying not to stir the air too much.
There was a rustling as well, and droppings. She didn't bother to investigate those areas too closely.
Some doors were locked, and she moved past those, careful to make scuff marks in the dust. Her little lamp burned bravely, its light steady and reassuring.
She started humming to herself, if only to hear another sound besides her breathing. Not that she was afraid, really. The empty rooms and hall didn't speak to her of menace. It felt like sorrow.
Although if her little brother had been with her, he'd have hidden in those wardrobes and jumped out at her just to hear her shriek.
Her heart clutched at the memory, and her eyes welled up. Grief swept over her, but then with a teary laugh, she could almost hear his joyful laughter.
Warna wiped away tears, took a shuddering breath and continued on.
But the next break in the hall, she had to make a choice. She could head up the small spiral staircase to her right, turn down a hall to her left, or continue straight on. She paused for a moment, and bit her lip.
Up. She wanted to see those windows.
There were arrow slits along the way, and she could see the walls, and down into the courtyard. There was a line of shadow as well, and she knew that soon enough she'd lose any sunlight. Besides, Lord Verice had said he'd be back at sunset. Best to be out and cleaned up before he arrived.
The stairs opened up into a dark hall, and again she chose to go to the right.
Here now, were the chambers of the keep. Each with an arched window that let so much light spill into the room.
This room had a large bed, covered with thick blankets and hung with heavy bed curtains. A woman had slept here, there were bright dresses in the wardrobe. Warna took a closer look, mindful of the flame of her lamp.
The dresses were lovely, vibrant and rich. But when Warna reached out to touch one, she pulled her hand back. It didn't feel right to disturb these things. Except for the layers of dust, it felt as if the lady would burst into her chamber at any moment, laughing, ready to change for a night of dancing and music.
Whatever had happened to her, she hadn't taken her things.
Warna sighed and moved on, peeking into rooms as she went. All bore the weight of their departed residents, even to perfume dried in bottles long unused. The hall went on, but she could not. Warna turned back, and returned to the spiral staircase she had ascended.
She paused there, holding the lamp, and considered. Up or down?
She went up.
Breathing hard, she emerged into a small chamber. There were linens here, some stacked on shelves, some bundled for the laundry. It had to be a servant's supply room. The door beyond was open just a crack, and there was a faint glow of sunlight beyond.
She pulled open the door, gasped in delight, and then sneezed.
Sunlight flooded through the huge arched windows and down the length of a long room, High and clear letting in a lovely light. Between them were four vivid colored-glass windows, staining the white marble below them with reds and golds and vibrant greens. This had to be the main hall of the keep, the Great Hall. Warna followed along the one wall, staring at the designs.
Only two on each side were of colored glass. The first depicted spring, with fresh green glass, and a lovely oak tree that arched over the scene: a meadow of flowers. The details were amazing, with animals of the forest at the base of the tree, and the birds building nests and courting in the high branches.
Warna hurried to the next. This one was summer, with the deeper greens, and the animals feeding and raising their young.
A glance showed her that the other side had to be fall and winter. She darted across the room, stirring the dust and coughing as she hurried to see the other designs. But the center of the room stopped her in her tracks.
Shattered chairs, tables and benches lay strewn about like broken toys.
There'd been a gathering of some kind. There were some tables still set with dishes, others overturned, with crockery broken on the floor. Something had happened here, something terrible.
The sunlight was diffused here, but she still had her lamp. There were wine-stains on the floor, and food dried in the bowls. The air was stiff and stale. Mice droppings on the tables and floor. Some of the debris was weapons, swords and daggers left where they'd fallen. There was a shield with a blade wedged deep within.
No bodies, thank the Lord and Lady.
Almost against her will, her gaze turned to the high table. It was overturned as well, the cups and plates smashed. The actual high seat was broken, splintered and cracked, as if it had been used in defense. And in the space before the high table?
Warna stopped just at the edge of the reddish-brown stain. It covered a huge area, with signs that someone had struggled within it. There were smeared hand-prints, and drag marks all around the deepest darkest part.
Warna could barely breathe.
She lifted her head as a breeze touched her cheek. In the wall behind the high seat there was a large circular window, its glass shattered and gone, open to the sky.
"Warna." The voice, low and deep, came from behind her. She wasn't even startled to see Verice standing in the opposite doors.
There was such pain in his face, and she knew instantly that she was the cause. She stood frozen, holding the tiny lamp before her like a shield. "M'lord, forgive me. I didn't think—"
"Come," Verice said, holding out his hand. "You should not be here."
Warna advanced to place her hand on his wrist. His skin was cool under her fingers, his eyes dark. Her mouth dry, Warna licked her lips, afraid, but unable to stay silent. "M'lord, what happened here?" Her voice was a whisper against the silence.
His eyes grew more shadowed, his mouth set in a line. "Death. Betrayal." He drew a slow breath, turning his back on the room. "Come."
He led her slowly down the main staircase, to the wide double doors at the base. Out in the courtyard, his men waited, with Captain Narthing, their horses, and a very pale Constable of the Watch.
"Lord Verice," Ricard stammered
"At ease," Lord Verice said. "Lady Warna did not know, and I neglected to tell her that the keep is forbidden to all. I failed to give her instructions in the matter. You are not to blame."
Ricard relaxed, mumbling his thanks.
Verice gestured, and Warna handed the small lamp to Ricard. "Return that to the kitchen area, and secure that door," he said.
Ricard bowed over the lamp.
Verice gestured again, and the huge main doors slammed shut and bolted themselves. Warna jumped at the violent sound, startled at Verice's action. Everyone else reflected the same surprise.
"If you will join me, the evening meal is ready" Verice inclined his head to Warna. "After you've freshened up."
Warna blushed, noting her tunic and trous were covered with dust and cobwebs. "Yes, m'lord." She fled to her chamber, feeling guilty and ashamed and yet so filled with curiosity. She wanted to know more but...
Her dress was dry now, so Warna washed fast, and changed. She got the cobwebs and dust out of her hair, and braided it, all the while knowing that she'd hurt him.
Why did she feel so guilty?
He'd kidnaped her, after all, used magic on her person, imposed his will on her without so much as a 'please' or 'will you'. He required no protection from her actions, needless to say.
And yet.
She cursed her stupidity, and her thoughtlessness and her idle curiosity, and wondered how she could really make amends. Such a fierce, strong warrior, and she'd wounded him by wandering into the keep. His face—
She dropped her hands into her lap and sighed. She'd no clue how to make amends, beyond the words she'd already said. She felt horrible.
Maybe she could send word that she was ill. Ask to be excused, beg off eating with him. It was true enough. Her stomach was in a knot.
But then she'd be a coward on top of it all. And there'd be the morning to face. It wasn't going to get any easier.
One of the serving lads bowed to Warna and gestured her through the door.
Lord Verice was standing by a chair, waiting to seat her. A fire burned in his hearth, and lanterns glowed in every corner, with one set on the table besides. The other door was shut; she presumed those were his sleeping quarters.
"Good evening, Warna," Verice said.
"Good evening, Lord Verice." She curtsied, and sat as he eased in her chair.
"If you'd be more comfortable, I can have someone sit here in the room with us." Verice offered.
Warna glanced back at the warrior who had escorted her to Verice's chambers. "That's not necessary, m'lord."
Verice dismissed the warrior, with thanks. "I'll leave the door open, nonetheless, lady." He settled in his chair across the plain wooden table from her. There was the sound of running feet and clattering china outside the door. "Shush," someone admonished, and then silence descended. A timid knock on the door frame came next.
Verice's grimness gave way to an odd look of patience. "Enter," he called.
A lad started across to them ever so slowly, carrying a covered dish. He placed it on the table, took a step back and bowed, before dashing off, almost colliding with the next lad, slowly making his way with a covered bowl. That brought an end to any attempt at decorum. The lads all ran in, deposited their burdens, and took off at high speed, leaving the table tottering, but no food spilled.
Warna laughed despite herself.
"They do try," Verice said. He lifted a bottle. "I drink no wine, but for you, m'lady?"
Warna shook her head. "No, m'lord. It's been so long, I would fear to keep my wits."
"The water here is very good, and there's kav for after." Verice placed the bottle to the side. "We'd best eat while it's hot."
"M'lord, I wish to apologize to you again," Warna said. "Except the lamp, I disturbed nothing. I am so very sorry that—"
"Apology accepted." Verice lifted the lid from a serving dish. "Chicken?"
Warna stared at him for a moment, then accepted that the matter was closed. She raised her plate. "Yes, thank you."
They dished out the meal to each other. Baked greens and onions with cheese, chicken roasted with rosemary and onions, and a loaf of bread.
Warna tore off a hunk as Verice cleared his throat. "I'm the one who should offer an apology. I fear that I have been...less than courteous in our dealings. This conflict within the kingdom has destroyed much that was graceful and fair, including my manners."
"You're used to taking command, issuing orders, and seeing them obeyed," Warna said softly. "I suspect that aspect of your leadership has saved more lives than either of us knows."
"I do not deserve your understanding," Verice said. "But I thank you for it. Pernard's roses are lovely, don't you think?"
"Oh yes," Warna smiled. "I do so love flowers."
"Well, I must tell you then, that some of his are cuttings from my gardens," Verice said. "I make a point, when I journey, to see if I can find a new flower or plant to add to my collection. Those roses are from Soccia, if I remember correctly, from a small village—"
Verice lulled her with talk of roses, all the while drinking in the sight of her. How long had it been since he'd talk of things other than war and troop movements? He could not remember.
She sparkled, brown eyes glowing gold as she talked. He felt her warm to him, relaxing and talking about flowers and their care. She shared stories of her mother's garden, her bright brown eyes only occasionally dimming with the memories. She took pleasure in the meal, even though the fare was plain.
So, he kept the talk light as they ate, not wanting to see the shadows in her eyes, although he knew the pain was there, under the surface. Time enough for that.
"So, were you trained in music?" he asked finally.
"No," Warna chuckled. "My family was far too practical for that. My father saw no profit in those skills. No, I was trained to run an estate, with the hopes that my father would arrange a marriage to a minor lord or landed knight, who in turn would aid my brothers to noble wives. My father loved us dearly, and had ambitions for us all."
Verice nodded, understanding. "But you are not wed? Or pledged?"
"My mother sickened shortly before King Everard's death," Warna said. "With the chaos, and her illness, my father delayed a formal betrothal. After she died, the Lord High Baron called every able man to arms. My father, brothers took up arms and..." She trailed off.
"How did you survive?" Verice asked.
"When word came that the Usurper's forces were upon us, Father and Grandfather hid me," her voice was filled with pain. "When the flames started, Father stayed to try to protect his warehouses. Grandfather got me away. He died a short time thereafter. I've been running ever since."
"That explains your song," Verice said quietly.
Warna lifted her head, and he could see the tears gathering in her eyes. "Grandfather always told me, 'Pain's part of the agreement, Warna. Part of the price.'" She blinked away her tears. "I didn't really understand him, because it sounded so cynical, so bitter somehow. I didn't want to think that life was like that."
"Now you know it's just the truth," Verice said. "Your song expresses it well. How did it go again?
Life is fleeting, life is pain
What need then to dance in the rain?
What need then to sleep in the night
Safe in the arms of my lover held tight?"
Warna listened, her amazement clear as he sang, keeping his voice low. He'd impressed her, and it pleased him that she blinked away tears.
"It sounds so much better when you sing it," she whispered. "Were you trained in music?"
Verice shook his head. "No, not really. There was a time, before I took the Barony of Tassinic, when I thought to become a bard. But after about ten years or so, I realized that it was not truly my gift."
"Ten years?" Warna asked.
"Yes." Verice stood to retrieve the kav pitcher that sat by the fire. He returned, offering some to Warna. "So, I decided to seek my fortunes in the human lands. I offered my sword and my fealty to King Jeverard, and he accepted it. Later, he awarded me Tassinic for my services to the crown."
"King Jeverard was King Everard's grandfather," Warna said slowly, as if trying to absorb what he was saying.
"Oh yes." Verice gave her a wry look. "And I know the answer to your next question."
Warna stared at him blankly. "My next—"
"I'm seven hundred and ten years old," Verice said.
Chapter Seven
"Seven hundred and ten?" Warna's breath caught. It was one thing to be told that elves lived long lives. It was quite another to hear one say it so casually.
"Give or take," Verice shrugged, then chuckled. "It always hits you humans oddly. Every time I say it, the humans around me get the strangest look on their faces, as if it couldn't be."
"It's just that your voice is lovely," Warna said. "And ten years studying music seems to me almost a—" she hesitated. "A lifetime."
"For you, perhaps." Verice nodded. "War and magic leave little time to perfect other arts. But I always encouraged others in their endeavors."
"Tassinic is known for its love of music and dance," Warna said.
"It was," Verice agreed. "There is little time for such pleasure now."
There was a tap at the door frame, and at Verice's 'Enter', the serving lads swooped in, removing all the platters, bowls and plates at a rush. Warna managed to save her kav, but the rest was gone in a flurry of clattering crockery.
The door closed behind them, and Warna became conscious of the time. "It's late, m'lord. My thanks for the evenin—"
"What were your plans?" Verice asked. "If I hadn't taken...command?"
"I'd hoped to go back," Warna said. "Try to salvage what I could and rebuild. But no one was sure what was happening, and until the Lord High Baron took control again, it wouldn't be safe to go back. Grandfather had a brother, a wine merchant in the Barony of Wyethe, who would have sheltered us. At least, that was the plan."
Verice studied his cup, then looked her right in the eye. His were so startlingly silver-blue, glittering in the lantern light. "The reports I've had say that Farentell has fallen, and under the control of the Usurper's forces. The Lord High Baron is dead. Farentell is no more."
Warna closed her eyes against the pain welling deep within her.
"The Usurper has crushed any resistance, and seems determined to level every town and village. Slavery is now the law in the areas under his control. There is nothing to return to, Warna."
She tried to hold back a sob, but it escaped her. She covered her mouth as the tears started to flow.
"I've upset you." Verice leaned forward.
"Not you, m'lord," Warna choked out. "But the Usurper has much to answer for."
"In that, we are in agreement," Verice responded. He rose to his feet, and offered his hand. "Tomorrow, I'll take you to see Charrin, a Bard who used to grace my court. He will give an honest assessment of your skills. You will stay with him and some friends of mine, for a time, until you decide what you wish to do."
"M'lord?" Warna rose.
"You are my ward, by virtue of my...taking command." Verice took up the lantern from the table. "But your life is your own, Warna of Farentell, to make of it what you wish. Once you know what that is, I will see you established."
She was having trouble taking it all in, and wanted nothing more than to find her small bed, and crawl within. She reached for the lantern, but Verice shook his head. "I would see you to your chamber, lady."
He allowed Warna to lead the way, careful to hold the light so that she could see. The sorrow was still thick in her eyes. It wasn't the way he'd wished to end the evening, but he owed her the truth.
Not that it was any great distance to her chamber. Up the stairs to the attic of the barracks, down a hall with rooms full of snoring warriors to every side, to the base of a ladder that led to her tiny loft.
"Give me a moment to light a candle," she murmured as she reached for the rungs.
"Take this," Verice handed her the lantern. "There's a mage light within. Far safer than a flame in tight quarters. And see," He flicked the small shutters. "You can control it this way.
I see well enough without it."
"Thank you," She paused, staring at him.
He stood there for a long moment, returning her stare, feeling somehow...disappointed. He took a step back, and bowed. "Good night, Warna." With that he walked off, just far enough that he knew she could not see him.
He paused then, listened to her climb the ladder, and the rustle of her clothing as she prepared for bed. Waited as she crawled under the blankets.
Waited as she whispered a soft prayer for the souls of her family and Farentell.
Closed his eyes as she started crying for her losses, her sobs muffled by her pillow.
Verice cursed the night then, cursed the Lord of Light and Lady of Laughter, cursed his Ancestors, cursed life itself that caused such pain to one so undeserving.
Almost, almost he went back, to climb the ladder and catch her eye, and cast a spell of dreamless, sweet sleep. The urge was strong. But she'd not thank him in the morning, he was certain of that. Let her mourn her dead, let her grieve for what was lost.
He stood guard, bore witness to her pain, listened in the dark as she cried herself to sleep. Once her breathing evened, he turned away, seeking his own bed.
As he climbed within and pulled up the covers, he knew he'd see her off safe in the morning.
It was for the best. This was no place for a human woman. He and his men were prepared for attacks; they were warriors who could defend themselves if need be. There was no comfort to be found here, no safety. She could not stay.
The nightmares claimed him through the night, but the innocents he'd failed to protect all had golden hair, and brown eyes flecked with gold.
Chapter Eight
Warna woke well before dawn, with a raw throat and scratchy eyes.
She rolled to her side, flipped her pillow and burrowed down into its coolness. She'd left the shutters on the small window opened, and moonlight filled the room.
Her heart lay numb and cold, a terrible empty feeling in her chest. It was all gone, and she'd known it before Verice had confirmed her fears. Known it by the dead look in her father's eyes as he'd kissed her mother's coffin. When word had come of the deaths of her brothers. When she'd held her grandfather's hand, and sung him to sleep for the last time.
'Your life is your own, Warna of Farentell, to make of it what you wish.'
All well and good for him to say so, but the thought filled her with dread. It might be freedom in his eyes, but to her it looked like a great, yawning maw of 'unknown'. She'd no skills to speak of, and while Lord Verice thought her songs were special, Warna knew full well they were not.
What did she want? She wanted what she'd had. A home, a future planned for her, a family who loved her and were loved in return. She'd looked forward to building a life with a husband of similar mind, and a family of her own.
Exhausted, drained, she closed her eyes, and fell back asleep with just enough consciousness for a simple prayer. "Lord of Light, Lady of Laughter, hear my prayer. Grant me grace and strength, Lord. Grant me wisdom and peace, Lady. Show me the way..."
In the morning, Warna stepped out into a crowd of waiting men and horses. "What's going on?" she asked Constable Ricard quietly.
"It's your escort," Ricard responded just as quietly. He carried the woven lidded basket that held her clothes on his shoulder. "Lord Verice ordered it doubled."
"Looks more like I'm being escorted to my execution," Warna said.
"That's not funny," Verice ground out from behind her.
Warna jumped, startled. "M'lord," she started, then paused when she saw his eyes. "If you'll forgive me, you look like you didn't sleep."
"I'll sleep better when you are safe," Verice growled. "Constable, you will have command."
"Aye, m'lord." Ricard heaved her basket up onto the back of one of the horses, and secured it. He gave Warna a nod. "Be well, miss." He lowered his voice. "The Lord and the Lady go with you."
"With you as well," was all she had time for as Verice took her elbow, and guided her to a horse.
"You can ride?" he asked.
"Yes," she said shortly. She reached for the saddle and mounted quickly, glad she'd chosen tunic and trous for this day.
Verice mounted the horse next to hers. He'd braided his hair, and now wrapped it around his head and put on a helmet. "Narthing, you have point. No ceremony."
"Aye," Narthing called from the front of the group. "Mount up," was the command, and all obeyed. Warna felt dwarfed by the maels around her as they took to their horses.
"Forward," Narthing called, and the group started out, hooves chiming on the stones as they walked toward the great gates. Warna admired the huge doors, which swung open silently, pulled back by the great chains she could hear rattling overhead.
But as her horse's head cleared the gate, some force pushed her hands back, as if she was against a wall. "What is—?" she exclaimed. Her horse continued on, but her body was forced back, pushed back by some kind of barrier. The pressure slammed her knees and chest, and she felt the horse walking out from beneath her—
A strong arm wrapped around her waist, pulling her from the horse before she fell. She gasped, clinging as Verice turned his horse away from the gate, cursing under his breath.
"What happened?" she asked. The warriors milled about her, some stopping her horse. Narthing was calling commands to halt.
"Nothing," Verice growled in her ear. "Let's get you back on your horse."
She became conscious of his arm, holding her up, pressing her body against his. She flushed. "Thank you for the rescue, m'lord."
Verice said nothing, just lowered her to the ground as her horse was brought back.
Warna re-mounted, settled herself in the saddle and grasped the reins tightly.
Verice hovered, whispering something under his breath that she couldn't quite understand.
She urged the horse forward at a walk, and the animal plodded forward patiently, passing through the massive gate without a problem.
Confused, she concentrated on staying in the saddle as they rode forward, at least until she happened to look up. Then the view took her breath away.
She'd caught a glimpse of it when she'd tried to throw herself from the balcony of the keep, but it had only been a glimpse, and she'd been...distracted. But now, the walled city below the castle was spread out before her. The whole thing gleamed white and shining in the sun. The odd thing was, there seemed to be green within the walls.
It didn't take long before they were at the walls, answered the challenge, and through the gates. Warna discovered, to her delight, that there were trees, and even gardens, some with flowers, some with vegetables. The buildings weren't piled on top of one another, like in the towns she'd seen in Farentell. These storefronts and homes seemed crisp, somehow. Everything planned, and in its place. It was lovely, but it felt so different from her home.
The people were the same, going to and fro with tasks and chores. Warna's group didn't draw much attention as they passed down the wide street at a trot.
She glanced over at Verice, who rode straight and tall, his helmet hiding his face.
He met her eye for a moment, then looked away.
They continued on for a while, then Warna grew conscious that the group seemed smaller than when they'd started. When two more warriors pulled away from the group, she knew she was right. She stopped staring around, and focused on where they were going.
Two more warriors stopped at a fountain, announcing that they would water their mounts. That left two riding beside them. Verice continued on, slowing their pace. "It's not far," he offered quietly.
Which was good, because Warna hadn't been in a saddle for some time, and she was starting to feel it.
"Here," Verice stopped in front of a bakery and dismounted. "Best sweet buns in town."
Warna dismounted as well. The warriors with them took the horses, seemingly headed to a smithy down the way. Verice took her lidded basket from one of the horses, and motioned her to a door.
He ushered her in to a small room with a long counter. The three women inside looked up from their work. The oldest one smiled and walked forward.
"Lord Verice," she dusted flour from her hands, and curtsied, even as she darted Warna a glance filled with curiosity. "We were told of your coming, Lord."
"Which door?" Verice asked.
The woman laughed. "You know him, m'lord. Tis through the necessary." She paused, with a twinkle in her eye. "Might be wishing to grab a cloak."
Verice shook his head, which just made the woman chuckle. He shifted her basket to one hand, and headed through a side passage, down to a door. Warna followed.
They passed through a cloak room, and here, Verice gathered up a heavy woolen cloak. "Here," he said. "Put this on."
"But," Warna objected.
Verice ignored her, setting the basket down and sweeping the cloak over her shoulders. "Trust me," he said, clearly amused by her confusion.
Warna huffed out a breath, but left the cloak in place. Verice picked up the basket and led the way.
The door opened into a kitchen garden with a privy beyond. Verice opened the door with its moon carving, and bowed her through.
Warna had brothers; she gave Verice her best 'what-are-you-up-to look'. But he just shook his head in denial of any trick. "Watch the first step," he said as she entered.
She found herself on a high mountain trail, ice and snow glittering in the moonlight, the fierce wind stealing her breath.
Chapter Nine
Warna staggered, for she had stepped from bright warm day into crystal cold night. She felt Verice's warm arm wrap around her waist.
"Told you." His breath was warm on her ear as the cold wind swirled tiny snowflakes around them.
The path was clear, but not the peaks. Hard, sheer spikes of stone, decorated with the rims of frost sparkled under the moonlight. What stars could be seen were bright in the midnight sky. It was beautiful and terrifying all at once.
She breathed in. The air seemed thin and insubstantial, as if her breath was not enough to sustain her. And the bitter cold cut right through the cloak. A gust of wind hit them, carrying sparks of icy snow that stung her face.
But Verice stood behind her, warm and strong. She wasn't afraid; although a glance back showed that there was no door behind them. "Where are—"
The rock face farther down the path split open, spilling warmth and light. "Verice! How good to see you," an elderly elf with wisps of white hair poked his head out the door. "And company! Even better. Come in, come in!"
Verice guided her the few steps up and through the door. "Wolfe, it's good to see you."
It was a small room, that smelled of leather, soap, and bread. It was lined with shelves, and cloaks hanging from pegs. Warna watched where she stepped. The floor was cluttered with boots tucked under benches, and parcels and baskets at her feet. Winter woolens spilling from the shelves.
There was a scrabble of nails on wooden floors, and they were surrounded by a pack of large smooth-haired dogs, noses lifted to take in the scents, tails high, barking in their excitement. Warna laughed, trying to scratch as many ears as she could reach.
"Now, now, stop that, settle down," The old elf closed the door, cutting off the cold air. The dogs ignored him as they milled about, knocking into Warna, scattering parcels and tipping over baskets.
"Sit," Verice commanded.
The dogs all sat, tongues lolling out of their mouths, uttering muted whines of excitement and happiness. They were various hues, running from dark brown to soft gray, long noses and all leg.
"They're beautiful," Warna said, as Verice took her cloak. The whole room reminded her of home so much. Her brother's hunting dogs, her father's boots. She blinked away her tears, reaching out to pet the closest. The animal wiggled all over, darting pleading looks at Verice. "Down," Verice said, shaking his head.
The dog yipped as it collapsed onto its side, rolled over and begged Warna to rub its belly. Warna laughed, and obliged.
"Shameless," Verice said gruffly, as he gave the others attention.
"None to blame but yourself," the older elf snorted. "Since they're your dogs."
"They are?" Warna glanced up to find him staring at her, his gaze flicking to her ears. Suddenly self-conscious, she stood.
"They were," Verice straightened. "Wolfe, may I present—"
"No, no, let's wait until Kalynn is with us," Those considering eyes were now twinkling with some inner joke. "Come up, come up," The elf smiled at Warna. "We're on the roof. It's a bitter night, but perfectly clear." He led the way to a door opposite, which opened onto a spiral staircase. "Kalynn will want to hear every word."
Verice gestured, her lidded-basket still on his shoulder. Warna followed the elf up the most cluttered staircase she'd ever seen. The staircase was narrow, the stone steps all worn in the center from years of use. The light was warm, welcoming and steady, but it was as if the very stones glowed, since there were no torches she could see. Even the wooden doors they passed glowed yellow with age.
On each side of every step was a basket, crock, chest, with piles of books and scrolls adding to the clutter. All filled with such a variety of things that Warna's head was spinning before they'd gone a single flight. Baskets of crystals, of rocks, of yarn and cloth. Beads in one, and gold coins in another, none of which she'd ever seen before. Shells, and feathers and dried plants all haphazardly piled in various boxes and containers.
The walls held swords and daggers, shields and lances, all displayed with animal skins spread out between them. At one point she saw two crossed lances, and between them a large rib bone decorated with beads and feather and a strip of bells.
She actually stopped before one beautiful tapestry, showing a warrior-woman on the back of what at first appeared to be a winged horse, carrying a glowing blue sword. But a closer look showed that it was more of a hawk-horse, with fierce eyes and clawed front feet. Still, it took her breath away, the details of the feathered mane, and the light in the woman's eyes.
"Airon," Verice said behind her, re-balancing her basket. "They are called airons. Fierce fighters, and rulers of the skies."
"It's lovely," Warna said, but then she jerked her head at a further thought. "They really exist?" She stared at the skull hanging next to it, covered in etched engravings. "Is that a dragon skull?" she breathed.
"Wyvern." Verice said.
"Are you coming?" Wolfe asked from the stairs above. "Watch your step," the old elf said, as Warna hastened up. "I fear I've fallen behind in my cataloging."
There was a snort from Verice. Warna glanced back to see him shake his head.
The dogs swarmed around them, heading up the stairs, knocking things over as they scrambled past.
"Here now," Wolfe said irritably.
"Don't blame them," Verice said.
"It's my tower, lad," Wolfe retorted. "Age has its privileges."
"Age is not an excuse to avoid cleaning," came a female voice from above.
Warna climbed up the final flight of stairs and found herself emerging onto a rooftop. She stopped dead, and Verice had to urge her up the last few steps.
There were chairs in the center of the roof, clustered around an area rug and a table. Chairs with padding, the kind that Warna had heard of but never seen. But that wasn't what commanded her attention. It was the night sky above them, clear and crisp, with stars scattered over a velvet sky, and the moon low over the mountains that surrounded the tower.
Yet the air was warm. She took a breath, and laughed at the wonder.
"Amazing, isn't it?" a low female voice asked. A woman stood at the table, smiling at them, dressed in embroidered robes of red and gold. Her skin was the color of dark honey, and her white hair was piled on the top of her head. Her eyes were the same silver as Verice's and filled with welcome. Warna couldn't see her ears, but she had the same air as Wolfe, and she looked as what Warna had imagined elves to be, when reading her childhood tales.
"May I present to you Warna of Farentell," Verice said, coming to stand next to Warna. "Warna, these are my friends and mentors, Mage Wolfe, and Seer Kalynn."
Warna would have curtsied, conscious of her tunic and trous, but Kalynn stepped forward and took her hands. "Come, sit. Farentell, eh? That's a barony in Palins, is it not? Next to yours, I believe, Verice."
"It was," Verice said. "Farentell has fallen to the Usurper now. Warna came to Tassinic, fleeing the conflict. She is under my protection, now."
Kalynn drew Warna to one of the stuffed chairs. She sat, trying not to notice the startled looks on the faces of Wolfe and Kalynn. The dogs had followed them up the stairs, and were settling all around them, sprawling on the rugs.
"Protection?" Wolfe asked sharply.
Kalynn silenced him with a glance. "You are most welcome, Warna. It's not often we have visitors."
"As to that—" Verice set his burden down and settled on a chair next to Warna's. "I've come with two requests. I'd ask that you shelter Warna for a time. For her own safety, she cannot continue to stay at the castle."
"Continue?" Kalynn asked sharply.
Wolfe now silenced her with a glance. "She'd be welcome, of course."
"And the second, lad?"
"I'd like Charrin to hear her sing, and evaluate her skills in music," Verice said. "I believe that she has a gift for music that should be nurtured and protected."
Wolfe and Kalynn both stared at Verice. Warna concentrated on the dogs, avoiding the looks of dismay on their faces.
"Verice, are you sure that's wise?" Kalynn asked quietly. "Charrin is still healing, and I am not sure that he would..." Her words trailed off as she glanced at Warna again. "I am not sure this is advisable."
"At the very least, its damned insensitive, lad." Wolfe shook his head. "There are other Bards who could evaluate her abilities."
"Yet you'll shelter her," Verice pointed out.
"Of course," Wolfe said. "And we'd resolve any issues that came up as a result. Might even do him good, to live with a—" He stumbled over a word. "To have other people around. But to ask Charrin's opinion about her talents is just asking for—"
"Whose talents?" A warm, baritone voice floated over to them. Warna turned to see another elf coming up the stairs slowly, with a stick in his hand. She drew in a sharp breath. Unlike Verice and Wolfe, this elf's hair was black, a silky curtain down his back. But his face—
An ugly, raw gash crossed both eyes, empty sockets sightless and staring.
Chapter Ten
Warna caught her breath at his scars, then regretted her rudeness. It hadn't been loud, perhaps he'd not heard—
The blind elf turned his head slightly. "Who is that?"
"Charrin," Kalynn rose gracefully from her chair, and moved toward him, her robes swishing against the stones. "Verice has brought a guest who will be staying with us for a while. Her name is Warna and she is of—"
"Why are you speaking the human tongue?" Charrin stood stiff and straight, not advancing further into the room.
"Warna is of Palins, of the Barony of Farentell," Wolfe said firmly. There was a warning note in his voice when he added. "She is a guest in my home."
"She is an innocent, Charrin." Verice said. "She fled her own home in the face of the Usurper's—"
"My Lord Verice, welcome." Charrin's voice was hard. "It has been some time since you graced us with a visit."
"It has," Verice said mildly. One of the dogs at his feet whined softly and pushed its head into his hand to be petted. "Far too long," he added, stroking the dog's ears.
"The demands of your office, I am sure," Charrin said. "Being the High Baron to a savage people."
"Charrin," Wolfe growled.
"Charrin, let me aid you to—" Kalynn reached for his arm.
"No," Charrin bit out the word. "I need no aid." He moved forward, his steps deliberate but confident. The dogs were quick to move out of his way. Charrin sat in one of the chairs, settling himself with an easy grace.
"You seem to be getting around well," Verice commented.
"A spell," Wolfe said. "It occurred to me that it might be possible to allow him to—"
"See?" Warna blurted out.
"No," Charrin said. "It allows me to perceive. To sense the space around me. But it is not sight. There is no color, no depth, no...beauty."
Warna bit her lip at the venom in his tone. "I'm sorry. I—"
"A human," Charrin's voice was flat now.
"I have taken her under my protection," Verice said. "She has a gift of—"
"And we all know how well you protect your own," Charrin snapped.
Verice's head stayed down. His hand paused, then he continued to pet the dogs.
"Charrin," Wolfe growled again, but Kalynn touched Warna on her arm. Warna looked up into her warm smile.
"I think we could all do with hot kav before this conversation continues," Kalynn said. "Would you help me?"
"Of course," Warna stood quickly, more than ready to leave the room.
"I'll brew a fresh pot," Kalynn said to the men. "We'll return when it's done." She paused before descending the stairs. "Try not to destroy the furniture, Wolfe."
Warna followed, down the cluttered stairs. She waited until they were out of sight before speaking. "M'lady, I am sorry that—"
"You are not the cause, Warna." Kalynn glanced over her shoulder with a sympathetic look. "Verice can be insensitive at times, don't you think?"
"Well," Warna said, thinking back. "He expects his word to be law, that's certain."
Kalynn laughed, and led the way down and then through an arched doorway into a bright kitchen with round windows that let sunlight stream in and pool on the stone floor. Day into night; night into day. How marvelous. There was a small fire in the hearth, and a pot of something that smelled wonderful suspended over it, bubbling away.
"This doorway wasn't here before." Warna stopped in the archway, glancing back at the stairs. "And the sun—"
"It's Wolfe's mage tower, dear," Kalynn went to the hearth and pulled over a kettle. "It's what it needs to be."
Warna moved farther into the kitchen, marveling at the idea of a mage tower. On the far side of a wooden table, a cat lay in a patch of sunlight. It had the oddest mottled coat of black, brown, yellow and a kind of green. Not pretty exactly but—
The cat fixed its watery yellow eyes on her, and rolled onto its back, inviting a belly scratch.
"Oh, you pretty thing," Warna crooned, and reached down—
"Careful," Kalynn said sharply. "She—"
Its fur was warm and soft and Warna gave it a good rubbing, careful not to scratch too hard. The cat started purring, a rough rumble that seemed to echo through the room. Warna enjoyed the moment, then straightened. "My family had cats in the stables and—"
Kalynn was standing there, staring at her unwaveringly. Her light silver eyes seemed unfocused.
"Lady," Warna asked tentatively, worried that she had offended.
Kalynn blinked, then her eyes became sharp. "How long have you known Verice?"
"A few days," Warna said cautiously.
Kalynn nodded, gave her a patient look, then prodded, "And how did you meet?"
"Well, truth be told—" Warna started.
"And it's always best to tell the truth," Kalynn said. Her eyes softened.
"He kidnapped me," Warna blurted out.
"Ah," Kalynn set up the kettle to brew. "To keep you safe, I suspect."
"Well, yes," Warna admitted.
"Still, unsettling, isn't it?" Kalynn had a soft, smile on her face, as if remembering something. "For what it's worth, I do believe he has your best interests at heart." Kalynn gestured at the kettle. "While we are waiting, let's find you a room for your stay."
"If it's no trouble," Warna said.
There was a slight rumble, as if of thunder, coming from overhead. Kalynn shook her head, and took Warna's arm. "No trouble at all, dear. You have much to show me."
Warna tried to puzzle that out, but she must have misheard.
Kalynn lead the way out the archway. "Up, I think," Kalynn suggested. "For a better view."
Warna watched carefully as they went up a few steps, and found a door on what she could have sworn was an exterior wall.
Kalynn clicked on the black iron handle and pushed.
"Oh my," Warna breathed.
It was a lovely room, with a small sitting area, and doors leading off. A fire crackled in a fireplace, but what really caught Warna's eye was the large window in the wall opposite, sparkling with panes of clear glass in a diamond pattern. At the sides were heavy white curtains covered in large pink roses. "Oh, this is marvelous," Warna whispered, and reached out to undo the clasp and open the windows wide. Kalynn stepped to her side.
Under a dark night sky filled with stars, a frozen lake stretched out below, surrounded by snow-covered fields as far as she could see. A breeze caught a flurry of snow and it sparkled as it danced over the windowsill.
On the far shore of the lake, Warna could just make out a crowd of people, dancing slowly and stately in the light of the torches they carried.
Warna took a deep breath. "Oh my." She laughed in amazement as she glanced at Kalynn. "That's all the words I can seem to find!"
But Kalynn's face was somber, not sharing her amusement. "Interesting." Kalynn tucked her hands into her robes. "Have you ever seen the like?"
"No, never." Warna shivered as the cold spilled inside.
Kalynn pulled the windows closed. Warna thought she caught a look of sadness in the woman's eyes, but when Kalynn turned to her, she was smiling. "What do you think of this? There's a bedroom through that door, I suspect."
There was indeed, and Warna took a few moments to explore the empty clothes press, and the privy. But what drew her was the bed. It beckoned her, with bed curtains and a thick comforter with the same flowered material. She glanced at the door, then climbed up onto it, lying flat. Above, the cloth top was embroidered with flowers and all manner of bees, insects and birds.
"Oh my," Warna breathed.
Kalynn chuckled from the doorway. "So, it will suit?"
"It's almost too much, M'Lady." Warna got up, and smoothed her tunic. She felt almost giddy at the idea of living here, sheltered and safe in this lovely room. Yet she wasn't quite sure. Was this what she wanted?
She knew what Verice wanted.
"I'll have Verice bring your wicker basket down before he goes." Kalynn opened the empty clothes press and paused before continuing. "We can see about getting you what you need tomorrow." She closed the press, and turned back to the door. "Let's check the kav, shall we?"
Back on the stairs, Warna frowned. "How will I find my way back?"
"It will be there when you want it to," Kalynn said absently. "I think we should find something for the men to eat. It's harder for them to argue if their mouths are full."
The kitchen was bright and warm, and now smelled of brewing kav. Warna settled on one of the benches as Kalynn pulled out a cutting board and a knife. "Here. Slice some of this cheese, and I'll cut fruit."
"M'Lady," Warna hesitated, then blurted out her question. "What happened at the castle? I was in the keep, and I saw the broken window, and dried blood on the floor.
"Dried blood?" Kalynn paused, and shook her head. "Oh, Verice." her voice filled with soft sorrow. She went silent for a moment.
Warna waited.
"Warna, I wasn't there when it happened." Kalynn sighed. "And we can't leave our menfolk alone for an extended time. Wolfe's temper will only hold for so long. But still—" Kalynn took a deeper breath. "You need to know."
Chapter Eleven
Warna held her breath, waiting for answers.
"During the Festival of Light and Laughter, the castle and keep at Octara were attacked from within by the Usurper's forces. The castle was filled with celbrants at the time. Many were killed, more were left badly injured." Kalynn shook her head. "One of those who died was Summer, Charrin's mate. Charrin was blinded. Summer died in his arms."
"Oh," Warna whispered.
"Verice blames himself, even though he barely survived. Healers have a rule, you see. Save the one you can over the one you can't," Kalynn said. "Verice wasn't conscious when the healers made the decision to treat him instead of Summer. Verice blames himself for all of the deaths, not just Summer's. He commanded the keep be abandoned, and has forbidden any entrance. He maintains a military presence within the castle walls, but that is all."
Warna nodded, thinking it over. "It's all there, untouched, as it was that night?"
"So far as I know," Kalynn said. "And he's gone to extremes to protect everyone and everything he cherishes. His staff and servants scattered among the various towns and villages, kept safely away. A mistake, to my way of thinking. The stars alone know how it will turn out."
"But, you are a Seer?" Warna was confused. "Can't you see the future?"
Kalynn's smile faded, and her eyes grew distant. "If only that were so. What I see are possibilities. They swirl about us through the air, like the scent of roses lure one into a garden." She looked at Warna and wrinkled her nose. "Or the scent of muck pulls you to a midden."
"Oh," Warna said softly. She had rather hoped otherwise.
Kalynn's lips curled gently, as if sensing her disappointment. "You are not the first to wish for answers, child. But life does not offer answers. It offers choices. There are endless choices in our lives, Warna. Each choice influences another."
Kalynn's voice was soft and warm, her movements slow and precise in the afternoon sun.
"Every so often, a seer can influence one person. Show them the possibilities. Just a few words can make all the difference in a person's choices. Now, where is that crock of honey?"
Kalynn turned back to the hearth, reaching for a small crock on the mantlepiece, then poured the hot kav into a pitcher. Warna arranged the cups on a tray, and loaded up the cheese and fruit.
"There, all done." Kalynn smiled. "It will be so nice to have you here. Perhaps between the two of us we can organize Wolfe's collections."
"It won't be a problem for me to stay?" Warna asked. "I noticed Verice didn't ask permission before we appeared on your doorstep."
Kalynn laughed. "We've known Verice a long time, dear. Wolfe was his mentor. If it was an imposition, we would have declined, trust me on that. If you decide to stay, we would welcome your company." She gestured to the other tray, and Warna picked it up.
"Decide?" Warna said.
"I'm sure you were a dutiful daughter, Warna of Farentell." Kalynn headed for the stairs. "But now your life is your own. You are free to live as you wish, but that means that you make choices, and live with them." Kalynn turned up the stairs. "Not always easy."
Warna followed, frowning. "Verice told me much the same thing," she said.
"Did he?" Kalynn's voice echoed on the stone walls. "That bodes well, don't you think?"
Warna paused on the step. Honestly, it did. If he was sincere. If he truly allowed her to make her own choices.
"Come," Kalynn's voice echoed down to her again, pulling her from her thoughts. "Let's return before Wolfe decides to express himself with bolts of fire. I rather like those chairs, and he'd melt them to slag without thinking and apologize afterwards."
Warna blinked, then followed.
The air was thick with strain as she and Kalynn emerged onto the roof. All three men were taut, each face stiff with disapproval.
Warna glanced at Verice as she set the tray down. He didn't look up, so his eyes were hidden from her. His face was carefully blank, concealing his thoughts.
Kalynn ignored the frigid silence. "Verice, I think you take your kav black and sweet, yes? All that honey is going to rot your teeth."
Verice flashed a tight grin, showing his perfect teeth. "Not so far."
"Give it time," Kalynn replied, handing him the mug and the crock.
Warna poured for Wolfe, who thanked her.
"None for me," Charrin said. "Lady Warna, the Lord High Baron Verice has expressed a desire to know the true potential of your musical abilities."
Warna set the pitcher down slowly, almost afraid to breathe. He'd been so angry before she and Kalynn had left the room; she wasn't sure she trusted this turn-about.
Charrin's back didn't touch the chair, his hands still in his lap. But his face seemed composed and professional.
"Lord Bard Charrin," Warna returned formal with formal. "I would be honored, but I would not seek to impose. I would fear to waste your time—"
"Service to one's craft is never wasted," Charrin replied. "But you understand that mine will be an honest assessment? I will tell you the truth."
Warna glanced over her shoulder at Verice. "Lord Bard, you should know that my father had me sing for a human minstrel a few years ago. He—"
"Your pardon," Charrin said, "but a...minstrel's...opinion is nothing to me. Let us begin. Do you have any formal training in music or voice?"
"No, Lord Bard," Warna said. She smoothed down her tunic front, then stilled her hands.
"Very well," Charrin said. "Verice says that you compose."
"I make up lyrics and tunes to go with them." Warna said.
"Then sing for me, Warna of Farentell," Charrin commanded. "And we shall see what you have within you."
Chapter Twelve
Warna froze. She hadn't planned, hadn't practiced. What to sing?
Her 'flower' song wasn't done yet, so that wasn't a possibility. The room was so tense, and there was so much grief in them. Nothing sad, then. She drew a slow breath, relaxed her shoulders, and lifted her head.
"The farmer's lass was tall and fair;
her beauty was her fame
Her suitors came from miles around
to try and make their claim."
Warna breathed, trying to pace her voice and her tone, making sure to hit the notes clearly and evenly.
"Daily she'd to market go,
selling cheese and butter.
They'd stand before with hat in hand
their troth to spit and stutter."
Charrin's face was blank, his head down and slightly tilted as he listened. But Wolfe and Kalynn were smiling.
"The lass was also quick and sharp,
her wit like knives a'slicing
She'd toss her hair and lift her chin
and sing out this reprisal."
Warna tossed her own head, tapped her toe three times fast, and broke out into the chorus, giving it her all.
"Hie thee hither and get thee hence,
art not the lad for me.
Hie thee hither and get thee hence,
art not the lad for me.
The lad I'll love is tall and dark
and handsome as can be.
So, hie thee hither and get thee hence,
art not the lad for me."
Kalynn laughed, Wolfe smiled. Verice leaned back in his chair, his face stoic, but with crinkles in the corners of his eyes. Warna felt the fleeting tingle of having pleased her audience, and joy welled up inside. She posed like a saucy maid, and continued:
"Then came the day, a lad rode in
with kind and smiling eyes
Fair, and tall and dark and strong,
he clearly was her prize."
The lad I'll love is tall and dark
so sweetly sang, did she.
So, hie thee hither and get thee here,
thou art the lad for me."
She paused then, waited for their attention, and when she had it, spoke. "And then he sang,"
"Hie thee hither and get thee hence,
art not the lass for me.
Hie thee hither and get thee hence,
art not the lass for me.
The lass I'll love is sweet and kind
and gentle as can be.
So, hie thee hither and get thee hence,
art not the lass for me."
Kalynn and Wolfe laughed and clapped, exclaiming their pleasure. Warna smiled, and curtseyed, risking a glance at Verice.
He was looking at her, his face still set in that bland, neutral look. But there was sparkle in his eye, and the shadows were gone. Warna reached for her mug and sipped her kav, satisfied.
"A sprightly tune," Charrin said. "A peasant's song in nature, certainly not meant for this type of audience. More appropriate to a tavern, I should think. I would have made other word choices, but you carried the story well, and the ending is a pleasant, if obvious, one." Charrin reached for the pitcher, and his mug.
"Come, come," Wolfe said. "Don't leave her waiting. What of her voice?"
Charrin ignored him, pouring the liquid carefully, then returning the pitcher to the table with a slow grace. "Your pardon. I was collecting my thoughts."
He took a slow sip of kav.
Warna settled herself in a chair, her kav in her hand. One of the dogs saw an opportunity and came over, its brown eyes begging. She reached out and scratched its ears.
"Lady Warna, your voice is pleasant, and you have some basic understanding of breath control and pacing," Charrin said. "but you lack the training necessary to develop any further. In comparison to other professional singers, yours is, at best, mediocre. Even if you were to undergo training, I fear you would be unable to advance much past a very basic level."
Warna nodded, hiding her face in her kav. No more than she expected, to be honest, but it still stung.
"Well, I thought it was very good," Wolfe huffed.
Kalynn was about to protest as well, but Warna just shook her head. "Kalynn, that's what the minstrel told me too." She chuckled to ease the shock in Kalynn's face. "But she also told me that the joy of creating is just as important as perfection of the art. Perhaps more so. And that she'd sing with me anytime."
"A human attitude, certainly," Charrin sniffed. "Of course a human would think as much. With no time to achieve perfection, why attempt it? It's amazing that they crawled from their caves and learned to walk, really."
"Charrin, that is uncalled for," Wolfe snapped.
"And rude," Kalynn said.
"It is simply the truth." Charrin made a small dismissive gesture with his hand. "Their lives are as snowflakes, harmless and melting if they fall on your skin individually, but dangerous and deadly as they multiply. They will destroy us all."
"Palins and Valltera have lived in peace," Verice said calmly.
"Because you are the buffer - and what has that created? A barony rife with half-breeds and—"
"Charrin," Wolfe said low and dangerous.
"I'll not be silenced," Charrin cried out. "Why have you come here, Verice? I expected word that you had avenged the attack on your people, but that isn't the case, is it? Why haven't you taken vengeance, Verice?"
"You know why." Verice's voice was flat. "If I gather my forces to attack Edenrich, the Black Hills will rise against me. Rumor has it that the Baroness Elanore has turned to the dark arts to create an army."
"If that is true, then every one of your dead makes her that much stronger." Wolfe grimaced.
"I have no assurances that Summerford or Wyethe would not turn on me as well," Verice said. "And while King Barathiel of Valltera has never threatened, still, he has eyes on my land as well. So, I hold to my own borders and ward them. The time may come when I can strike at the Usurper, but that time is not now."
"Yet the blood spilled cries out for vengeance," Charrin said hotly. The dogs raised their heads, roused by the rage in Charrin's voice. "The Ancestors cry out for it. I cry out for it. You take no action, and that human filth sits on the Throne of Palins and mocks all that is fair and noble. Had I my sight, my sword would be in my hand, and his blood—" Charrin was shaking, his face distorted. He jerked to his feet and threw his mug across the roof where it shattered on the stones.
The dogs sprang up, putting themselves between Verice and Charrin. The one next to Warna shifted slightly, keeping a wary eye on the trembling elf.
"You must have loved her so very much," Warna whispered.
"She was my all," Charrin seemed to collapse in on himself as he sank to his chair. "She was..." He trailed off. "And now here I am, unable to avenge, unable to even breathe."
"I am sorry," Warna said.
"How can one such as you understand?" Charrin turned on her, the rage back in his voice. "How can you even comprehend—"
"It's a deep physical pain, like a part of your soul is gone," Warna struggled to get the words out. "A wound no healing can touch, not that it's healing you want. I've tried to put it into a song, but I can't find the words. My throat closes, my heart breaks, and the tears just come."
"How dare you think you know my pain." Charrin covered his face with his hand. "I have not sung since her death. I do not know if I ever will again."
"You will, Charrin," Kalynn's voice was firm. "Summer would not wish it otherwise."
Charrin turned to Verice. "You could send assassins." His voice held a compelling note of pleading. "As they did. You could open a portal into the castle, and pour your warriors into their midst, as they did."
"Target the innocent, as they did?" Verice's head came up, his anger clear. "Kill the women and elderly, and strike to maim, as they did? Is your honor completely consumed in your hatred?"
"Why should it not be so?" Charrin was on his feet again, his voice a pained cry into the night sky. "Is not my life destroyed?"
Warna feared they'd come to blows. She stood as well, backing away from the two men.
Verice paused, as if her movement had brought him back. He glanced at her, then away. "This was a mistake," he said, shaking his head. "We should not have come. Kalynn, Wolfe, I ask your forgiveness, and thank you for your hospitality. Warna will return with me."
"Flee, then," Charrin spat. "Leave my presence, and carry my rage and despair with you."
Wolfe shook his head. "Charrin, we've tried to help you move past this—"
"Past this? Forgive this?" Charrin cried out again. "Never, not so long as there is life within me."
"A mistake," Verice repeated. "We should go. Come, Warna."
"Is that a command?" Warna asked.
Chapter Thirteen
"What?" Verice stopped, taken aback. What had she said?
"Is that a command?" Warna asked him, standing there with an honest question in her eyes. "Do I have a choice?"
Verice stared at her as the dogs milled around his legs. Choice? Did she have a—? He opened his mouth to answer, but the words died in his throat. He'd planned to leave her here. But Charrin's attitude, his rudeness...but now it seemed the safest place for her was at his side. Wasn't it?
Yet, she'd taken his insults in stride, they had to have stung, but she hadn't lashed out at Charrin, hadn't...she hadn't let those harsh words dim her light.
He'd told her that she had a choice, and he'd meant those words, but a strange conflict rose in his heart.
Warna was looking at him, her brown eyes showing her as puzzled as he was. Wolfe watched intently, his eyes flickering between her and Verice. Charrin's lips were pressed in a thin line, his head tilted to the side, frowning. Kalynn had an odd half-smile on her lip.
"Of course you do," Verice said slowly. "But under the circumstances—" he stopped again. "I should make other arrangements. To keep you safe."
"Nonsense," Wolfe said warmly. "You've made it clear that your castle isn't safe. She's more than welcome."
Verice shot him a quick glare. Trust Wolfe to point out the contradictions in his words and actions.
"It would be lovely to have you here, Warna," Kalynn said, that half smile still on her lips. "But it's your choice."
Warna was still staring at Verice, giving him a considering look. He dropped his gaze, frowning, glancing at Charrin. She couldn't stay here; the atmosphere was too poisonous. To say her talent was mediocre; Charrin was lashing out. Verice felt sick. He'd made a mistake bringing her here, a mistake to expose her to—
Warna's voice cut through his thoughts. "Wolfe, Kalynn, I thank you for your kind offer, but I will be returning with Lord Verice."
"Well, in that case, I'll walk you out." Wolfe said. "You can take the dogs with you."
Charrin's stomach roiled with anger as he perceived Verice and his pet human disappear down the stairs, dogs in tow. Wolfe followed behind, insisting that Verice take his animals with him. Charrin's lip curled. All of Verice's animals, to his way of thinking. How dare Verice, one of the Blood, bring a human here. How dare he express concern for one so—
"An interesting turn of events," Kalynn observed.
Charrin frowned at her. She was watching them depart as well, but even in the grayscale of his perception, her expression was...interested.
"What was that I heard?" Charrin demanded, his shoulders tensing. His hands were in his lap, but balled into fists. "I heard something. Something in their voices."
"Yes," Kalynn rose and started to pick up the shards in the pool of kav. "Something starting. Something...fragile. A possibility."
"That can't be," Charrin said.
"I don't think they even know," Kalynn said.
"You think he cares for her?" Charrin spat, his voice an octave higher than he intended. He struggled to calm himself. "That's not possible. She's human. Verice is of a Bearer of the Blood of Tethnar, One of the Founders of the Kingdom of Valltera."
"A kingdom that rejected him," Kalynn said. "and that he rejected in turn. He is of Palins now. By his own choice. Has been for some hundreds of years."
"A passing fancy," Charrin sat back in his chair. "Nothing more." He snorted. "Imagine thinking she'd have a voice worth anything."
"Yes," Kalynn stood. "As to that, Charrin—"
"They're gone," Wolfe bounded up the stairs, rubbing his hands together, looking smug. "Took the dogs with them, thank the Ancestors. Don't know why I ever agreed to care for them." He glanced at the shards in Kalynn's hand. "Let me help you with that."
Ash pan and broom appeared, twirling and hopping up the stairs. Kalynn smiled as they whirled about and the shards themselves danced over to be swept up. "You're in a good mood."
"They took the dogs," Wolfe said with laugh. "And I may be old, but I recognized the look in their eyes."
"Love?" Charrin sat up, his voice sharp.
"Utter confusion," Wolfe chortled. "Both of them. They have no idea what's happening. Pity she decided not to stay. Would have been fun to watch."
"So, you think they love?" Charrin demanded, finding new fuel to his rage.
"How would I know?" Wolfe scowled. "Kalynn's the seer, not me."
"I don't see into men's hearts," Kalynn demurred.
"Ridiculous," Charrin huffed. "Verice knows full well the treachery those vermin are capable of. He'd never—"
Wolfe turned, his face contorted with a rage Charrin had never felt before. Charrin jerked up, suddenly remembering who he had just angered.
Kalynn held up her hand.
Wolfe stopped.
"Charrin," Kalynn's voice was curt. "It would appear that you have forgotten my heritage."
Charrin grimaced, keeping a wary eye on Wolfe. "Seer Kalynn, I—"
Kalynn interrupted. "Wolfe and I offered you sanctuary while you were recovering from the assault. I had also hoped to heal your heart as well, but it would seem that will take you more time."
Charrin went stiff. "It would seem I have offended you. But—"
"You have," Wolfe growled.
"You were rude to Warna," Kalynn shot Wolfe a hard glance, keeping her voice low and firm. "Wolfe and I will not tolerate such a lack of courtesy in our home."
"I ask your forgiveness," Charrin said. "I was taken by surprise at Verice's appearance."
"We accept your apology," Kalynn said.
Wolfe threw his hands up in the air.
"But even so," Kalynn continued. "The time has come for you to take up your life."
There was a long moment of silence. For an instant, Charrin felt stricken, bereft. But he straightened, his pride reasserting itself. Clearly, they did not understand his pain, his anguish. He inclined his head. "I've had many invitations from the Great Houses. The King of Valltera himself has asked for my services."
"It's time to emerge from your isolation, Charrin. A bard needs his audience," Kalynn said. "Wolfe will open a portal to aid your journey, wherever you decide to go. By noon tomorrow, shall we say?"
"I thank you for your care, Lady Kalynn." Charrin rose. "I'll withdraw now, and consider my options."
"On the morrow, then," Kalynn watched as he left, his steps slow but certain. "But Charrin—"
He stopped at the stairs, about to start down.
"The possibilities swirl around you, Charrin," Kalynn said. "'Ware your choices."
Charrin didn't turn back, but headed for the stairs with a slow and steady pace. He'd go, certainly. To where others shared his pain and grief. And would aid him to revenge.
Kalynn settled back into her chair with a sigh. There was a heaviness within her, a feeling building behind her eyes.
Wolfe eyed the stairs, waiting a bit before he spoke. "You handled that well," he said softly. "Better than I would have, that's certain sure."
"Perhaps." Kalynn shook her head, feeling the heaviness settling on her shoulders. "I'd hoped to help him release his hate. But it festers too deep for my skills."
"He lost his love." Wolfe came up behind her, putting his hands on her shoulders. "That's not a hurt that heals easily."
Kalynn sighed and leaned back into his warmth. "Beloved, a seeing is upon me."
She felt him tense then, going serious and still. "What do you need?" he whispered.
"My sketching supplies," she whispered back, and heard his movement as the heaviness grew behind her eyes. It washed over her, dragging her down. She felt Wolfe's hand as he placed parchment and charcoal in her hands before moving the table closer.
Then the power claimed her, and she knew nothing but the dark visions of fire and horror that emerged from the depths of her mind. Her hands moved. She could feel the grit of the paper, and the fine dust on her fingers.
When she returned to herself, Wolfe was kneeling at her side with an anxious look and a cool cloth for her face.
He gave her a moment before he spoke. "What have you seen, flame of my heart?"
"The time is almost upon us. It will be soon," her hand shook as she wiped her face.
"Here," Wolfe took the cloth, and stoked her cheeks. "Rest first,"
"No," Kalynn reached for him and he came into her arms even at that awkward angle. "The time has come and there is that which might be, and that which must be."
"One never really knows all the consequences of one's actions," Wolfe sighed into her neck, his breath warm on her skin. "For good or ill."
Her breath caught in her throat at the weariness in his voice. But then to her surprise, he started to chuckle.
"Ah, but I know you, Seer." He pulled back, and gripped her shoulders, looking at her with quiet mirth. "Is that 'soon' as a mountain understands time? Or an elf? Or as a fruit-fly would define it?"
Kalynn shook her head at his mirth. "I know not," she admitted to his laughter. "But Wolfe, I have seen. This must be."
She tapped the parchment, and they both looked at the picture of a man, scarred and horribly burned.
Wolfe grew even more thoughtful. "This is what you've seen?"
"Yes," Kalynn confirmed. Bile rose in her throat, but she knew the truth of her vision. "It must come to be. We must make it come to be. If what was lost is to be restored, this must happen. At our hands if need be."
Wolfe sighed. "I do not doubt you, Seer."
She reached out to cup his cheek.
"When?" Wolfe asked.
"I—" she answered without having to think. "There's time."
"How far?" he rose, studying the sketch.
"Far," she answered, looking off at the horizon. "Perhaps too far for us to be there in time."
"It would help if the visions were a bit more specific," Wolfe said dryly.
"It will come when it needs to be," Kalynn rose.
"The absence of magic means no portals," Wolfe said. "We must gather supplies, get out the riding leathers. We'll get Charrin on his way, and then start preparations. If it can be done, it will be, Kalynn." He reached out his hand to help her rise. "What brought this to you now, I wonder?"
"I am not sure," Kalynn whispered. "But Warna's been touched by its wings."
Chapter Fourteen
Verice always had to re-orient himself to the right time of day and weather when he returned from a visit to Wolfe's. He blinked in the afternoon light, and tried to ignore Narthing's raised eyebrow when he emerged from the bakery with Warna, her basket and the dogs in tow.
"Back to the castle, m'lord?" Narthing asked, as Brindle reared up, planted his forepaws on Narthing's shoulders and licked his face.
"Yes." Verice handed Warna's basket off to a warrior. The dogs milled about their legs, tongues hanging out. "Warna will return with us."
Narthing raised both eyebrows at that.
"By her own choice," Verice said.
Warna flashed them both a smile as she mounted.
"As you wish, m'lord." Narthing signaled, and the others mounted as well.
Verice settled into his saddle, gathering the reins, gesturing them to start. They'd pick up the rest of the company as they rode, retracing their steps back to the castle. He didn't have to give it much thought; the path and routine was a familiar one. No, his thoughts were free to focus on the woman riding next to him.
What had he been thinking?
If the visit to Wolfe's tower had been a military campaign it would have been a disaster. He'd known that Wolfe and Kalynn would open their arms to her; they offered shelter to any in need, but he should have anticipated Charrin's rage. He'd been a fool to go there blindly, thinking that Charrin would treat any human well.
The horses were walking at a steady beat, their hooves ringing on the road. The dogs ran all around the horses, their tongues lolling out, their nails clicking on the stones. The rhythmic sounds made it easy to stare at his reins and think.
Warna was a distraction from his purpose. Verice shook his head. He'd allowed her brown eyes and lovely voice to come between him and his obligations. The fact that she was a genuinely nice human was also a factor. Still, there was no excuse.
Verice glanced over to see her looking around at the buildings lining the street. Hopefully Charrin's remarks wouldn't cause her to abandon her songs. He'd been too harsh a critic.
He'd find another place for her. Somewhere with more of her own kind. Except that put her in parts of Tassinic that were closer to the borders with Edenrich and Farentell. Too dangerous by far.
There had to be a way to keep her safe. The castle was strictly for military housing. A base of operations and a target for the enemy. It was no place for her.
The sun felt good on Warna's face as she swung into the saddle. After Wolfe's Tower, it was nice to find the weather and time to be what she expected it to be.
"By her own choice," Verice had told Narthing.
Warna flashed them a smile as Verice spoke, hoping they couldn't see how nervous she was. She was grateful that they started out at a walk, her horse content to move at a gentle pace along with the others. It gave her a moment to breathe.
How had she found the nerve to challenge him?
Verice was Lord High Baron, and while she was not of Tassinic, she was certainly under his care and authority at the moment. She'd faced him down, and her stomach was still in knots about it.
She hadn't wanted to stay in the Tower. Wolfe and Kalynn seemed very nice, and the room had been lovely, but isolation wasn't what she wanted. Though she didn't have a clue as to what it was that she wanted, it definitely wasn't that.
She wasn't completely sure of anything right now, other than the warmth of the sun on her face, and the sway of her horse as it walked.
"Your choice, Warna," Kalynn's voice echoed in her mind.
She supposed that she should be glad that she was free, but her heart still grieved the loss of her family too much to rejoice. Actually, the thought that she could choose was...unsettling. More frightening than anything else. Her father and mother had planned her life, seeing that she had the skills and deportment to marry well. Now that was gone, and the future seemed unknowable and scary.
Warna glanced around at the buildings and streets, trying to distract herself. The city was quiet now, the afternoon lingering on. Folks were closing up their shops and turning toward their homes. Few heads turned to note their passage.
She breathed again, trying to enjoy the warmth and quiet.
Verice was just ahead of her, the sun glinting off his silver hair. The warriors around them seemed relaxed, but Warna saw that they were always looking about, alert to any threat. Hard to believe that was possible on a drowsy, sunny afternoon.
Verice's horse pranced a bit and he settled it down, stroking its neck. He was a fine sight, his armor and sword hilts glittering in the sun.
"The elven lord went riding, oh," new words and a tune danced in her head. Warna repeated the phrase to herself, trying not to lose the notes, watching her source of inspiration. How to capture him in a song? His strength, his sorrow...
What did she want?
Warna frowned as the thought refused to go away. She really had no idea, or maybe she was just overwhelmed by it all. Her life had been planned, organized by her parents. Simple. And she'd been comfortable with those plans. But now it felt like a vast emptiness. Without her family, what did it matter? What did any of it matter?
Warna tried to prevent the tears that threatened to fall. She didn't know what she wanted. She didn't know what to do.
But she did know what needed to be done.
The castle needed cleaning. Restoring. Restocking, even. And if she knew anything, it was how to scrub and polish. How to maintain a manor house as fitting for her future husband. She could bring her skills to bear on the castle of Lord High Baron Verice.
And while she did that, she could think things through. Make some decisions. Plan a future.
She relaxed, the tightness in her shoulders easing, the knot in her stomach letting go.
Oddly, she started to notice more people on the streets, pressed against the various buildings, staring at them. Well, staring at Verice.
The warriors around them were exchanging amused glances and it slowly dawned on her what was happening. She almost burst out laughing. Verice had forgotten his helmet, and Narthing was keeping their pace slow.
She couldn't help smiling. If Lord High Baron Verice had problems with his castle being cleaned and restored, she suspected she'd have the support of his people.
Warna caught the eye of some in the crowd. They returned her smiles, going so far as to wave. She lifted a hand in return, and her approval was enough for the crowd. They started to move closer to the road, and wave kerchiefs of various colors.
Verice was still oblivious, lost in his thoughts. It was only a matter of time before—
"All hail Lord Verice!"
Chapter Fifteen
"All hail Lord Verice!"
Verice started out of his thoughts to find the streets lined with people, all gazing at him. He lifted his hand to acknowledge the hail out of habit. Delighted smiles flashed over the faces in the crowd, and the cheers began in earnest, growing in volume.
With a sigh, Verice noted his helmet dangling from his saddle. Wryly smiling, he acknowledged the crowd again, and made eye contact with Narthing.
They continued to move forward but in answer to the unspoken command, Narthing slowed his horse, and maneuvered to Verice's side. The crowd thinned a bit, but now they were waving handkerchiefs and ribbons in addition to their greetings.
"You could have reminded me about the helmet," Verice chided his captain quietly.
"You seemed lost in thought, m'lord. I didn't wish to disturb you."
Verice snorted. "You could have picked up the pace as well."
"It's been some time since the people have seen you, m'lord," Narthing's voice held no apology. "Besides, the Lady Warna seemed to be enjoying herself."
She was at that, smiling at the crowds and waving back to them.
"Remind me to reassign you," Verice growled, lifting his hand and nodding his head in acknowledgment of the crowd. "To one of the southernmost bogs, perhaps."
"Certainly, m'lord," Narthing allowed Verice to take point. "I'll make a note."
There was nothing for it. Verice sighed, and picked up the pace just enough that it wouldn't take all day to get to the castle gates.
He cast a glance back at Warna, but there was no reason to worry. She met his gaze fearlessly. There was a twinkling in her eye and enough laughter in her smile that he knew she was enjoying the jest as well.
A woman darted forward then, holding out a roll of parchment, tied with a ribbon. "Pray, oh Lord, hear my petition!"
Verice accepted the roll, and placed it in his helm.
They continued on for a while, people calling out, wishing him well. There were others with petitions. Once his helm was full, he passed back any others to Narthing. They'd all have to be seen to, of course.
They entered the square to find the Lord Mayor and his lady on the balcony of their home, overlooking the fountain in the center.
"Welcome, Lord High Baron," The Mayor seemed a bit out of breath, and his chain of office was slightly askew. The crowd around his house quieted to hear his words. "Had we known of your visit, we'd have prepared a far better welcome."
"An informal visit," Verice called up to the man even as he kept his horse moving. "Impromptu on my part, I fear. I thank thee for thy gracious welcome and ask pardon for the disruption of your peace."
"There is no disruption." The Lord Mayor leaned on his balcony. "And our peace is your doing, m'lord."
"My thanks," Verice said. "You are gracious."
The mayor smiled. "And this lovely lady is...?"
Warna called out in response before Verice could say a word. "Warna of Farentell, your lordship. Octara is lovely!" Her smile was infectious, and the crowd cheered in response.
Verice tensed, and his horse shifted nervously in response. He hadn't wanted to bring any attention to Warna, much less give any information. He brought his horse under control with a firm hand. It was time to leave. "Our thanks, Lord Mayor, but we must be on our way." He gestured to Narthing to continue, but the Lord Mayor pressed up to the railing, looking anxious.
"M'lord, I would inquire..." His words faded as he waited.
"Yes?" Verice asked, trying not to let his impatience show.
"The Festival of Light and Laughter," There was a note of apology in the Lord Mayor's voice. "The date fast approaches, and—" He hesitated. "We've made no plans, waiting on your Lordship—"
The pain in Verice's chest must have been visible on his face, for the man cut off his words abruptly. "Forgive me, Lord High Baron. I—"
"It needed asking," Verice managed. "I'll consider it."
"My thanks, m'lord." The Lord Mayor bowed his head, and raised his voice. "May the Lord of Light and the Lady of Laughter bless thee, our Lord High Baron!"
The crowd cheered at that. Verice bowed his head and waved his thanks, still in shock. Had it been a year? He shook his head to clear it. "Narthing," he called, and let his tone speak for itself.
Narthing took the lead, and set as fast a pace as Verice could wish toward the other end of the square, only to find the path bared by a group of men, bearing banners, and flags. There were jugglers, acrobats, some singing, some playing horns and drums. The activity and the music stopped as they approached, and the leader stepped forward. He wore a cooking pot on his head, and bore a scepter in his hand, adorned with fake gems and false gold. "Stand and deliver, Verice of Tassinic!" the human boomed out in a loud, deep voice.
Verice's horse snorted, too well-behaved to act up, but not happy with the noise, but Verice knew the man well enough. "Master Zester." He gave the man his best forbidding look. "What means this?"
"Lord High Baron Verice, stand and deliver," Master Zester called out. "You owe tribute to our patron, the Lady of Laughter, for your failure to attend our follies and performances."
There were cheers from the crowd. Verice scowled at the man who'd opened a theater a number of years back.
"We have missed your patronage greatly, m'lord, and I would remind your lordship that all must pay the homage due to the Lady of Laughter, or risk her wrath." Zester spotted Warna, and removed his cooking pot to execute a low bow. "But now I see why m'lord does not attend us," he cried out. "He pays homage to another lady, and is lost in her obvious charms."
"Or mayhap your follies and performances aren't very good," Warna called back, startling Verice.
The crowd roared at her comment, and Zester held his pot over his heart, and shook a mocking finger at her even as he grinned. "Oh, ho, now here is one that follows the teachings of the Lady of Laughter well! Bring her to our theater, my lord." Zester donned his pot once again. "We'll restore a smile to your face."
"For now, Master Zester, clear the road," Verice growled.
With a bow, Zester gestured, and the acting company cleared the road.
With a snort, Verice led his men past, making sure that Warna was not harassed. They were through the town gates quickly, and he broke into a swift gallop as they started up the road to the castle. Warna seemed to have no trouble with the gait, her hair coming lose from its braid.
The grim faces of the gate guards gave Verice a clue that there was a problem even before the constable appeared in the courtyard. Ricard's face was grave. "Trouble on the border, m'lord."
Chapter Sixteen
Verice swung down from the saddle. "Where was the attack?"
"Word's come from Benton's Warren."
"When was the attack?" Verice demanded.
"Not long ago, m'lord." Constable Ricard's response was calm. "Injuries, no deaths reported. The messenger awaits in your chambers." The man's eyes widened as he spotted Warna on her horse. "M'lady, you—?"
"I'm back," Warna said. "If someone will help me with my basket, I'll disappear and leave you to your work."
Verice moved to her side, and held her horse's bridle. Warna dismounted. She grimaced a little as she landed. She shook her head when Verice gave her a concerned look. "No, it's nothing. It's been a while since I've ridden that far, is all."
"I must deal with this," Verice said quietly. "We can talk later."
"Yes," Warna agreed. "Go."
She meant it, to his relief. Verice gave her a grateful nod and headed toward his chambers.
Warna watched him go, hoping that the news wasn't too grim. The constable hovered near her, and caught her eye. "Beg pardon, m'lady, but this is a surprise."
"A sudden change of plans," Warna said, trying not to smile at the man's discomfort. "No way for you to have known."
"Well, but since you were gone, I shifted the men around a bit, and put two in that loft where you were."
"Two?" Warna asked.
"The smaller lads," Constable Ricard explained earnestly, then huffed with frustration. "We need to be in a proper barracks," he said, glancing at the empty buildings along the walls. "I've raised the issue, mind, but, well—" he sighed again.
"I do understand, Constable," she said with a laugh. "Although I wonder how you managed two in that space. How about I wait in the kitchens for a while to give you a chance to sort it all out? This will just be for one night," she added confidently. "There'll be a new plan in the morning."
With a grateful glance, the constable picked up her basket. "Let's see you to the kitchens."
Warna settled on a bench by the hearth, and accepted a mug of hot kav with thanks. Oddly, the cooks were only making kav and setting out the tables. There was no cooking going on. When she asked, one of the men shrugged. "Not enough room to cook here, and M'lord won't let us use the proper kitchens. So, the food's cooked in town and carted up for the meals."
"That's—" Warna stopped, not sure she wanted to say the words out loud.
"Aye," the man gave her a sardonic look. "They cart it up, we warm it here, and then serve it out. Never mind if there's a change in plans, or the number fed, or aught gets spilled or spoiled.
"I see," Warna said slowly. "That means there are no stores of supplies here, either, doesn't it?"
The cook shot her a satisfied look. "You know housekeeping, eh? I think you do understand, m'lady."
The clatter of boots pulled their attention to the door, as Verice walked in. The rest of his men continued on to the courtyard.
The cook hustled back to his duties as Verice strode over.
"The reports are worse than first thought. I need to go now. It can't wait until morning."
"How bad is it?" Warna asked, as memories arose of burning buildings, and fleeing her home.
"Bad enough," Verice said grimly. "I need to see for myself." He hesitated. "The constable told me he'd reassigned that loft room."
"To two men, if you can believe. But it's not his fault, Verice, he couldn't know that—"
"Agreed," Verice held up a hand to stem her flow of words. "I told him to put you in my chambers for the night. He's seeing to fresh bedding, then the room is yours. We'll see to other arrangements when I return, probably after the nooning."
"Safe travels, Verice," Warna said
"My thanks," Verice said, and then he hesitated, staring down at her. He reached out a gloved hand, and stroked her cheek. "Sleep well," he said abruptly, then turned and left the room.
She watched him go with a sigh, and a swift prayer to the Lord and Lady for his safety. Then she took a sip of kav, and turned back to the cook. "Tell me more about the castle kitchens."
It was early when she finally retired to Verice's chamber. She'd eaten with the men, after she'd watched the cooks carrying in large kettles and roasted haunches from carts outside. Then she'd walked around the keep again, noting the buildings along the way, and paying closer attention to their purposes.
She'd kept her distance from the keep.
After all that, she was well and truly ready for sleep, yawning as she mounted the stairs. There was a guard at Verice's door, but he saluted her through, and closed the door behind her.
The outer room was much the same, with maps strewn over the table and weapons on the walls. But what drew her was the large bed, heaped with pillows and blankets. It looked wonderful.
She used the basin and pitcher for a quick wash, and then stripped off her clothes, and pulled on her sleep shirt. She threw back the blankets and crawled in, enjoying the welcoming softness. It was warm enough, she'd only really need one blanket and she curled up, hugging one of the pillows.
Warna let out a slow breath, feeling her body relaxing. She had a plan. Not much of one, but it was her own, and it was her decision, and it felt good. It wasn't all that dramatic, or even very exciting, but she was satisfied. She yawned as she closed her eyes.
Of course, Verice might not agree...
She smiled even as she drifted off to sleep.
Chapter Seventeen
"Good riddance," Wolfe muttered as he snapped the portal shut behind Charrin.
Kalynn narrowed her eyes at him. "You practically shoved him through," she scolded.
"After the headaches I had to go through to open a portal in the Royal gardens?" Wolfe snorted. "Permissions for this and authorizations for that and scribes to the Under-assistant of the Herald to the King?" Wolfe flapped his hands in frustration. "Bah. I should have opened the portal during their stupid Ceremony of the Bedchamber. Dumped Charrin on the heaps of blankets and linens and been done with it."
"And be barred from the Elven Royal Court for life, no doubt." Kalynn shook her head.
"Look at me," Wolfe waggled his bushy white eyebrows at her. "So devastated. So heartbroken. Crushed by the very idea."
Kalynn rolled her eyes. "Now that he's gone, we need to consider supplies. Have you checked the flying tack? It's been a while since we used those saddles. Although if we could portal—"
"First, come to the workroom," Wolfe took her hand and pulled her toward the stairs.
"Why?" Kalynn followed, knowing full well there was no use in protesting.
"Still no idea of where we need to go?" Wolfe asked.
"No," Kalynn sighed. "I've tried to focus, but—"
"Hard to do with an unwanted guest," Wolfe continued down the steps.
"Why is it?" Kalynn smiled at the back of his head as she dodged the clutter along the stairs. "Why is it that the stairs are crowded with your books and collections, but your workroom is—"
"Hush," Wolfe opened the door to his workroom, and sure enough the room was empty, without a trace of dust. Mage lights shown above them, glimmering on the stone walls, ceiling, and floor.
"Stand here," He pulled her into the center. "I have an idea."
He closed the door, then stood against it. She watched as he dimmed the mage lights with a slow stoke of his hand through the air. Wolfe had his eyes closed, his fingers spread out, and the hint of a smile on his lips. It warmed her heart to see him so. She loved these moments when he worked the power, his face so intent and serious, yet she could sense the joy within him.
"Watch," Wolfe said, and the floor beneath her feet glowed, and images formed. It was there, their world, all laid out on the floor. Continents, islands, oceans wide and sparkling.
"So many places we have yet to see," Wolfe said softly. "So many places we have yet to go."
"What are you—" she asked, but Wolfe shook his head and the pictures at her feet changed, and grew. Tiny horses raced beneath her feet, through tall grass.
"The Plains," she breathed. And the images around her solidified, of rolling open grasslands. The images tilted slightly, and then grew.
Kalynn sucked in her breath, pressing her hand to her chest. She was standing on the Heart of the Plains.
All around her, the grasses stirred in a breeze she could not feel. They were browning slightly, under the heat of a summer sun she could not feel. Beyond, toward the south, she saw the lake, the waves lapping at the rocky shore. Yet for all the lack of her senses, her heart soared at the sight of home.
"Wolfe," she whispered, not wanting to break the spell. "Have you sent my spirit wandering?"
"No," his voice was soft. "I brought the spirit of the lands to you." Part of her knew that he was standing by the door, but to her it appeared he stood just off the edge of the Heart.
Her tears welled at the sight, with grief and joy and a deep longing. Kalynn tore her gaze away, looking toward Wolfe.
"I know," Wolfe's eyes were warm, his voice was the barest whisper. "But we need answers."
Kalynn nodded, not trusting her voice at that moment.
"Power first," Wolfe said, raising his hand. "Show me," he commanded.
Over the grasslands small bits of light appeared, some dim, some strong, scattered in no particular pattern around the Heart.
"So few," he said. "There's little power left on the Plains, and even less between the Heart and Xy. Not enough to trust to portals. We will take airions."
Kalynn studied the Heart below her feet. No life, no magic pulsed under her feet; the Heart was cold and silent. She'd known that would be the case, but she hadn't been prepared for the reality.
"Flying will be hard on both of us." Wolfe continued. "Been a long time since I have spent much time in the saddle. We could use portals, cut off some travel time, if we—"
Kalynn cut him off, "I'm looking south."
"Well, yes," Wolfe cleared his throat. "But, beloved—"
She ignored the warning tone in his voice, and looked over her shoulder, due north.
"Xy," she said.
There, bright against the mountain at the high end of the valley glowed a blue spark, bright and clear and blue as the morning sky.
"Kalynn," Wolfe warned again. "She will not welcome us."
"She needs to know," Kalynn said firmly. "We need to warn her of what is to come."
"What might come," Wolfe said firmly, his voice pulling her back to look at him. "We can argue the point later. First, we need to find out 'where'. How's about you point out where we must do what must be done."
"Show me the Tribes," Kalynn said.
"It's the Season of War," Wolfe said. "There are scattered thea camps but the armies raid."
The Heart fell away, and shrank. She could see all of the Plains, and the mountains that surrounded them. Below her feet, tiny herds of horses ran, with tiny birds flying overhead.
All around, on the edges, she could see armies attacking, the glow of fire and war. She drew in a breath, let it out slowly, and let her eyes drift close. There was a tug, the faintest of pulls against her heart.
"Where, love?" Wolfe prompted.
"Hush," Kalynn took a step forward, concentrating. "It's like following the faint scent of perfume to find a person in a crowd." She took another step, and moved, slowly following the trace of possibilities through the stream of potentials.
"Here," she said finally. "Here." She swayed as visions came, of an army approaching, raiding and looting. Children taken, foodstuffs seized, and men and women killed. "Oh Wolfe, it's—" She drew in a ragged breath and pressed her hands to her chest. "So much hate, so much destruction. The fire, the death...it's—" Her breath came in harsh gasps.
She felt his warmth as he stepped to her side, his strong hands on her shoulders. "Come back, Kalynn. Come back to me."
Her eyes snapped open, and she returned, back to the room and the map and her love. She sagged, trembling and Wolfe wrapped her in his arms. "Wolfe," she wept. "Will it never change?"
"We'll go," he tightened his arms around her. He looked down at a town on the border with the Plains. "How much time do we have?"
"Weeks," she said. Between their feet a Warlord's army advanced, raiding as they went.
Wolfe nodded, and the map faded away as the mage lights brightened above them. "Best we be about it, then."
"We have to do this," she clung to him, looking for reassurance.
"We'll try." Wolfe promised. "We'll leave as soon as we can."
"We should tell Verice." Kalynn leaned against Wolfe as he helped her to the door. "I want to check on Warna."
"That's fine." Wolfe said, and then she felt the vibration of a chuckle in his chest. She looked up to see his eyebrows dance, his eyes gleaming. "Verice can look after the cat."
Chapter Eighteen
Constable Ricard was seeing to inspections when he saw the Lady Warna emerge from the barracks.
The lads were lined up in the courtyard at attention as he marched between the rows, expressing his opinion at their slovenly state at the top of his lungs. Fine way to start the morning, to his way of thinking. A solid breakfast, a strong mug of kav, and a good stint of admonishments, criticism and assigning punishment details for the worst offenders.
Aye, a good morning.
At least until Lady Warna appeared.
She stood in the morning sunlight, blinking at the brightness, her golden hair aglow in the sun. She'd fixed it in a bun, and there was an air of determination about her. Standing there in her tunic and trous, she looked like a woman with a plan for the day.
"Morning, m'lady," he said. "Is there anything you might be needing?"
"Good morning, Constable," She smiled. "That's the healing hall, isn't it? With the red door?" She nodded off to the building next to the barracks.
"Aye, m'lady." Ricard replied.
"I'm going to need buckets, soap, and hot water." With that, she went right to the door of the healing hall, opened the door, and walked in.
The constable blinked.
There was a rustle of amusement from the ranks, and he turned on them with a glare. They all stiffened again, and he opened his mouth to roar when slam. The shuttered window on the first floor opened. Lady Warna could be clearly seen, and she gave him a wave, then disappeared.
That brought a few chuckles, and Ricard turned back, putting forth his best bellow. "Seeing as you've so much energy, forward march!"
The men headed off, marching in step, keeping the spacing between them, to make the round about the keep.
Slam. Another window opened. The sergeant glared up, to see the lady now leaning out of a second-floor window. The Healing Hall had been one of those sealed up. Lord Verice had left no orders about this, not to his knowledge. He opened his mouth to call to her, and then closed it.
He'd no orders about this, but then Lady Warna wasn't under his command, now was she? Her and the Lord might have had discussions he'd not been privy too, might'n they? And he'd no reason to think to the contrary, now had he? And this needed doing, now didn't it?
He was still considering that when the top-most window opened, and Lady Warna poked her head out. "There's a tiny room up here, perfect for me," she called down. "Buckets, soap, and plenty of hot water, Constable."
A woman with a plan, it would appear. In an instant, Ricard reviewed all his options, and made the best, safest choice.
"Aye, lady," he called up. "And a few on punishment detail to aid you in the work."
It was a lovely room, to Warna's delight. Not huge, like the one in the mage tower, but a nice bed, with a small table and chair. Even better, a press for clothes and a small cupboard off to the side. A woven rag rug covered the wooden floor. The stone walls were cool, and the air was chill and musty. There was a thick layer of dust and a lace of cobwebs in every corner.
Well, soonest started, soonest done. With the window open there was a bit of a breeze. In a great cloud of dust, Warna stripped the bed. She bundled up the bedding, gathered up the rug, and threw the lot of them down the stairwell.
She clattered down the stairs behind, and started poking in cupboards and storage areas, looking for soap and rags. It seemed this place had been stripped bare of personal items and healing supplies before being closed up, but she found a few rags and some wood polish in one of the cupboards just as the clomp of boots came through the door.
It was two of the constable's men, each with a bucket of warm water and carrying brooms and dust pans, soap, and a basket of rags.
"Excellent." Warna smiled, a feeling of satisfaction rising in her chest. "Let's get to work."
The shadows were long when Verice finally returned with his men, having been gone longer than he had planned. The attack had been more than a raid, of that he was certain. The local commander was a good man, but Verice feared the Usurper was testing the border, looking for a weak spot. And if a weakness was found, no doubt a bolder thrust would follow. He shook his head. He'd need more scouts in that area.
But as he swung out of the saddle, all he really cared for was a meal and sleep. He was short on both. It had been a long two days since he'd taken Warna to Bode's tower.
He'd have to make arrangements for Warna, or find another place to sleep himself. She'd been in the back of his mind the entire time, as he'd tried to determine what was best for her. So far, he'd not made a decision, and that irritated him to no end.
Constable Ricard came toward him and made a quick salute. "All's well, m'lord."
"Thanks be for that." Verice stretched. "All I ask is for a chance at a meal and a bed. Do you know if Warna has eaten?"
"As to that, m'lord, she's not even taken a nooning that I am aware of. She's one for work, make no mistake." There was an odd note of respect in the constable's voice. "Her standards are higher than mine, when it comes to what's proper."
"What's proper?" For his life, Verice couldn't figure out what the man meant. "What has she been doing?" The horses around him shifted as they were led off to the stables, and he caught a glimpse of a bundle of laundry in front of the Healing Hall.
"Cleaning, m'lord," the Constable said matter-of-factly. "Right proper job, too. The lads on punishment detail are none too happy they picked this time to err in their ways, I have to say. Did my heart good to see them poor sods beating out the mattresses."
"Cleaning?" Verice blurted out, staring at the Healing Hall just in time to see a hand emerge from a lower window and shake out a dust cloth. "What cleaning?"
"Perhaps that's a discussion you might have with M'lady. She's within," Ricard added, nodding toward the building. "Let me see to the meal for these men, and I'll tell the cooks to send yours up to your chambers, once you've convinced her to stop her work, that is." And he was gone.
Verice frowned. He'd given no orders to open the Healing Hall, of that he was certain.
The door was open, and he stepped within. The room was thick with dust, except the stairs and the tracks leading up.
He mounted the steps two at a time, to find a hallway that smelled of soap and water and two of the younger warriors scrubbing the floors with big brushes and resigned expressions. The one lad was tired enough that he looked at Verice without recognizing him for a moment before his eyes went wide.
"M'Lord!" They both sprang to their feet, and stood at attention.
"At ease," Verice said. "Where is Warna?"
"Above, m'lord." One of the lads gestured above.
"My thanks," Verice hesitated on the steps. "Best return to your duties, lads."
They both heaved sighs as he continued up the stairs.
Many doors led off the upper hallway. Verice didn't need to search each one, he could hear her singing toward the back. She sounded so joyful. Charrin's harsh words hadn't spoiled that for her then. That pleased him.
She didn't look up when he entered, so he leaned on the doorjamb watching her polishing the mantel of a small fireplace. A glance told him this room was done, with the smell of drying wood and polish mingling together.
"Warna?"
She turned then, startled, but clearly happy. "M'lord, you're back. Is it mid-afternoon already, then?"
"More like mid-night than mid-morning," Verice said.
Surprised, she glanced behind him to the hallway windows. "Oh, Lord of Light, I lost track of time. And I've kept these poor lads at it all day," Warna shook her head, and moved forward. "I need to set them free. We can finish tomorrow."
Verice moved to block Warna with his body, and she gave him a startled glance, her brown eyes wide and clear. "I gave no order that this building be cleared," he said softly.
The barest blush crossed her cheeks as she lowered her gaze. "M'lord, I thought—"
Her stomach rumbled.
"You owe me an explanation," Verice said firmly. "Over our meal."
"Of course, m'lord." Warna's blonde head was still down, her hands twisting the rag between her fingers.
He held his position for a moment more, until she looked up, her guilt quite clear in her eyes. He moved then, giving her just enough space to slide past him and down the stairs.
Chapter Nineteen
Warna waited nervously in Verice's outer room as he cleaned up in his quarters. The serving boys had already rushed in with plates, kav, and covered dishes. They'd set the table and vanished as quickly as they'd come.
She could hear him in the other room, moving around, water splashing as he washed.
What had seemed like a wonderful idea this morning was feeling not-so-clever now. She'd changed quickly, putting on her only dress for this meal. She smoothed the skirts down as she stood by her chair. The dogs were sprawled all around the room, and seemed to sense her nervousness. The sandy-colored one even came over and leaned against her, looking up with big brown eyes, as if it understood her fears.
Of course, it might have been more a desire to be petted than expression of sympathy; Warna chuckled at the thought, and started scratching its ears.
Verice emerged from the back, in a loose white tunic and his leather trous. His hair fell free, flowing down his back, slightly damp at the temples from his quick wash. He gestured to the table, and Warna sat, bracing herself for his anger.
But Verice just uncovered a bowl of rabbit stew, thick with vegetables, and gestured for her bowl. She handed it to him and reached to unwrap the warm bread, tearing off chunks for both of them.
Verice served her and then himself, and started eating immediately. Warna didn't waste any time starting on her own bowl. The stew smelled wonderful, and she hadn't eaten at the midday meal.
Verice passed a crock of soft cheese, and they ate in silence.
He filled a second bowl for himself. "More?" he asked.
"No, thank you." Warna was still working on her first. "Bread?"
"Yes, thank you." Verice accepted the basket, and tore off another hunk. "Why did you take it upon yourself to clean the Healing Hall?"
Warna stopped eating, and used her napkin. Verice didn't seem upset; his face was set and controlled. There was no hint of emotion there. But there'd been none at Wolfe's either. "It needed doing," she said quietly. "I didn't know the details of the attack, but what would happen if there were wounded that needed tending here? The place was in no state fit for ill or injured warriors, that was certain. And this building is overflowing with the healthy already." Warna raised her chin. "Besides, I needed a place to sleep. The poor sergeant couldn't keep shifting men around to suit my needs."
The worst of it was that she was right.
He should be furious, because even if she wasn't aware, his men knew full well that he'd shut down the castle for security reasons. But—
"In the past, the worst hurt were brought here to my healers. They were the best." Verice admitted, more to himself than to Warna.
"They were Elven?" Warna asked.
Verice snorted. "Elven healers do not concern themselves with human or half-elven anatomy, Warna. They tend to focus on magical healing, and rarely deign to touch a human. No, our healers were half-elven for the most part, from around the barony."
"Where are they now?" Warna asked.
"Most are scattered along the border," Verice said. "Three are housed in the town, in case of need here. They are but a short ride away." He winced a little. That sounded foolish, even to his ears.
"The building sleeps a good many," Warna said.
"Some of the rooms were meant for the ill and injured," Verice said.
"There may be wounded that need tending here at the keep," Warna said. "Best to have the place ready, in case of need. There's a lovely small room at the very top, and I can sleep there."
"I'd thought to send you away, again," Verice said. "Somewhere safe."
Warna dropped her eyes, but he caught the flash of resistance. "Where were the attacks yesterday?" Warna asked.
Verice sighed, and pushed his bowl away. "To the south, along the border with Edenrich. We suspect the Usurper is probing, looking for a weakness." He poured himself some more kav. "We are spread too thin as it is."
Warna nodded as Verice talked in detail of troop placements, and the difficulties of protecting a large border. Most of it went over her head, the names and places unfamiliar to her. But his concerns, his fears for his people came through clearly. He seemed to take comfort in talking, as if it helped him see the situation in his mind's eye.
Finally, he stopped, clearly frustrated, and took a sip of kav. Warna took a breath, and spoke quickly, almost afraid of his response.
"Lord Verice, it strikes me that there is nowhere as safe as here."
His eyes were tired and his pain clear. "It hasn't been, in the past." He stared into his mug. "I think it best that I send you somewhere else. To start your life, Warna."
"That's the problem," Warna said, ignoring her fear. "I don't know what I want yet." She hesitated, surprised she was confiding this to him, but wanting him to understand. "It's all too new, too unsettling. Cleaning though..." she laughed wryly. "Cleaning is something I am all too comfortable with. It keeps my hands busy. Lets me think."
"New songs, perhaps?" Verice said.
"Or finish the ones I've started." Warna smiled, but she let it fade as she grew serious. "I need time, m'lord. Time to think."
Verice stared into his kav, but then he slowly ran his fingers through his hair. "I'm not convinced it's all that safe, but I admit that I don't have an alternative. At least until the Healing Hall is clean."
"I'll see it done," Warna assured him as she reached for more bread. "And I can see it stocked, if you wish. Best there are supplies in place before a need."
He didn't want this.
The kav turned bitter in his mouth, and heavy in his stomach. He knew where this was going. Common sense and simple logic cried out for both castle and keep to be restored.
His heart cried out against it.
He closed his eyes, wanting to hold it all back, stop time and space, make no changes. The lump of pain in his chest grew until he didn't know how his heart had room to beat anymore.
The dogs stirred; Brindle got up and nudged his arm with his nose. Warna was silent, spreading cheese on her bread, her head down, giving him what privacy she could.
In his pain, the mental image of Charrin raging out his grief flashed before his eyes, and Verice felt a flash of sympathy for the elf. How did one ever deal with such anguish?
He opened his mouth, wanting to deny Warna, wanting to order her to stop, order her to lock the Healing Hall back up, order her to leave—
No. He didn't want that.
"Not the keep, Warna." He managed to strangle out the words. "Not the keep."
She lifted her gaze, and her brown eyes were warm, and understanding. "I promise, Verice."
He held her gaze, and knew without knowing quite how, that he could trust her.
A blush rose on her cheeks, and she glanced at the dog beside him, its head just above the table. "M'lord, perhaps you'd introduce us? I still don't know their names."
Chapter Twenty
The next morning Captain Narthing was tightening the girth on his saddle when the Constable Ricard sidled up to him, and muttered something out of the corner of his mouth.
"Eh?" Narthing gave the men around them a glance. They were all preparing to mount. Lord Verice had returned to his normal routine. The day before had been a nice change of pace, but they were back to it this morning.
"My orders have changed," Ricard said again.
Narthing straightened, and gave the man a puzzled look. "Verice changed your orders?"
"Aye," Ricard said.
"Really?" Narthing glanced at his Lord, who was checking his own gear.
"I've said, haven't I?" Ricard replied, his face straight.
Narthing rolled his eyes over to him. "You're enjoying this," he said.
"First change in how many months?" Ricard's mouth quirked.
"And the change?" Narthing demanded.
A stir in the men drew his attention away from Ricard. The Lady Warna was weaving her way through the horses and men. She came right up to both of them, and gave them a warm smile. "Good morning, gentlemen."
"Morning," they both responded. Narthing found himself returning her smile, feeling his spirits lift.
"Ricard, I'm going to finish cleaning the Healing Hall today, and I'll be sleeping there from now on. Would you have someone carry over my basket?" Warna said. "It's in my room, ready to go. You can reassign that space as soon as you wish."
Narthing blinked.
"As you wish, m'lady," Ricard replied. "I've four lads who need to be shown the error of their ways. I'd thought to have them flush the privies, but if you've a need..."
"That would be lovely," Warna said. "Many hands make light work." She gave Narthing a nod. "Travel safe, Captain."
"My thanks," Narthing said, but Warna was already moving, seeking out Verice. The Lord exchanged a few words with her, and then she headed toward the Healing Hall. Verice turned back to his horse, a calm expression on his face.
"Ancestors," Narthing swore. "What's—"
Ricard nudged his elbow. "My orders," he said.
"What?" Narthing asked.
"You asked about my orders," Ricard's smile was a broad one.
"Yes," Narthing narrowed his eyes. "What did Lord Verice say?"
Ricard chuckled. "'Let the Lady Warna have her way.'"
Warna was surprised at the amount of comfort she took from her task.
She'd feared that the mindlessness of the work would force her to think about things that she wasn't ready to confront. But the regular swish of a broom on the wood floor and the slap of a soapy cloth on a dusty surface were sounds she could lose herself in. There was no past, no present; there was simply dust and dirt, and it all had to be dealt with.
It was soothing, to worry about dirt her 'assistants' had missed, or to scan the ceilings and corners for cobwebs. Maybe the peace she found in doing these things was a false one, but it was still a peace.
The Healing Hall was finished by early afternoon. She'd released the lads assigned to her, and they'd escaped quickly. But not before the constable grabbed them, and had them carry her lidded-basket and bedding to the top-most bedroom. As tired as she was, Warna still wanted to make the room as comfortable as she could before she sought her supper.
Not that there was much to arrange. The clothing the supply clerk had provided were all tunics and trous, worn and soft, perfect for cleaning. Warna had to sigh over the state of her skirt and blouse. The hems were all worn, and they were almost grayed out of any color they once had. She'd have turned them both into rags, but they were the only womanly clothes she owned at the present.
She had a comb from the supply clerk as well, along with a bit of soap and towels. Yet there were other things that an army clerk probably couldn't provide. She paused as she put the folded clothes into the press, counting the days. There was time yet, but she couldn't wait too much longer. Although the idea of outright asking the clerk for moon pads made her blush.
She shook out the sheets and blankets and made up the bed quickly, smoothing out the pillow and giving it a pat. This would be better than the barracks, by far.
For an instant as she stood in the clean, small room, however, her heart returned to home. To her old room, scattered about with pillows, the smell of bread baking in the kitchens below, and her brothers' laughter coming through the window as her father called them to task. Grief caught her unaware, and was all the more powerful because of it. Tears welled, threatening to spill, as she stood in that strange, silent, empty room.
"Warna?" Verice called from below, his footsteps echoing as he mounted the stairs, his voice loud and slightly annoyed.
Verice had thought that Warna would be waiting for him, so that they could eat together. He took the steps two at a time as he called out to her. "Warna?"
He stopped, caught by the look on Warna's face. She looked so sad, so...bereft. Standing there, her clothes stained and damp, her hair bound up with strips of rag. Suddenly, all he wanted was to ease her sorrow. Replace that pain with a smile.
He glanced around the room. "Settling in?" he asked.
Warna looked away. He could tell she was wiping her eyes. He hesitated, not sure what comfort to offer, then his gaze fell on the bed.
"You know, if you were the Queen of Valltera, it would take thirty handmaidens and half the morning to make your bed."
Warna turned then, staring at him with reddened eyes. "Really?"
"Oh yes," Verice said. "Each of the twenty has their own task. It's considered a high honor to plump the pillows, place them on the bed, and smooth them to perfection."
Warna sniffled, then laughed weakly. "You're teasing me."
"As I stand before my Ancestors," Verice placed his hand over his heart. "I'll tell you about it over dinner. There's chicken and mushroom pie tonight." He paused. "If you'd join me."
To his relief, Warna's face cleared. "Just let me wash up, and I'll be right there."
Chapter Twenty-One
Verice stood by his chair, and patiently waited.
The table was set. The food was still covered, but the smell of hot chicken pie filled the air. The dogs were all settled around him, curled in their normal positions. Brindle sat by Verice's side.
Normally he'd be impatient, waiting like this. But he was feeling something entirely different.
Anticipation.
It struck him that he'd not looked forward to anything in some time. The last few months had all been taken with the care of his lands, the safety of his people...
It felt odd that it felt odd. That he wanted to share the story of the formal rituals of Valltera. That he was going to share a meal with Warna again, someone who wasn't concerned with troop placements, or scouting reports. He'd not done this with anyone else, and certainly not since...the guilt rose from his gut and kicked him hard, remembering those who had died. Who would never share another meal, another laugh, and all his—
Brindle whined and pushed his head into Verice's fingers.
A soft knock, and Warna slipped into the room. Her eyes red-rimmed, she gave him a tentative smile, seeing his expression. "I took too long. Forgive me."
She was hurting; the sorrow was deep in her eyes. Maybe he could help her forget her pain, if only for a moment. It was something they shared, that grief.
"Not at all. They just brought our supper." Verice gestured her to her chair. "No, I was thinking on the Ceremony of the Bedchamber in Valltera." He paused for dramatic effect. "Thinking on it, I think it's more like thirty people required to make the King's bed."
"Now I know you are teasing me," Warna said. "What would they all do?"
"Well, first, the Warder of his Majesty's bedchamber summons the nobles—"
"Nobles?" Warna asked. "To make a bed?"
"A King's bed," Verice pointed out. "And the ritual is the same for the Queen, by the way. At any rate, they are all summoned to the outer room, where they line up in order of precedence." Verice shook his head at the memory. "They gather up the clean sheets, pillows, and blankets. Two carry in the fresh feather mattress—"
"A fresh mattress?" Warna's eyes went wide. "Every day?"
Verice offered her the gravy pitcher for her pie. "So, they file into the room in perfect order. The Four Lords of the Curtains each pull back one of the bed curtains, and hold it away from the bed for the entire ceremony.
"The four Lords of the Bed stand at its sides, their hands upon their sword hilts, as the bed is stripped down to the straw mattress. A nobly born esquire then leaps on to the bed and rolls around, checking that the straw has no weapons concealed therein to the King's harm."
"Lord of Light," Warna exclaimed. "Truly?" She gave a startled laugh as Verice nodded.
"The fresh feather mattress is then laid over the straw one, and fluffed." Verice poured kav for both of them as Warna cut into her pie. "And then begins the placement of the sheets and the blankets, each sheet then being spread out and smoothed, because they dare not leave a single wrinkle to offend the King's body."
Warna shook her head. "They all stand around while this is done?"
"With somber stares, for their presence is an honor, and a right by virtue of their blood," Verice said. "Woe betide any that hold the wrong curtain or fluff the wrong pillow. So, to finish my tale..."
Warna laughed. "There's more?"
"Of course," Verice said. "Once the pillows are in place, the bed curtains are closed and the bed is sprinkled with scented water, and blessed by one in service to the Ancestors, then the entire lot troops back to the outer chamber and are served wine. This happens each and every night, even if the King is not in residence."
Warna shook her head. "What a waste. Their time could be better spent, I think."
"So did I, in my youth." Verice grimaced. "I'm afraid that if I hadn't left the Court of Valltera, I'd have been banished before long."
"You were a trouble-maker?" Warna asked.
"Let's just say I was an impetuous youth, who chafed against every rule, every restriction." Verice said. "If it weren't for my weaponsmaster, I'd have certainly been sent away in disgrace."
Warna tilted her head. "How so?"
"He sat me down after a practice, and told me that being at Court was like fighting a bout. 'Three basic rules, lad. Speak only in response. Answer, but never ask. And never make the first move.'"
Warna shook her head again, mopping up the last of her gravy with bread. "That worked?"
"Yes," Verice said wryly. "After that, I knew well exactly why I was in trouble."
Warna choked on her bread, laughing and sputtering as she reached for ale.
Satisfied, Verice set about finishing his own few bites.
Once she got her throat clear, Warna sat quietly as Verice finished his meal. The silence was a comfortable one. She had so many questions, but each one had the potential to raise the past in a way that might hurt Verice. It made her feel awkward and rude, and suddenly the weaponsmaster's advice made perfect sense.
The efforts of the day were starting to catch up to her, and she was looking forward to crawling into her new bed. She glanced around at the crowded room, the chests lining the walls, and the weapons hanging there. There was a pile of papers that had been cleared off the table, and next to them, the petitions that Verice had taken in town.
Verice caught her glance and grimaced. "I haven't gotten to those yet, and I should.
The petitioners will be expecting a response in a day or so."
"What do people petition for?" Warna asked.
"Various reasons," Verice said. "To complain of an official without drawing his ire or ask pardon for a loved one. Sometimes they wish for money, or aid." Verice pushed his plate back. "I normally have a scribe deal with them, but..."
"What would the scribe do with them?" Warna asked.
"Sort through them and investigate." Verice said.
"You must still have people working in that regard," Warna said hesitantly. "Just not here."
"Yes," Verice said slowly.
"Send them to him, then," Warna said. "Or send for him."
Verice went silent, studying the table in front of him. It went on for so long that Warna thought she had offended, but then he nodded. "I will," he said. "My thanks, Warna."
Warna gave him a smile, that turned into a yawn.
"You're tired." Verice stood, and all the dogs rose with him. "I'll walk you to your new chambers."
Chapter Twenty-Two
The night air was cool as they walked the few steps to the Healing Hall. The dogs paced beside them quietly.
Warna opened the main door, and stepped within to utter darkness. She paused as Verice came in behind her. "Just a moment, I'll strike a—"
Verice whispered a soft word under his breath and every candle in the room flared to life.
Warna gasped in utter delight. "Lord and Lady," she breathed. "I tend to forget you can do that."
Verice raised his eyebrows. Standing in the center of the rug, he seemed to pull all the light to him, tall and commanding. The dogs had piled in with him, and were sniffing everything in sight.
"My thanks, m'lord," Warna said.
"For lighting your candles?" Verice asked.
"For the meal," Warna answered simply. "For the work, the shelter, the...haven."
"You'll be comfortable here?" Verice peered up the dark stairs. "Alone?"
"I'll be fine," Warna took up one of the small lanterns. The candle within flickered and flamed.
"Wait," Verice moved closer, reaching for the lantern's door.
Warna held it higher, suddenly conscious of Verice's warmth as he leaned down and removed the candle. His scent tickled her nose, his silver hair brushing her arm like silk. Part of her wanted to step back, to seek her own space. Part of her wanted something more. Something exciting, and terrifying at the same—
"Let's make this a bit safer." Verice held out his hand, and started to chant quietly. A small swirl of light started to coalesce in the center of his palm. Sparkling strands of light wrapped themselves in a tiny ball.
Warna caught her breath, afraid to breathe for fear of destroying it.
Verice chuckled. "It's not fragile." He placed it inside the lantern and worked the shutter, dimming and brightening the light. "You see?"
"Will it fade?" Warna asked, admiring the golden glow.
"Eventually," Verice said. "All things do."
Warna glanced at his face then, saw the weariness in his eyes. "You're tired," she murmured. She lowered the lantern, and eased back from his warmth. "Thank you for the escort, m'lord."
Verice frowned slightly. "Sand, Gray," he waited for the dogs to turn their heads, then nodded toward her. "Guard."
"That's not necessary," Warna protested as the dogs heaved themselves up and walked toward her.
"For company, if nothing else," Verice said firmly.
"Thank you." Warna took the lantern, and started up the steps, the dogs following. It felt wrong. She hesitated, glancing back, not really wanting to leave. No, not really wanting to leave...him.
She caught him off guard. For the barest of moments, she saw a flash of heat in his eyes, gone so quickly she must have imagined it.
Verice bowed to her. "Sleep well," and then he was gone, the other dogs with him, the door pulled quietly closed behind him, the latch catching with a click.
His desire caught Verice off guard.
She paused on the stairs, the lantern in one hand, the other on the railing, half-turned in the light to look back at him. The gold of her hair gleamed and her skin glowed.
His body reacted, but he denied it in an instant, stifling the impulse to follow her up the stairs. There must have been something in his face, since her blue eyes went wide, startled but unafraid.
He bowed, hiding his eyes. "Sleep well," and slipped through the door as quickly as he could. He stood there, catching his breath, listening to her fading footsteps. He waited until he heard her above, then he left, cursing himself for a fool.
Warna shifted, restless under her blankets.
The room was cool and dark. Both dogs were sprawled on the rug next to the bed, giving the occasional soft snort.
The little lantern sat at her bedside. She'd left the shutter open slightly, and the dim light was just enough for her to see by.
The bed was comfortable, the blankets warm. She wasn't hungry, frightened, or hiding in a ditch. She just couldn't sleep.
And when she closed her eyes, all she saw was Verice.
She shifted on to her back, and huffed out a breath as she stared at the timbers over her head. She'd imagined it, of course. Verice was a Lord High Baron, so far above her station as to be...not to mention being an elven lord. What was she thinking?
Warna huffed again. Well, pretty clearly, she wasn't thinking, at least not with her brain.
Her mother had warned her that the spirit might be wary and careful, but the body had its own ideas sometimes. "Nothing wrong with looking," she'd said. "just don't act on those thoughts."
Your life is your own, Warna." Kalynn's voice floated through her mind.
Warna caught her breath.
Then she snorted at her foolishness, shifted on to her side, and thumped her pillow into shape. One of the dogs started and raised its head to look at her. Finding nothing amiss, it yawned and returned to sleep.
Warna hugged her pillow. She was reading too much into a glance. Verice had been kind, had extended his protections to her, given her food and shelter and work. Nothing more than that, and she would not interpret his kindness as some sort of interest. She owed him more than that disrespect.
Lord High Baron Verice was a man caught in his sorrow and grief. The fact that he was reaching out to her; was letting her take actions he himself couldn't bring himself to take, was a matter of trust. Spoken or unspoken, she'd not take advantage of him.
She closed her eyes firmly, and tried to avoid thinking about elven eyes that burned silver-blue. She thought about dust, and soap, and stocking the shelves and cupboards of the healer's house.
But her last conscious thought was how terrible it would be...if the one thing she wanted was the one thing she couldn't have.
Chapter Twenty-Three
In the morning, Warna delayed going down to breakfast until the dogs were whining at the door, staring at her over their shoulders. "Sorry, boys," she whispered as she opened the latch.
Verice and his men had already departed the castle, which had been her intent. Still, she felt oddly disappointed as she slipped into the dining area and managed to snag a bowl of porridge and a mug of kav. The cooks had scraps waiting for the dogs.
"Aye, he's off," one of the cooks told her. "Said he'd be later this night getting back."
Warna shrugged her agreement, but couldn't help worrying that he might run into fighting on his travels. Still, his absence suited her plans. Warna drained her mug with thanks, and headed for the QuarterMaster's offices. Outside were three carts, filled with casks and duns of ale and beer.
Inside, was complete chaos.
"I tell you, the account is overdue." A rather large man of decidedly more girth than height filled the small area in front of the high counters. He carried with him the scent of yeast and hops. His face was set and he was clearly determined to be heard. "I'll have it paid this day, or know why."
"And I'm telling you, it's been paid." Quartermaster Farnor snapped. "But we can't find the reckoning. If you'll have a bit a patience—"
"That's what ya said the last time and the time afore." The man rumbled. "I've no mind to run a credit until you're—"
Warna slipped in and pulled the door closed behind her.
The big man turned and frowned. "Who's this, then?"
"M'lady," Farnor started, but Warna forestalled him.
"I'm Warna of Farentell." She smiled at the man. "Are you the brewer of that fine ale we've been drinking?"
The man blinked in surprise. "Aye, aye, although I'd naught know'ed the army was taking women into its ranks."
"It's not, Pierson, you daft fool," Farnor snapped. "The lady is here under the Lord's protection."
"The same as what rode through town with him the other day?" Pierson was giving Warna the once over, and she couldn't help but notice his eyes flick to her ears. "Well, then, pleased ta meet ya, lady."
"The same," Warna responded. "I take it there's trouble with the accounts?"
Both men erupted back into their argument, each talking over the other. Warna saw the younger clerk scurrying in the background, searching for something.
She raised a hand, and both men went quiet. "Pay him half," Warna said.
"Eh?"
"You're been dealing with each other for years, yes?" Warna raised an eyebrow at both of them. "Neither of you is cheating the other, it's just a matter of resolving the accounts. Pay him half of what he asks, then settle the matter when the books have been located." She waited patiently as they thought that through. "Or waste more time yelling at one another," she added.
Both men looked at each other, then Pierson huffed out an explosive breath. "Aye, that's well. If you think so, Farnor."
"I'll find the accounting by your next delivery," Farnor agreed. There was a swift exchange of coin, and Pierson was on his way.
"My thanks, m'lady," Farnor said with a sigh. "This mess is enough to drive me into my cups. Wasn't this way before."
"Where were your old offices?" Warna asked.
"Second barracks," he said. "Right across the way. A place for everything and room to work," he said. "Not that his Lordship's not within his rights. But..." His voice trailed off.
"But just the same, it causes chaos, doesn't it?" Warna shook her head.
They shared sympathetic looks, then Farnor squinted at her. "So how can I assist you?" he asked.
"I want to order supplies for the Healing Hall," Warna said. "We need to make sure that it's supplied in case of need."
"Well, we never kept that stocked." The clerk frowned. "The Seneschal took care of that aspect. I've lists of the supplies the units carry on the field but that's not what you are looking for."
"Is the Seneschal in town?" Warna asked.
Farnor shook his head sadly. "No, lady. He was slain—" his eyes shifted in the direction of the keep.
"Oh," Warna said. That was right, and it explained quite a bit to her, especially about Verice...Lord Verice's actions. "Well, who else would know?" Warna asked.
"Priest Dominic," Farnor said. "He's the head of the Church, and assigned himself to run the Hall. He's in town now, far as I know."
Warna nodded, thinking. "What about Lord Verice's staff. His clerks—"
"All in town," Farnor said. "The lord shut the castle down, but work of the barony still goes on as best it can."
"So, they are still working with Lord Verice?"
"Oh, aye, Lady. More 'in spite' of than 'with', but aye. The Lord kept them all on, but won't allow them within the walls." He shrugged. "Lord Verice doesn't give the work the proper attention it—" He stopped when he saw her frown. "No disrespect intended, m'lady. Lord Verice is a warrior, and he's seeing to that right well."
"But there are other aspects to ruling," Warna said quietly. "Things that involve paper and ink, and not quite the level of excitement."
Once again, they exchanged understanding looks.
Warna made her decision. "Very well then, I am going to go into town. I will talk to them, and see what needs doing." She hesitated, but then went on. "I also need a few supplies. Would it be possible to get a few coins..." It was her turn to let her voice trail off, trying not to show her embarrassment.
"Oh, aye," Farnor chuckled. "Lord Verice left instructions." He busied himself for a moment, then plunked down a bulging coin purse on the counter.
Warna opened the bag, and gold coins spilled out into her hand. She caught her breath, then shook her head. "No. I am not taking this much,"
"Lady?"
"Silvers and coppers," she said firmly, pushing the bag back. "And not nearly this much."
"But—"
The argument was fairly short, and didn't last long. There was no way she was carrying that much money around with her. She made sure that Farnor counted out the smaller coins, fully intending to account to him for every copper.
Although she might not mention moon pads specifically.
On her way out, she stopped and asked Ricard for a mount and a guide through town. Then she ran up the stairs to change into her skirts. She'd see the healer, talk to the clerk, and then see to her own needs. Maybe a few pieces of older clothing, or cloth and thread, although needles were dear.
She emerged into the courtyard, eager to go—
To find Ricard holding her mount, and an escort of twenty armed and armored men in a semi-circle around him.
Chapter Twenty-Four
The twenty warriors were unnaturally still, their armor gleaming in the sunlight. Their horses too, stood without so much as a twitch of their tails.
"What's this?" Warna asked.
"Your escort," Constable Ricard replied. "Ustov knows the town well. He's in command."
Ustov saluted her.
"Did Verice order this?" Warna asked.
"I have no orders as such," Ricard replied.
"Oh, well, then—" Warna started to smile.
"But then I have no orders against it either," Ricard continued.
"Constable," Warna fixed a glare on him. "I'm not—"
"Let's take a moment and consider," Ricard said. "The town watch is under-manned, what with almost all able-bodied maels going to the borders to serve."
"Constable," Warna started.
"And the tide of refugees coming in, means that the town's awash in ruffians and ne'er-do-wells in the streets."
"This is silly," Warna said. "There's no need for—"
"What happens if harm comes to you?"
Warna snapped her mouth shut, and pressed her lips together.
"My Lord Verice would not be pleased, seeing as he entrusted your safety to me."
"But—"
"But more important," Ricard interrupted. "Far more important to my way of thinking, is what he's entrusted to you."
"What?" Warna snapped.
Ricard took a step closer to her, and lowered his voice. He stared right at her, his voice calm but emphatic. "For the past ten months, that lad has been afflicted, m'lady. Same routine, same narrow focus every day. You've got him moving. Slow, true enough. But moving. If ought happens to you, what then, eh?"
Warna opened her mouth, then closed it.
"Aye to that," Ricard stepped back and raised his voice. "This is a good start, but I've a mind to add a few more. A foot patrol, perhaps, with some stout crossbows."
"Why not a drum, to keep the beat?" Warna crossed her arms over her chest.
That provoked a twitch from one of the men.
"Not a bad idea, lady. Give me but a moment more—"
"Constable Ricard," Warna could not believe her ears.
"We'll have you fixed up and on your way—"
"Constable, I am not taking a small army to buy moon pads," Warna snapped.
Silence. Utter and complete silence.
Warna blushed furiously. From what she could tell, so did Ricard.
"Stand your men down," she threw her hands up in surrender. "If you can provide messengers..."
"Milo, front and center!" Ricard bellowed. One of the men dismounted and led his horse up to her.
"I've a message for the Priest Dominic, of the Church of the Lord of Light," Warna looked up at the man. "You know it?"
Milo nodded.
"My compliments to the Priest Dominic. I'd like his advice about restocking the Healers Hall with supplies. If he could provide a list of all the items required, I'll see it done." Warna said.
"Wait for an answer," Ricard commanded.
Milo nodded and mounted.
Ricard gestured to another man, who trotted his horse over.
Warna looked up. "There's a clerk, one Ersal, who used to aid Lord Verice with petitions. My compliments, and would he call at his convenience and collect some pending petitions that Verice needs assistance with? Tell him to ask for me at the gate."
"Off you go lads," Ricard commanded, and both started off toward the main gate. "The rest of you, return to your normal duties."
The men dismounted, leading their horses back to the stables, removing their helmets.
"As to the other matters, miss," Ricard lowered his voice. "I could talk to my wife, m'lady and..."
"Yes. That would be lovely," Warna figured the day couldn't get much worse than what it already was. "There's no rush," she added quickly, with visions of mounted messengers being sent out across the land.
She turned back toward the Healing Hall. She'd change, return the coins, and find something to clean within an inch of its life.
That thought made her pause at the door then spin on her heels. "Constable?"
"Yes, miss?" Ricard called from across the yard.
"Where is the Second Barracks?"
By mid-day, Warna felt better.
Not surprisingly, her escort of warriors all magically appeared to aid her in cleaning out the barracks. Their motivations were pretty clear, since they'd started discussing the reassignments of quarters before they were even done with the floors.
She, in turn, made it clear that the first ones to move in would be the supply clerks, and sent one lad running over to warn the Quartermaster to start packing for the move. "We need this all done this afternoon," she told the Ricard. "Before Lord Verice returns."
He didn't disagree.
She had to do more supervising than cleaning this time around, firmly explaining that splashing hot water and soap around did not really count as 'cleaning'. But the work got done as the day progressed and at a much faster pace than if she'd done it by herself.
The dogs lounged outside in the sun, occasionally raising their heads to watch the comings and goings. "You're getting fat, you lazy things," she said at one point as she went for more soap.
Brindle yawned, and rolled over to invite a belly scratch.
Warna shook her head, and leaned down to oblige. "We'll have to see about that," she told him.
By mid-day, the entire barracks was clean and done. Still damp from the scrubbing, but the windows were wide open to let it dry.
Warna stood in the clerk's office, looking at the various desks and shelves. She felt hot, tired. Her tunic and trous clung to her skin, damp and stained, and her stomach was telling her it was past time for a meal. But she still had a rush of pleasure in looking at the results of their efforts.
Most of the warriors had trailed out, carrying the last of the buckets and rags. Ricard ducked in the door and came up to her. Warna welcomed him with a grin.
"Can you get them all moved in this afternoon? Before Lord Verice returns?"
"Aye," Ricard seemed confident.
"Before he sees anything more than normal activity? Even the clerks?" Warna continued, giving one of the counters a final wipe. "It would be best if he didn't have a chance to object."
"Yes," Ricard said. "Lady Warna, you've had a response to your messengers."
"Really?" Warna asked, heading for the door. "Lovely, that will give me something to do after—"
"Wait," Ricard said, but she already had the door in mid-swing, stepping out into the sunlit courtyard.
Only to find a crowd of assorted men and women gathered about, staring at her. The dogs were up among the crowd, their tails slowly wagging.
At the very front was a tall elf, with long, straight black hair, a Priest of the Lord of Light.
He raised his head, glaring at her with pure disdain. "You are Warna of Farentell?" he demanded.
At her nod, his mouth twisted. "Just who in the darkest hells do you think you are?"
Chapter Twenty-Five
The Constable stiffened. "Here now—" he started, but Warna held up a hand.
"Priest Dominic?" she asked.
The elf lifted his chin to regard her, his robes rustling as he gave her an imperious look.
Warna was sure he'd notice every stain on her trous, but she wasn't about to back down. "How kind of you to come so quickly." Sand and Gray came trotting out of the crowd to greet her. She reached out to stroke their heads, while making sure her expression was warm and welcoming. "And these others are...?"
A tall woman spoke up from the crowd. "We're Lord Verice's staff. We've come to—"
"We have come to learn just who you are and what is happening," Dominic snapped, raking Warna with a withering glance.
Brindle had also appeared, followed by the other dogs. Sand and Gray were leaning against Warna's legs. Brindle just sat, facing Dominic.
"Of course," Warna said. "We've just finished cleaning out this barracks. There's plenty of room within. Perhaps we could go in and talk?" She threw the rags onto the pile just outside the door. "Just give me a moment to clean up, will you?"
Dominic opened his mouth to protest.
"I'll see kav brought, m'lady." The Constable opened the door. "Priest Dominic?" He asked, gesturing for him to enter.
Dominic huffed, but he strode past Warna and into the building. Warna didn't wait for another protest. She just started forward, pushing past the dogs to walk through the crowd. She smiled at everyone, and headed for the Healing Hall.
She didn't let herself hurry until she was through the door and taking the steps three at a time to her room. A quick wash, fresh clothes, and she'd be ready. Her heart was racing and it wasn't just the steps. What if Lord Verice saw this crowd, and they demanded an explanation from him? There was a good chance that Verice would escort them to the gates and she wouldn't chance that.
She was headed down the stairs when the door below opened. The constable and the dogs were all pacing the main room.
"Dominic's the one in charge of the Healing Hall?" she asked breathlessly.
"Aye," The constable was peering out the window. "I've got them all settled and drinking kav. I don't think we want the Lord to see..." he cast a glance at Warna.
"I know," she said. "Who are the others?"
"All part of the Lord's household, before the castle was closed," he said as he followed her out the door and back across the courtyard. "The tall faelle is Janella, the Castle Chamberlain, and Ersal was the Master Clerk," he reached out to put a hand on her arm just as they reached the door of the barracks. "The thick man, with the beard is Roath, the Master Gardener. Warna, what will you tell them?"
She looked up at him and huffed out a nervous breath. "The truth, of course."
Priest Dominic was speaking as she opened the door, and his voice cut her like a knife.
"Why would he listen to her? She's a human woman," he said scathingly. "Who'd want to have anything to do with one of them?"
Warna stood in the doorway, frozen for a long moment, staring right at Dominic in the silence of the room. 'Lady of Laughter, make him regret those words someday,' she thought, then dismissed it as she faced them all down, stepping forward to let the constable close the door.
"I am Warna of Farentell." She walked through the seated group, then took a chair facing them. "Let me explain how I came to be here."
She kept it short, talking of her 'rescue', and Lord Verice's extension of protection. "I want to work, is what I told him." She looked down at her hands, folded carefully in her lap. "I need to lose myself in a task, and while he's not given me permission, he's not prevented me, either."
The constable had moved behind her, to stand at her shoulder. She felt his quiet support, but so far, he'd remained silent.
"So, what is your intent, Warna?" Ersal spoke first.
"I've cleaned the Healing Hall, and this building," Warna said promptly. "I'll start on the Third Barracks next. By then, I'll find a need to restart the kitchens and the laundry."
"And everything else will flow therefrom," Janella said. "And the keep?"
"No," Warna said. "I made him a promise, that I would not touch it. I must keep my promise."
Janella nodded slowly. "It will work," she said looking at some of the others.
"This is ridiculous," Dominic stood, imposing in his fine robes of white and gold. His long black hair shimmered in the light, a stark contrast to the pale points of his ears.
'Every inch an elf,' Warna thought.
"If," Dominic emphasized the word. "If it's as you say, then all we need do is go to Lord Verice and ask to be allowed to return."
"No," Warna looked up at him. "Do that, and you'll ruin any chance. The castle must come slowly alive around its Lord, and—"
"Lord Verice will come alive with it," Ersal said with a spark in his eye.
"Nonsense," Dominic scoffed. "We've only to ask—"
"We've asked over and over for the last few months," Janella pointed out. "We even had Lord Mayor Penard to ask on our behalf. Much good it's done us."
"Then we ask again," Dominic said. "He's clearly changed his mind. I'll—"
"You'll do no such thing," the constable said, startling all of them by breaking his silence.
"I'll not let you put him at risk," Warna added.
Dominic looked at her with narrowed eyes, then arched an eyebrow. "And for you, Lady? Perhaps you plan to warm his bed?" His lip curled. "Bring him back alive, so to say?"
"Dominic!" Janella gasped.
"Not that it's likely, given your blood," Dominic continued.
The constable growled.
"Constable," Warna said sharply.
He stopped, glaring at Dominic.
Warna kept her voice steady. "Priest Dominic, Lord Verice has offered me shelter and protection. If I can do this for him, it still will not be full recompense for his kindness."
"And if we don't go along with your plans?" Dominic demanded. "What would you do then?"
"I believe you are under orders from Lord Verice to remain within the town," Warna said. "I would ask the constable to enforce his orders."
"Who are you to speak so to us?" Dominic demanded.
"Who are you," Janella interrupted. "to claim to speak for all of us?"
Dominic huffed.
"She's right, and you know it," Ersal said. "We've not set foot within the castle since he ordered us out. This is the first bit of hope we've had since that day."
"Since that night," Janella whispered.
"You were there?" Warna asked. "When it happened?"
"Aye," Ersal rubbed his hand over his face. "We all were."
Warna threw a glance at the constable, but he shook his head. "Not me. I was in town, on leave."
"Would you tell me?" Warna leaned forward, looking at all of them. "What happened that night?"
Chapter Twenty-Six
Her request was met with bent heads, averted eyes, and a few stifled sobs. "I'm sorry," Warna said, regretting her question. "Kalynn told me the story, but she wasn't there and didn't know the details."
Dominic's head came up, his eyes narrowed. "You met Seer Kalynn? And—" he hesitated. "And Wolfe?"
Warna nodded.
"She needs to know," said one of the women in the back, a round, sweet-faced lady with brown hair laced with gray. "If she's to aid him, she needs to know."
"Aye," Janella said. "But the telling is hard."
There was a shifting in the room as they all exchanged glances, tight-lipped, their eyes full of pain. But there were also nods, and Warna could see the determination spreading. As if by silent agreement, they had made their decision.
Ersal cleared his throat. "It was the Fourth Night of our Festival of Light and Laughter, when we celebrate the Gifts of the Lord of Light and Lady of Laughter. T'is our custom, here in Tassinic, you see?"
Warna nodded in encouragement, afraid she'd stop the flow of words.
"Third Night is the Gift of Music and Dance," he said. His voice trailed off, his gaze fixed on the air behind her.
"Oh lady, it was such a grand night," Janella said softly. "So filled with light and laughter, warmth and music. The whole castle fair glowed."
"We'd prepared for weeks," another voice piped up from the back. "Decorating and cooking."
"Planning the presentations," someone added. "Practicing dance steps."
One rough looking man in the back spoke, his voice a rumble. "The castle and keep were all lit with mage lights. So much magic your skin tingled with it, you know?"
"She doesn't," Dominic said sharply. "Humans rarely have the gift," he continued at Warna's unspoken question. "All those of elven blood can sense it. Not all can manipulate it, but all feel its use."
"Laughter flowed freely that night," Ersal said with fondness in his voice. "Everyone was making merry, dancing, laughing, talking. And in the Great Hall, Lord Verice had broken out the applefire—"
A chuckle from the back. "And wasn't Betnan upset by that?"
The chuckles spread about the room.
"Applefire?" Warna asked.
"A liquor, lady, and highly prized," Ersal smiled at the memory. "There's only one brewer that makes it, and they only put up one pressing a year, and then it's set aside to age. It's said that they've only twelve trees that bear the right kind of apples. There's magic in the making of it, or so they say."
"And Lord Verice orders his stock opened, and a sip for all. And Betnan, who had charge of the buttery says 'Surely, you mean the noble folk alone, m'lord.' And Lord Verice, he says 'For any and all within my halls this night, Betnan.'" Ersal shook his head. "Betnan looked so miserable, opening those bottles," He chuckled but then the laughter faded from his face. "May the Lord and Lady keep his soul."
"Lord Verice opened his cellars in honor of Bard Charrin and his Lady Summer, who had come to hold Festival with the Lord," Janella picked up the tale. "It was such a lovely Festival up to that point. If I could just somehow keep that moment in my mind and preserve it, not remember the screams, not see—" She put her head down into her hands and wept.
Ersal moved over, and put an arm around her shoulder. "Charrin had just finished his last song. The room was stirring, there was applause, and then the Usurper—"
"Regent," Dominic corrected.
Ersal's face darkened. "The bastard sent—"
"The Regent denies it, and we've no proof," Dominic said. "She has asked you for facts, not speculation."
"Fine," Ersal spat. "A messenger, named Daress, stepped forward. He was a human, sent by the Regent of Palins with messages for Lord Verice. He'd arrived that morning with an entourage, and Lord Verice had invited him to the Festival, saying that the business could wait until the morrow. Daress pressed him, but his lordship would have none of it."
"We all knew that most likely he'd brought demands from the Regent, insisting that Verice attend one of the High Baron Councils in Edenrich," Janella explained.
"He is the Lord High Baron Verice's liege," Dominic said.
"The Seneschal announced him, and they stood before the high table, just to the right of Charrin and Summer. Lord Verice acknowledged him, welcomed him," Ersal said. "Daress had this smile on his face," He took a breath. "I remember thinking that he looked like a child with a terrible secret."
Ersal was tense, rigid, his eyes fixed on the wall behind her. Warna listened as he spoke in a flat tone, as if he dare not let any emotion into his story.
"Daress said something," Ersal continued. "I didn't catch the words. Then he gave a crackling shout of laughter. It must have been a signal. Because he turned and attacked Charrin."
Ersal closed his eyes. "The blade glittered as he swung. I suspect he was aiming at Charrin's throat, but he caught his eyes instead." He choked up, unable to continue.
Janella picked up the tale. "Charrin screamed. Summer moved, put herself between Charrin and Daress, so the blade plunged deep within her, not him."
"Lord Verice launched himself over the table at Daress, he'd an eating knife in each hand," Ersal said. "The other four with Daress all pulled out their knives, and they all went for our Lord. But that's when—" he gulped.
"When the screams started from all around us, and from the balconies above." A thick-waisted man in the back spoke up. Warna frowned, trying to remember his name. Roath, that was it.
Roath continued, "Armed warriors appeared within the keep, attacking unarmed celebrants."
"Lord Verice was holding his own, and many of the noble lords sprang to his side. The Seneschal, his aide, they grabbed up whatever they could as weapons," Ersal said. "Betnan grabbed up a bottle and shattered it on the table, wielding the jagged shard..."
"They cut through us like wolves among lambs," he said, rubbing his thigh. "And just as quick. The guards and the mages, they reacted, but it had all been planned by that bastard Daress. They aimed to maim, you see, as much as kill."
"In the end, we took them all down to the last. But not before Lord Verice was fallen, blood spurting from his thigh."
"We got to him in time," Dominic said. "But it was a close thing. We got the bleeding stopped, then littered him out to the courtyard. No further - we feared he'd start to bleed if we took him too far. Captain Narthing ordered the keep evacuated, fearing there were others hiding within."
"What of Charrin?" Warna asked.
"Oh, that was a horror, lady," Janella whispered. "He'd gathered poor Summer in his arms, and he was keening there in the Great Hall. We couldn't get him to move for the longest time, and he wouldn't let us take her body. We had to carry them both out."
"There was nothing you could do?" Warna asked Dominic.
"She was dead when we arrived," Dominic said. "I'd more wounded and dying than healers. Charrin's wounds were not life threatening. Lord Verice was our first concern."
Ricard stirred. "As soon as we heard the alarms, we ran up from the town, through the gates and started dealing with the attackers. Narthing led the search, and I organized the courtyard."
"Narthing came out, grim, his sword still out. They'd combed the keep and brought out the bodies. He was standing on the stairs..."
"Lord Verice regained consciousness," Dominic said.
"He'd lost blood, weak as a kitten until he heard Narthing's report," Ricard said. "But the rage boiled up within him. He staggered to his feet, all the healers trying to stop him, and with a gesture he slammed every door shut, and commanded that no one enter the keep."
"Of course, he then fell back into our arms," Dominic said. "He'd used the last of his energy and his wits."
"And when he woke, he ordered the entire castle emptied," Ersal said. "It was insane, of course. We argued but—"
The gate horns blew, announcing Verice's arrival. Warna started at the sound, they all did. Warna hadn't realized it had gotten so late.
"Lord Verice must not see you," Warna stood. "Ersal, I'd ask you to come with me. Please, the rest of you, wait here until the constable can see you slipped out the gate."
Dominic folded his arms over his chest, glowering, but Warna ignored him. "I'll send a request in the next day or so, for supplies for the Healing Hall. Over a period of time, as I see fit, we will see it staffed during the day, and then the night, and gradually ease into having healers in residence."
She looked around the room, catching their eyes. "I will continue cleaning, and will send for you all gradually. Be patient." She focused back on Dominic. "Or ruin all that has been accomplished so far."
Chapter Twenty-Seven
Verice swung down off his horse, sighing with relief to be out of the saddle. He gave his horse a pat on the neck as the stable lads led him off for a well-deserved bucket of grain.
"That, m'lord, was brutal," Narthing said, dismounting from his own horse with a sigh. "I'll confess this has not been a day I wish to see again."
"Agreed," Verice said. "But we got the bastards."
Narthing nodded, his smile reaching his eyes. "Birch Cove on the morrow, then. That's the village on Island Lake."
"On the morrow," Verice said, heading toward his rooms. He peeled his glove off, noting that a seam had given way. He felt as worn as the glove, and wanted nothing more than to peel out of his armor and wash. He could feel the grit on his skin, and the dried sweat itched on his scalp.
He took the stairs two at a time, already attacking the buckles on his armor. It felt good to have tracked down those bastards. Bandits, raiders, whoever they'd been, they would no longer threaten any of his people.
Verice strode into his chambers, and called his aide for water and kav, unbuckling his sword belt, and hanging it from its peg. That was another thing he needed to see to; the edge of his blade. He'd hone it while he and Warna talked this evening, after dinner.
He stripped to the waist, and started washing. There was a tune running through his head, a sprightly one that he didn't recognize. He started humming as he scrubbed his face. It would have been far better to have taken a long soak in the hot springs below the keep, but—
The keep was sealed.
Sealed because—
He stopped, standing with a towel in his hands, water dripping from his face and hair.
A cackle of laughter, a blade flashing through the air, glittering in the mage lights.
The pain washed over him, made worse by the guilt. For the fact that he'd forgotten. Forgotten the deaths, the betrayal, the pain.
All during the day, the chase, fighting, the return, standing here, he'd not once thought of the attack. Bitterness ate at the back of his throat. Ancestors, what kind of man was he to have forgotten—
The clatter of dishes in the outer room brought him back to himself. Verice dried off, and pulled out a clean tunic, feeling oddly numb. He took a deep breath before he opened the door to find Warna standing at the table, waiting by her chair. The table was covered with dishes and plates, all waiting for him.
"M'lord," She bowed her head, with her usual smile. Except there was something different. Verice bowed his head back to her, studying her face. Cheeks flushed, eyes bright, Warna looked as if she'd been up to mischief.
"Warna?" he asked.
"M'lord, I have taken a liberty," she said, her tone and manner very formal. "I saw that the petitions remained untouched," she glanced at Verice's desk where the forlorn pile still sat on a corner. "I'd thought to have one of your clerks come and assist you with them. I sent a message into town, and one Ersal is outside the door awaiting your instructions."
"Ersal?" Verice asked. He hadn't seen Ersal since...
Warna stood there, her hands on the back of her chair, watching him patiently, looking half-embarrassed and pleased with herself at the same time.
"I would have gotten to them," he said.
"I know," she said, suddenly serious. "But it's easier sometimes, with help."
He gave her a wry look. "I never liked dealing with petitions," he admitted. "Would you ask Ersal in?"
Warna stepped to the door.
"M'lord," Ersal put his hand to his chest and bowed.
"Ersal, it's good to see you," Verice said, stepping over to the desk. "As you can tell, once again I've a need for a rescue."
"M'lord, it would be a pleasure." Ersal accepted the bundle of documents. "I can have these sorted out for you quickly." There was the slightest hesitation in his voice, but then he continued on. "When would you wish me to bring them back for your review?"
Verice gave the man a glance. "I'll stop by your offices in the next few days," he said.
"M'lord, you told me that two months ago." Ersal said softly. "Your defense of the barony has consumed the majority of your time. Let me ease some of that burden by bringing the work to you."
"You know me too well, Ersal."
Ersal tilted his head. "This time tomorrow, m'lord? I promise to take no more time than necessary."
"That would be fine," Verice said. "My thanks, Ersal."
"My pleasure, m'lord." Ersal turned. "M'lady," he bowed his head to Warna and left.
Verice returned to the table and gestured to Warna to sit. "You look like someone who's gotten away with mischief," he said mildly.
"You're not upset?" Warna asked, as she started to uncover dishes.
"No," Verice said. "Not about that."
She paused, staring at him with those wide brown eyes, and Verice suddenly remembered the tune he'd been humming.
It was Warna's. She sung it at Wolfe's.
"I think your day was a bad one," she said tentatively, passing him the bread. "What happened?"
Verice shook his head, and started to serve himself. "No. I'd rather hear about your activities. Anything you want to tell me?"
"Well," Warna picked up her fork. Her lips curved in a smile. "I think your dogs are getting fat."
Chapter Twenty-Eight
A pounding on the door of the Healers Hall startled Warna awake. Sand and Gray both came to their feet, growling and barking at the stairs.
It took her a moment to orient herself. She'd had dinner the night before with Verice, they'd talked about a variety of things, he'd agreed to let Ersal deal with the petitions...
The pounding came again, more insistent. Now she heard raised voices...what was happening?
She threw on her tunic, went to the small window and leaned out. Three large carts were just below, and a small group clustered at the door.
"Here now," Ricard bellowed. "What's this then? Lady Warna is still sleeping, you rude dogs."
Warna laughed. If she'd slept through the knocking, his voice alone would certainly have woken her.
"She's sleeping here?"
That would be Priest Dominic, his tone implying some nasty things.
"We've supplies for the Hall," Dominic continued. "At her direction, I might add."
Warna darted a glance at the barracks, to see Verice's men gathered for their departure. They hadn't left yet.
Drat that priest. They'd all agreed to help her last night. If this was his idea of cooperation and patience—
"Constable," Warna called, cutting through the argument below her. "I'll be right down."
She pulled back inside, and dressed quickly, braiding up her hair as she ran down the steps.
At least Ricard had stopped bellowing at the top of his lungs. He'd switched to a low menacing growl, one that Warna could feel in her bones even before she opened the door. "—no need for this," he glared at Dominic.
"Every need for it," Dominic glared right back, looking imposing and regal in his white and gold robes. "I've not much time and a responsibility to see this Hall stocked and ready. We'll be done and on our way quickly." The disdain in his face as he gave Warna a glance slid into pure satisfaction. "I've received a summons to the Church at Edenrich, and the portal will open at noon."
"What, among all those humans?" Ricard raised his eyebrows.
"I wouldn't expect you to appreciate the nuances," Dominic's disdain was restored. He was staring down his nose at both of them.
"Constable," Narthing was calling from the midst of the men. Ricard frowned, giving Warna a concerned look.
"Go," she said.
He gave her a nod, and strode off.
Warna swung open the door behind her, and the acolytes started ferrying supplies from the carts into the hall. "I'll be back; I'm going to the kitchens for kav." And to make sure that Verice hadn't noticed this ruckus and interfere. "I'll return shortly."
"No need," Dominic said, taking a basket out of the cart. "We know what needs to be done."
"I want to know what needs to be done," Warna said. "So that in the future—"
"Please," Dominic sailed past her, his robes flapping. "You're little more than a pet, girl."
Warna lashed back. "And yet you are summoned to the human city of Edenrich, elf."
Dominic paused in the doorway. "To the highest offices of the Church I served, where the halls ring with the voices of highborn nobles. Humans, yes, but of the highest blood and breeding. I imagine I'll be most comfortable in their presence. Now, if you will excuse me." He whipped out of sight before Warna could open her mouth.
Flushed with the insult, Warna's hands formed fists, and she took a step to follow and berate the elf. But Verice's men were still milling about, and she desperately wanted kav.
She turned and headed to the kitchens, uttering a small prayer that the cooks had made it strong.
Verice came out of the barracks eager to be on his way, only to run into a bleary-eyed Warna entering the kitchens. Her cheeks were pink, her eyes flashing.
"You're up early," he said.
"I asked for someone to stock the Healing Hall with supplies," she said crossly. "I didn't expect Priest Dominic at the crack of dawn."
"Arrogant bastard, isn't he?" Verice said.
Warna rolled her eyes.
"Skilled though," Verice added, pausing to follow her into the dining area. "I'm surprised he's still in Tassinic. He was angling for assignment to the Church in Edenrich."
"Well, he's apparently received a summons," Warna said as she headed to the hearth, nodding to the men who were eating. "I need kav."
"Ah," Verice said, following her. "I wonder if he realizes what he's getting himself into."
Warna glanced over her shoulder at him as she poured herself a mug. "How so?"
"Let's just say that the Church in Edenrich is more concerned with its power base than its spiritual obligations." Verice shrugged.
Warna took another sip and stared at him over her mug. "Where are you off to this time?"
"Birch Cove," Verice said. "A small town, near a lake, by the Summerford border. We're not expecting trouble."
Warna stared into her mug before she glanced at him. "Take care anyway," she said softly.
Verice looked at her, her golden hair pulled back in a braid, with wisps of gold escaping, crowning her in the morning light. Suddenly, he wanted to sit with her, drink kav and talk about her plans for the day.
Narthing was hovering in the doorway, he had to go.
She gave him a questioning look over her mug, and he suddenly felt foolish. He bowed his head to her and left to join his men.
He mounted, feeling oddly bereft, as if he'd forgotten something, or lost a chance at—
He shook his head, lifted a hand, and started the chant to open the portal.
The glowing circle formed, a doorway of flowing white curtains of gossamer, moving in an unfelt breeze. His men formed up behind him; Narthing moved into position in front. They'd preceded him, so that he could take the portal down behind him as he rode through.
Narthing gave the order, and the horses moved forward at a walk, well used to this mode of travel. Verice waited until the last tail disappeared, then urged his own horse through, concentrating on the closure. There was a moment of white light, of disorientation, and then he was through on the other side.
To find the air filled with smoke and screams, and his men under attack.
Chapter Twenty-Nine
The skirmish won, the enemy in retreat, Verice followed the last of his men through the portal, emerging into the Castle courtyard, filthy and bone weary. With a savage gesture, he snapped it shut behind him, on the ruins of Birch Cove. Nothing left there but burning buildings, smoke-filled air, and the heads of the 'bandits' on pikes along the road.
A fierce bolt of satisfaction went through him at that memory, but the sight of the village dead lined up in the courtyard, covered in shrouds wiped any sense of gratification away. Far too many lost.
It was late, the night was still and quiet, the stars bright above his head. The walls burned with torches and he could see the watch making the rounds.
Constable Ricard appeared at his side, his face reflecting the strain of the day. He cast an eye over Verice with a frown.
"Not my blood," Verice reassured him.
Ricard's relief was in his eyes, but he gave a simple nod of his head. "We'd word you'd be at it till daybreak."
Verice stripped off his gloves. "It didn't take long to hunt them down." He indicated the rows of bodies. "What of—"
"The survivors of Birch Cove have asked to return and bury their dead," Ricard said. "They want to return to their homes as well. I've told them all that must await your decision."
Verice rubbed his face with his bare hand.
"The healers have seen to the wounded, my lord." Ricard gestured over to the other side of the courtyard. "We've housed the villagers as best we can. Some of the men have given up their beds for the night."
"Narthing?" Verice asked softly.
"Not as bad as they first thought," Ricard nodded toward the Healing Hall. "They've got him settled, and they drugged him stupid when he tried to leave his bed to return to your side. Won't be up for much until tomorrow."
"Nor will I," Verice said.
"You look done in," Ricard agreed. "There's naught else you can do tonight. I'll roust some of the lads, we can get you hot water—"
Verice shook his head. "I'll just draw up some water from the well, and wash the worst off." He started to unbuckle his breastplate.
"I'll send out towels then, and something to eat—"
Verice made a face.
"Try to get something down," Ricard said gruffly. "Leave your gear by the well, and I'll have the lads clean it for you," he held up a hand to prevent Verice's protest. "You'd best be to bed, there's more than enough that will need your attention in the morning."
Verice shrugged. No denying that.
His muscles protested as he lowered the bucket, and pulled it back up, brimming with water. It was cold. He stripped to the waist and plunged his hands in with relief. A lad appeared with towels and soap, and he carried off Verice's armor and sword. Verice kept his daggers.
He indulged himself by washing his hair, upending a bucket over his head, letting the cold water wash away the sweat, grime, and blood. The water brought a surge of energy for a time, letting him scrub and towel himself dry.
Ricard approached with a cool bottle of ale, and some cheese between two hard crackers. "Enough to take the edge off," he said.
Verice took a long swig. "You're sure Narthing's well tended?"
"Aye," Ricard said, throwing the towels and soap in one of the buckets. "And they'd not thank you if you tried to wake him or them." He chuckled. "Priest Dominic stayed once the wounded started pouring in; he's bedded down in there as well."
Verice looked over at the Healing Hall and the dark window at the very top. Truth be told, it wasn't Narthing or Dominic he wanted to talk to. He clapped a hand on the constable's shoulder. "Well, then I'd best see to my own bed. Make sure you see to yours."
"Aye," Ricard said. "Dawn comes quick enough." He headed off to the gate, presumably to finish his rounds before bed.
Verice set about eating the crackers and cheese between pulls on the bottle. The weariness of his body had more to do with the magical energies he'd expended rather than the fighting. It was an effort to chew, but he did it, watching the crumbs gather on his trous. The ale was cold, and sweet. It replaced the bitter taste of ash in his mouth.
It was dark and quiet here; the only sounds came from the night watch pacing the walls. A sense of isolation washed over him, an ache of loneliness. The aftereffects of battle, he knew.
He stared up at Warna's window again, trying to will the flaring of a light that showed she was awake. He really wanted to check on her, to see if she was well, maybe talk for a moment. If anything was amiss, he'd have been told. Anything he had to tell her could wait until the morning.
He padded through the barracks bare-footed, silently walking the halls and climbing the stairs. There were soldiers lining the halls, rolled up in bedrolls, asleep. He frowned, thinking about the challenges of relocating the people of Birch Cove. They could rebuild, of course, but he wanted to talk to the village elders before he—
A huge yawn cracked his jaw, and Verice shook his head ruefully as he opened the door to his chambers.
Someone had left a mage-lantern open in his sleeping chamber; its soft glow lit the outer rooms enough to see by.
The dogs were sprawled on the floor around the table, curled in balls. Brindle raised her head and wagged her tail. Verice crooned to her as he crossed the room. Once she saw that he was headed within, she lowered her head, and settled back down.
Verice yawned as he stepped through, just as happy to be seeking his own rest. Tomorrow would be—
Warna was in his bed.
It took a moment for it to sink, for him to understand that the fan of golden hair was hers. She was on her side, facing him, curled around a pillow, covered with one of his blankets. There was a faint frown on her face, as if her sleep was an uneasy one.
Verice hesitated, then leaned against the door frame, taking in the sight. He'd not disturb her. But after a day of death and horror, it felt good to see her so, sleeping safe within his walls.
At least he'd managed that much.
She was lovely, really. Those wide round eyes, and the softness of her face. She'd probably given up her bed in the Healers Hall for one of the healers or patients. Ancestors, he hoped it wasn't Dominic. A flash of irritation at Ricard was quickly replaced with common sense. He doubted the man even knew she'd ended up here.
There were extra blankets folded and the end of the bed. He'd curl up by the hearth in the kitchens.
He walked over, careful to be quiet, with every intention of taking a blanket and leaving. But he paused for just a moment, listening to her breathing, his eyes on her sweet face as she slept. Something ached in his chest suddenly; a want, a need for her to open her eyes so they could talk. Verice frowned at that, uncertain as to what exactly he was feeling.
Warna sighed, rolled over and opened her eyes, still half-asleep.
Verice suddenly knew exactly what he wanted.
Chapter Thirty
Sleep-filled, Warna's brown eyes focused on him and her lips curved in a warm, drowsy, welcoming smile. She murmured his name, clearly just on the edge of consciousness as she shifted under the blankets.
Verice sucked in a breath, his pulse quickening as pure desire swept through him. The shock of recognizing that fact would have -should have - made him stop, but he was already moving, bracing a knee on the edge of the bed, leaning over Warna. She blinked at him, her confusion clear.
He kissed her, pressing his lips to her softer ones, no more than that. He waited then, conscious of her every breath.
She pulled in a startled gasp against his mouth. His heart stopped for one long, agonizing breath, then leapt as her lips moved under his, clumsily returning the kiss, as if unsure as to what to do.
He groaned, buried one hand in her silken hair and took control.
Warna gave a contented murmur and opened her mouth to him.
Verice took what she offered, crushing her in his arms. She molded against him, warm against his bare chest. She tasted of peace, of home, but she was also Warna and he hungered for her and her alone.
She brought her arms up around his waist, clutching at his waist, returning the kiss.
Something within him broke open even as it sang.
Warna awoke fully, gasping her surprise against Verice's mouth. His lips were warm and dry and he seemed to hesitate just on the brink, waiting for something...waiting for her.
She wasn't sure what to do next, but she pressed up, her lips moving against his.
He pulled her into a tangle of blankets and arms, wrapping his arms around her to lift her up. His tongue teased hers and she opened her mouth to him. For long slow moments, there was nothing but him, his touch, his mouth. She felt so alive, her body on fire. Warna brought her own hands up, threading them into his silver hair.
Verice broke the kiss, and held her close, his face pressed into her neck. The warmth of his breath beneath her ear made her shiver. His arms trembled.
She wrapped her own arms around him, running her hands over his back, breathing in the scent of soap and leather.
He'd kissed her. Her lips still tingled with the lingering heat of his, his taste in her mouth. But he'd broken it off, buried his face in her hair, and now held her like he'd never release her.
"Verice?" she whispered, trying to understand. His kiss had set her on fire, but the desire was fading, leaving her confused. Until she felt his harsh breaths and caught the faint whiff of smoke in his hair.
"Verice," Now there was no question in her voice. She'd seen the wounded coming through the portal, had heard of the destruction of the village. She could only imagine what he'd been through.
Still he held tight, his hair a curtain around them. She tightened her hold, offering what comfort she could.
"Sorry," his voice was harsh and broken in her ear. He released her, his arms dropping away, but the tension was still there in his back. Warna tightened her hug even as he tried to slip from her grasp.
"I've no right," he whispered, trying to pull away.
"Hush," she murmured, and held on until he wrapped his arms around her again.
"You've every right, considering."
His breathing started to slow.
"I didn't expect you to return," she whispered. "They needed every bed in the Healing Hall, so I thought—"
Verice lifted his head, and she could see the exhaustion in his eyes. "I'll go—"
Warna shook her head, still keeping him close. "No," she said. "Don't go." She tugged him down to the bed.
Verice swayed as she pulled, resisting her. "Your reputation," he stuttered out the words.
Warna laughed, shaking her head. "That horse has fled the barn, Verice." She shifted, making room, trying to keep a grip on his shoulders. "Sleep on top of the blankets then. I trust your honor."
"You shouldn't," came his reply, cold and hard. There was a flash of something in his eyes that sent a bolt of heat through her. Warna caught her breath, quickly breaking eye contact.
"Sorry," Verice said. "I'm..." he ran his hand over his face. "I've offended you. I didn't mean to—"
"You are exhausted," Warna said firmly. She tugged again, and Verice obeyed this time, stretching out on the bed beside her. She reached down and covered him with the extra blanket. "Sleep," she whispered, settling back down.
He nodded, closed his eyes - but they opened again and he stared at her, his eyes blurring and unfocused.
She reached out from under her blanket, and took his hand, curling her fingers around his. "Sleep," she commanded.
He tightened his grasp for an instant then sighed, nodded, and closed his eyes. She watched over him as the tension drained and his breathing slowed. Watched as he slipped into sleep.
Finally, when she was sure he would stay asleep, she closed her own eyes.
But she left her hand in his.
Verice awoke alone.
Warna wasn't in the outer room, either, although fresh clothes and hot water were waiting for him. He stood staring for a moment, trying to decide if Warna had arranged that. And what it meant if she had.
He ran his hands through his hair, knowing full well that he'd broken faith by kissing her, and trying to remember why he'd thought that would be a good idea. Although he didn't remember thinking so much as feeling...his body tightened as the image of Warna in his bed flashed before him. He remembered that all too well.
He needed to face her.
The thought made him sick. He didn't want to see the betrayal in her eyes, or worse, the scorn. For violating her trust, breaking his promise of—
A knock at the door, and one of the serving lads peeked in, balancing a tray. "M'lord?"
Verice gestured him in, arching an eyebrow at the hot kav and breakfast. "You must have been sitting outside the door."
The lad nodded, intent on his task of delivering the tray to the table. "M'lady's orders. 'Let him sleep, feed him, then tell him Captain Narthing is asking for him.'" The lad set the tray down with a satisfied sigh.
So...he wasn't the only one who wished to avoid the issue. Or at least, avoid him.
Verice sent the lad off. He poured some kav, hot and strong, and tore at some of the bread, leaving the rest of the food untouched.
He washed, changed, stomped into his boots, and belted on his weapons. Best to find her and apologize.
Before he lost his nerve.
Chapter Thirty-One
Verice blinked as he stepped into the courtyard, the sunlight hitting his eyes. He'd slept later than he'd thought.
Brindle appeared beside him, followed by the rest of the pack. He whined, shoving his nose into Verice's hand, looking for attention. Verice knelt, and scratched his ears, glad for an excuse to pause for a moment.
The courtyard was quite the contrast from the night before. The dead bodies were gone. The whole place hummed with activity. Wagons rumbled through the main gates, filled with supplies. A few were stopped in front of the Healing Hall, unloading supplies. Other wagons clustered in front of the buttery and ovens. Men were unloading barrels and crates, heaving sides of beef on to their shoulders, calling to one another over the noise. Smoke was rising from chimneys long cold. It felt oddly...normal.
"Hup, hup," Verice said, getting the dogs' attention. He took a moment to concentrate on each of the dogs, checking them over, talking to each one in low tones, even as he glanced around the courtyard. They all gathered around him, vying for his attention. Sand and Gray weren't there, but he knew where they'd be.
He feared to look at the keep itself, but steeled himself enough to take a quick glance. The doors were all closed, the windows dark. He breathed then, feeling the fool. He'd have known if any had entered, after all. But it stood, silent and dark.
Warna had kept her word.
Warna...
He rose then, looking around, and found the constable at his side, waiting.
"All's well?" Verice asked.
"Well enough." Ricard said. "The men have secured Birch Cove, or what's left of it. They report that the remaining bandits have retreated over the border, and they did not pursue." His expression of disapproval told Verice what he thought of that order. "We've managed to get the villagers all fed and seen to. Captain Narthing is awake, and waiting to speak to you. He and Priest Dominic are going at it something fierce." Ricard grinned. "Last I left, Dominic was threatening to tie him to the bed."
"Warna?" Verice asked.
"She's got the women from Birch Cove helping her scrub down the Third barracks." Ricard rumbled, he raised an eyebrow and gestured in that direction. "Walk as we talk, m'lord?"
Verice nodded, and the dogs paced with them.
"M'lady said we need the sleeping space," Ricard said as they made their way past the keep. "She's ordered the buttery, ovens and laundry opened, because the barracks kitchens won't be able to handle much more work than what they've already got." Ricard pointed to the wagons. "We've got food and supplies coming in, but m'lord," and here the man hesitated.
Verice raised an eyebrow, inviting him to continue.
"M'lord, you'll be needing to name a seneschal and fairly quick," Ricard said apologetically. "I can handle it for a while, but you need a man on it to keep it running smooth."
Verice nodded.
"The Birch Cove elders wish to talk with you," Ricard continued. "And the Lord Mayor of Octara and the heads of the Merchants Guild are asking questions about trade. A few others be wanting your attention as well."
"Warna first, then Narthing," Verice said. "We can set up a meeting for the others this afternoon."
Ricard nodded his agreement. "I'll try to hold them off." He indicated a doorway where a cluster of men had gathered. "But they'll not be satisfied just talking to me for long, m'lord."
"They'll have to be," Verice snapped.
Ricard started, but covered it quickly. "Yes, m'lord." He gave a quick bow of his head, and turned toward the group of men headed their way.
Verice grimaced, regretting his sharp words. His irritation lay with himself, not his people. But delaying this conversation with Warna would only make it worse. He quickened his pace, determined to face the consequences of his actions.
There were women gathered before the Third Barracks, with buckets, mops and cleaning cloths, all talking at once. They were wringing out rags, pouring fresh water, surrounded by soap bubbles, wet cobblestones and endless chatter.
Another group was a bit farther along, away from the damp, beating rugs and stuffing mattresses with fresh straw. Children ran in and out of their midst with handfuls of straw, throwing it at each other in a game.
Warna stood at the heart of the activity, her blonde hair caught up in a twist. She was wringing rags with the best of them.
He hesitated, not sure if he should—
She lifted her head, and turned toward him, as if she knew...
Her eyes found his unerringly, like an arrow to the heart.
For one long instant, Verice feared the worst. He caught the red heat on her cheeks, the confusion in her eyes as she dropped her gaze.
Pain sliced through his chest. He was in mid-stride, or else he'd stop where he was, not really wanting to face her.
He caught his breath when she looked up again, her eyes back on his. Was the barest trace of an embarrassed smile on her lips, a light of welcome in her eyes?
He kept walking toward her, half-afraid to hope.
Chapter Thirty-Two
The crowd of human women silenced as he approached and then all curtseyed, their faces solemn. There wasn't a sense of happiness about them, not exactly. More a sense of contentment. Or satisfaction.
"Ladies." His voice sounded rough even to his ears. "Warna, I'd speak with you, if you've a moment."
Her blush was pink now, but the smallest of smiles was definitely in her gaze. "Of course, m'lord." She stepped out of the shelter of the gathering and walked toward him. The women returned to their work, although Verice could feel their eyes upon him.
Warna approached him, the heat still on her cheeks. He turned slightly away, standing close, hoping to shield her from prying looks. He lowered his voice, "Warna, I—"
She reached out a hand, and touched his arm. He felt the heat of her fingers through the cloth. "For all my training," she said softly, "I've no idea of the deportment required for this situation."
Verice huffed out a breath, feeling his tension ease. "I confess that Elven Court etiquette offers no suggestions either."
Warna chuckled and nodded, her head down. "So, I resolved to apologize for my inappropriate intrusion into your chambers. Except that..."
Her brown eyes darted to his, then she lowered her gaze to stare at the cleaning rags in her hands. Her lashes were dark against her skin.
Verice stepped closer. "Except that?
Her voice was the faintest whisper. "I don't regret the—"
"Excuse me, Lord Verice, but—" One of the merchants was approaching.
Verice lifted his head, throwing the man a long look.
The man blinked and retreated. "Your pardon, m'lord," was all he managed to stutter out.
"M'lord," Warna chided softly. She was standing so close, he could smell her hair.
Verice cleared his throat. "I will confess to you that I was going to ask forgiveness for my unconscionable actions, and beg your pardon," he murmured. "But I will return your honesty with my own. I've no real regrets. Except that..."
"M'lady, do you wish us to start on the next—" One of the women approached from behind. Warna shot her a glare that practically scorched the woman where she stood.
"M'lady," Verice chuffed at Warna as the woman fled.
"Except that?" Warna prompted him, her own eyebrow raised.
"Except that we stopped," he whispered.
She flushed again, but her lips curved upwards, lifting his heart with them.
"M'lord," Ricard said from a distance off.
Verice turned on him, at the same time Warna lifted her head. But the man was impervious to their glares. "There's a need," he said simply.
"We need to discuss this," Verice lowered his head to Warna's ear. "But I fear..."
She leaned in toward him, humming her agreement. "We've duties, m'lord,"
"True enough, m'lady," Verice stood for a moment more, sighed and stepped back. "Dinner, then?"
Warna's eyes were bright, filled with anticipation. "Dinner would be—"
Horns sounded from the walls, calling an alert, warning of assault from above.
Verice snapped his head up, scanning the sky. Two mounted creatures spiraled above. "Warna, get the humans into the—" He paused, frowning, and lifted a hand to shade his eyes as he studied the two figures. "Ancestors, there must be a new man on horn duty. That's—"
The horns sounded again, with an 'All's well'.
"What are they?" Warna asked.
"More like a who," Verice said, frowning. "It's Wolfe and Kalynn."
Warna caught her breath as the creatures from that lovely tapestry spiraled down, beautiful wings spread wide to slow their descent into the courtyard. They gracefully settled to the ground, folding their wings to allow their riders to unbuckle and dismount.
A streak of mottled colors jumped down from the pack on one animal's back and ran for the stables. Warna was fairly sure it was the cat.
Verice started in their direction, but Warna hesitated. Every eye in the courtyard was fixed on the two new arrivals, but there was little welcome there. All work had stopped as Wolfe and Kalynn dismounted and greeted Verice. The bustle of activity had been replaced with an odd stillness, wariness, and fear.
The women behind her had gathered at the door of the barracks, and the children were being hustled inside. The fear in their faces was obvious. As much as Warna would like to see the airons up close, she felt a need to respond to that fear. She walked back, trying to catch their eyes and offer reassurance. "There's nothing to fear. Just friends of the High Baron's come for a visit."
That got her stares of mingling disbelief and exasperation. "Lady," one of the eldest said. "That is the ChaosReaver."
"It's said he tears out the living hearts of his enemies," another whispered.
"No," Warna shook her head, thinking of the cluttered stairs of the Tower and Wolfe's smile. "He's—"
She heard footsteps behind her, and all the woman's eyes went wide. Warna glanced back to find the trio advancing on her.
"What is this?" Kalynn's voice was like a knife as her glare raked over Warna's cloths and the rags in her hand.
"Kalynn," Warna started her greeting, but froze as Kalynn spun on her heel, and confronted Verice.
"You were to care for her, claimed she was under your protection," Kalynn snarled. "And yet what do I find?" Fast as lightning, her hand rose, and she slapped Verice. "Humans are not slaves!"
Chapter Thirty-Three
Warna gaped at Kalynn, conscious all the while of the gathering audience. She glanced at Verice and Wolfe.
Wolfe snorted and rolled his eyes. "And people think I have a temper."
Verice stood there like a stone.
"Caged, dressed in rags, scrubbing out barracks," Kalynn's outraged voice was low and controlled but somehow managed to bounce off every wall and into waiting ears. "I took you at your word." Kalynn's glare was aimed directly at Verice. "You told me you'd offered her protection. I should have known that your own biases would—"
Warna couldn't believe that Verice was just standing there, his face grim and rigid, his cheek red where Kalynn had slapped him. Frustratingly silent, offering no defense as the seer spewed her anger.
"Kalynn." Warna grabbed her arm, and pulled her around. "Kalynn, you're wrong." Warna met her glare for glare. "You know nothing about what's going on here, and you are making something—"
"Really?" Kalynn folded her arms over her chest. "Where did you sleep last night? Beside some hearth?"
Warna flushed and just managed not to look at Verice.
"Ha," Kalynn exclaimed, taking Warna's silence as some sort of affirmation.
Warna straightened, lifting her chin. "Seer Kalynn, you are wrong. All who stand here with me know that. Lord High Baron Verice has offered us shelter, safety and the utmost courtesy. Something which you lack, Seer."
That shut her up. If Warna had slapped her, Kalynn could not have looked more shocked.
"This land is at war," Warna continued. "And we," she put emphasis on the word. "are working to restore, preserve and thrive in Tassinic. Did you expect to find me in ruffled silks and fine linens?"
"No," Kalynn shook her head. "Not that. But—"
"There was an attack," Warna pointed out, ignoring Kalynn's protest. "We've people to house and feed, and little daylight left. Your visit is unfortunate, for we cannot offer you hospitality at this time. If you wish to speak to Lord High Baron Verice, please to keep it quick. There's work to be done."
"Warna," Kalynn's tone was apologetic but Warna was in no mood to hear it.
"Offer your apologies to Verice," Warna snapped. "That's where they're owed." She turned on her heel, and stomped back to the third barracks, where the woman huddled, with fear on awe on their faces. "Ladies." She tried to keep the anger out of her voice. "Let's be about it, shall we?" She walked through their midst, and right through the door, her stomach in knots.
It wasn't until she'd set every able body to work, wasn't until she was on her hands and knees, scrubbing a non-existent spot on the floor, that she was willing to face the real reason she still felt sick.
"Warna, get the humans into the—"
Verice stood silent, his cheek burning from Kalynn's blow.
"Verice." Kalynn reached out to him, her hand hovering over his cheek. "Verice, I am sorry. I thought that...it looked like..." She sighed, and dropped her hand. "I fear that I overreacted."
"Really?" Wolfe said.
Kalynn glanced at him in irritation. "Verice, I am sorry. I apologize for—"
Verice lifted a hand. "While you may have misread the situation, there is still a truth to your words. A hard truth perhaps, but true nonetheless. Warna is correct, however. We had a village burnt to the ground by the Usurper's forces, and I—" Verice rubbed his cheek. "I have much to do. It would be best to have your say, and depart quickly."
"I'm sorry, lad," Wolfe said. "Kalynn and I will be traveling for a time, and I wanted you to know that we were leaving. Charrin is at Valltera, at the Royal Court, and I've secured the Tower, no worries there. You have the cat." There was a trace of malicious satisfaction in his voice. "It will be some time before we're back in touch."
"It's been years since you've left your home," Verice said. "How long will you be gone?"
"Months," Wolfe shrugged. "Maybe longer."
"That long?" Verice raised an eyebrow.
"I have seen," Kalynn said softly. "There's a task needs doing."
"And we must pursue it," Wolfe said. "The places we must go, we can't use any portals."
Verice gave his mentor and friend a long, steady look. "What aren't you telling me?"
Wolfe quirked his mouth. "So much, lad. So very much."
Kalynn looked over her shoulder at the barracks. "I'm going to speak to Warna," she said
and started off in that direction.
"How bad was the attack?" Wolfe asked.
"Bad enough," Verice said wearily. Yet another failure to place at his door.
"Will you retaliate?" Wolfe's voice was soft but his eyes were sharp.
"No," Verice said grimly. "We pursued them to my borders, and then stopped. I can't hope to take on the Usurper's army and win."
Wolfe pursed his lips and nodded.
Verice looked at the wiry old man, "But you could."
Chapter Thirty-Four
Wolfe stiffened.
"You could end this," Verice said in a low, urgent voice, not afraid to plead.
Wolfe gave him a quiet steady look. "You think so?"
"I know so," Verice said. "With your powers, you could portal in, kill the Usurper, and portal out."
"Perhaps." Wolfe looked after Kalynn. "After all, I did it once before, did I not? Why shouldn't I do it again? Blaze a bright trail of destruction from your door to his as the Chaosreaver once more stalks the land."
Shame flooded through Verice and he suddenly felt like the apprentice he'd been so many centuries ago. "Master, I—"
"Except that the last time I took such an action, the repercussions were far worse than the evil I thought to end. Innocents paid the price for my arrogance." Wolfe looked at him and the laughter in his bright blue eyes was gone. "Still pay the price, from what little I know."
"Forgive me, Master." Verice lowered his head.
"Answer me this, Apprentice," Wolfe's voice was a lash. "If the Usurper is struck down, who will fill the power void? Who will claim the Throne of Palins?"
"I don't know. One of the High Barons, perhaps."
"You?"
"No, Master." Verice shook his head.
"And if I don't like what actions the new sovereign takes?" Wolfe asked, still standing stiff, radiating anger. "Where does it end, Verice?"
"I do not know, Master," Verice said, his anger cooling.
"I've no time to enter ethical debates with you," Wolfe growled. "Kalynn has seen. We are needed elsewhere."
Verice closed his eyes.
"You are under duress," Wolfe took in a deep breath. "Or you would never have asked this of me."
"True enough," Verice said, glancing to where Warna had disappeared into the building.
Wolfe followed his glance and snorted. "But that's not all that has your head and heart in chaos."
Verice stiffened.
"Please," Wolfe rolled his eyes. "I don't have to be a Seer to see, Verice."
"You are not my master in this," Verice said sharply.
"As if I am going to give you advice about women," Wolfe barked out a sharp laugh. "But it's best for all concerned if you face the truth of it now. Before it goes much further."
Kalynn found Warna inside, on her hands and knees, scrubbing at one of the hearths. "Warna," she started, regretting her outburst. "I'm so sorry."
"Did you apologize to Verice?" Warna asked tiredly without looking up from her task.
"I did," Kalynn glanced around, but none of the other women were in earshot.
Warna sat back on her heels, and stared up at her, eyes filled with pain and questions. "Why would you even think that of him?"
Kalynn knelt down to look her in the eye. "I am sorry. I have never had reason to think that Verice holds humans in contempt, or treats them as slaves. I saw you at work, and it brought back—" she cut off her words as sorrow rose up in her chest.
Warna waited.
"Memories," Kalynn forced out. "Of a time long past." She swallowed hard.
"And how does Verice normally treat humans?" Warna asked, her brown eyes intent and serious.
"Like delicate flowers," Kalynn said, forcing a smile. "That bloom and fade, and bloom again, if tended well."
Warna looked at her hands, at the rags and the soap and the floor. She snorted out a weak laugh. "Little he knows," she said.
"He's never been around them enough to know better." Kalynn rose. "I regret this, Warna. We've a journey to make, and I'd only wished to say goodbye. Wolfe and I will be away for some time. I do not wish to be parted from you on this note."
"As if I've never regretted a hasty action or a harsh word." Warna stood, dried her hands on her skirt, and pulled Kalynn into a hug. "Safe travels, Kalynn. May the Lord of Light and the Lady of Laughter both be with you."
Kalynn hugged Warna back. "And the skies be with you, Warna."
Warna watched Kalynn go and returned to her scrubbing. As much as she'd like to see Wolfe and Kalynn take wing on the backs of their airons, she'd no wish to speak to Verice just yet.
She had some thinking to do.
The chatter and clatter of the other women was both familiar and strange. How many months had it been since she'd worked with her mother, talking as they'd sorted silks and spices? The familiarity of it made her heart ache for her family and home. The strangeness reminded her that there was a world outside the walls of the castle. A normal world, filled with regular truths. Where something so extraordinary as an elven Lord High Baron caring for a simple human woman was not to be considered. Not even to be contemplated.
"Warna, get the humans into the—"
She paused in her scrubbing, listening to his words in her head. He hadn't said 'get them to safety' or 'get the women to safety'...
"...get the humans..."
Warna knelt back on her heels, staring at the stain without seeing it.
Verice had stirred when she'd left the bed, as she'd slipped out from under the blankets. He'd reached out, searching, turning his head toward her. She'd whispered reassurances, and he'd settled back to sleep, never fully waking.
Her lips tingled at the memory of his kiss.
But that was part of the illusion he'd wrought, wasn't it? Verice had isolated the castle from the world, cutting himself off from friend and foe alike in the guise of safety. Cutting her off from what was normal, sane, and true.
The irony being, of course, that she'd set herself the task of pulling him back, of setting the castle to rights. And now it felt like the mundane, the normal routine was returning, only to expose the nature of her folly.
"It's as clean as it's likely to get, to my way of thinking." One of the older women was peering over her shoulder at the stain.
"I'm thinking you're right," Warna sighed.
"They've brought round soup, and kav, and sticky buns for the little ones," the woman said. "The work will wait."
"Thank you." Warna got to her feet. "I'm sorry, I can't remember your name...?"
"Lottie," the woman offered.
"Lottie," Warna dropped her rags in the bucket, tired of thinking. "You're right. Let's see to that kav."
Chapter Thirty-Five
The women had gathered round the tables, ladling bowls of soup to the children, who eyed the waiting treats in the baskets of sweet rolls. Warna saved a bowl about to spill from tiny fingers. She smiled at the little girl who stared at her with big eyes.
"What's your name?" Warna asked.
"Lily," the blonde girl whispered.
"Let me help you," Warna whispered back, sitting on a bench and pulling the girl into her lap.
She sat in their midst, and listened to the talk as the children ate. There was no discussion of their plight, not with little ears listening. The women focused on the food, making sure that the soup was actually eaten before handing out the sweets.
Lily managed the entire bowl, and half the bun before she was full. Warna smiled, hugging the child close. "Done?"
The tiny one nodded, her blonde curls falling in her eyes.
"Then outside with you," one of the women said. Warna opened her arms, and Lily slid from her lap to run through the door. Around her, the women were herding the children outside to play.
"We'll have a bit of peace with our own meal," Lottie ladled out another bowl of soup. Warna took it and gave Lottie a grateful nod of thanks.
There was a clatter of heavy boots in the outer hallway. "Is that our men?" Lottie asked, looking toward the door, ladle poised over a bowl.
"It is," An older man stepped in, and greeted her with a kiss. "Is there enough for us?"
"Oh yes," Lottie said. "We've been well provided for."
"That's good," He settled in at the table as others followed him into the room.
"The children are all playing," Lottie said. "No better time for news. What says the Lord High Baron?"
"You're the Lady Warna?" The older man focused on her as he settled on the bench opposite.
Warna nodded. Around them, the other men began talking to their womenfolk, taking up bowls of soup and settling at the tables.
"Well enough," he said. "I am Mayth."
"What news?" Lottie said sharply, placing soup and kav before him.
"Can't I get a bit of food first?" He grumbled, then reached up to stroke Lottie's cheek. "Patience, wife. The Lord High Baron sat with us a good long while, and we talked options. We've decisions to make, true enough, and we'll do that tonight, with all of us gathered."
"Options?" Lottie settled next to him.
"Aye," Mayth sighed. "He'll aid us if we wish to rebuild, but none of us are sure that's wise. He's offered to see us relocated, but that brings its own pain. In the meantime, he's offered shelter here, and time for us to decide."
Lottie let out a breath, and closed her eyes in weariness. "Mayth," her voice was just a whisper of pain.
"I know, sweetling," Mayth leaned over, and put an arm over her shoulder. "Eat something with me, eh? Put the heart back in you."
Lottie nodded against his shoulder, then straightened her back. "Only if you do the same." She nudged his elbow.
Mayth picked up his bowl.
"If Lord Verice made that suggestion he did so with your best interests at heart," Warna said quietly.
Mayth shrugged. "Still bitter on the ear, to hear that you must leave the village and land you were born to."
"Change always is," Warna said with a sigh. "But I'd think he'd only say that if it was true."
Warna excused herself to fetch more bread and kav, and returned, settling herself down to face them both. She placed the bread before them, and poured kav, giving them a moment to eat. "What's it like?" she said casually, taking some of the bread. "Living among the elves?"
Mayth raised an eyebrow at her.
"Warna's of Farentell," Lottie said. "She wouldn't know."
"Ah," Mayth grimaced. "You are one of the few that escaped, then." He took up bread, and reached for butter. "They say you're the Lord High Baron's ward. Under his protection."
Warna nodded, wondering what else had been said. But that wasn't what she wanted to know. "I'm told he treats humans differently,"
"I don't know who you've been talking to, but that is not true." Mayth looked her in the eye, serious and intent. "I've lived in Tassinic, in Birch Cove all of my life, as has my father and his father before him. Lord High Baron Verice is equal handed to all, no matter the point of the ear or the slant of an eye. No man can complain of less than fair dealing at his hands."
Warna's shoulders eased, and she let out a slow breath.
"But if she's staying, building a life here," Lottie spoke up softly. "Then there's a truth she needs knowing."
Mayth said nothing for a long moment, concentrating on his food.
"In Tassinic, we have a saying," Lottie said softly. "The ears have it."
Mayth snorted in agreement. "Aye, there's that."
"The ears?" Warna asked.
"Say you're in the market, and there's two stalls of bread side by side, one baker a human, the other of elven blood," Mayth said. "No difference in the bread, mind, or the quality of the baking. But in Tassinic, the honest truth is that the one with the ears will be thought of as better." He shrugged. "It's not deliberate, if you know what I mean. But elves, the pure ones, mind, they're such perfectionists, that everyone just assumes they'll be better. Whether or not they actually are."
"If you have lace woven by an elven blood and lace woven by a human, even if the human one is finer by far, the elven one will always be better," Lottie said. "And they always buy the elven-blood one, every time."
"Didn't I just say that?" Mayth asked.
"But that's not right," Warna said.
"It's wrong, certainly, but it's so common no one even sees what they do as wrong or offensive, you know?" Mayth shrugged. "Even humans will do the same and not think twice."
"How do you cope? Warna asked.
"Well, most have elven in the family, you know, and then there's some that hire elves to sell their wares, or work the booth. Some shrug and carry on." Mayth sighed. "We'd more trade with the human baronies than Tassinic, truth be told. That's one of the reasons rebuilding will be hard. There's no trade with those bandits roaming the lands."
The sound of other voices made them all lift their heads. The constable stood at the door, scanning the room and Warna raised her hand to call him over.
"M'lady," Ricard gave her a nod from the doorway. "A moment, if I may."
"Of course," Warna rose, ignoring the speculation in Lottie and Mayth's eyes. She threaded her way past the tables to walk with him to the door. "Is something wrong?"
Chapter Thirty-Six
Ricard looked flustered and strained. "Nay, naught beyond concerns for these people." he said. "Will these barracks be ready for them?"
"Yes," Warna said. "There shouldn't be a problem."
"Then they'll need bedding and blankets, and other such things." Ricard looked over the room. "Safe to assume they have nothing and start there."
"Constable," Warna started, but the poor mael cut her off, airing his frustrations.
"The bakery and buttery have started their ovens, and the cooks have started bickering over things I cannot fathom." Ricard was scowling. "Lord Verice is dealing with the scouts and reports from the border, but has left provisioning to me to deal with. Wasn't bad when it was just the lads and I, but now the castle is opened up again and I—"
"Not the keep," Warna gave him a worried glance. "We promised—"
"No, no," Ricard sighed. "Not that. But—"
"I'll see to the cooks and bakers." Warna wrinkled her nose. "And the needs of these people. Is Ersal here?"
"Aye, he's waiting with petitions for Lord Verice," Ricard said.
"The petitions will have to wait," Warna said. "Send him to me and we'll start in."
"My thanks," Ricard's relief was obvious. "Lord Verice said to tell you that he regrets that he may not be available for dinner."
A stab of disappointment went through her. "Understandable," she said.
"He's ordered that you're to sleep in the Healers Hall this night." Ricard frowned at her. "Ordered Priest Dominic to clear out that top bedroom for you. I'm to see to it that your things are moved back."
Warna nodded her thanks, but Ricard's frown deepened as he continued. "I didn't know you were squeezed out."
"My idea," Warna said shortly. "The wounded come first." Suddenly irritable with all of them, she frowned right back at him. "If there's nothing else...?"
Ricard paused, then glanced around the dining hall. "Is there a problem, lady?" he asked carefully. "Did someone say something? Or offer insult?"
"No," Warna said. "Nothing like that," she gave him a frustrated look. "But there's much to be done, Constable."
"Aye to that," he said. "I'll send Ersal to you."
Warna returned to Lottie and Mayth. "Lord Verice wants to see you all settled here as soon as possible."
"It won't take long to finish the cleaning," Lottie said.
"I'm off to see to bedding and whatever else you need," Warna said. "Soap, towels—"
"Swaddling cloths," Lottie said. "Oh, and-" she lowered her voice. "Moonpads."
"Of course," Warna sighed.
Verice sat in his outer chamber, confronting a sea of maps and scouting reports.
The tale they told was incomplete, jumbled, and set his teeth on edge. There was none with Narthing's gift for organizing information, and as such he'd a need to hear all the information directly.
"Is it the vanguard of a larger attack?" He asked the warriors clustered around.
Which brought out new maps, counters and another round of discussion. Because the information they had was uncertain and vague at best. Forces spotted here, camps spotted there, movement of troops in the distance. New scouts sent to re-check what others had seen. Discussions of the scrying that had been done, and the limited information it had produced.
Through it all, through the talk and the maps and the waiting, in the moments between, all he could think of were Wolfe's words about Warna.
"—face the truth of it now. Before it goes much further."
What was he thinking? Wolfe was right. For all that Warna was, well, Warna, she was still human.
It wasn't that he disliked humans. King Everard had been a good man for all that he wasn't of elven blood. Verice had friends that were human, although he didn't go out of his way to cultivate such friendships. Humans came and went with the seasons, never making a lasting impression on him, truth be told.
But Warna had.
Verice frowned at the map in front of him, without seeing it, his mind filled with images of brown eyes and—
"M'lord?" The man who'd placed it before him hesitated.
Verice shook his head to clear his thoughts. "Continue, please."
So, the afternoon wore on. By mid-day, his warriors were positioned, his strategy for the next few days set.
Verice was then free to talk with the people of Birch Cove and listen to their desire to rebuild. Which might indeed be best in the short run, but in the long view the value of that path was doubtful. Their trade with Farentell was gone, and who knew how long it would be before the trade routes with Summerford would be restored. The wiser course could be to rebuild in a new location, farther away from the border, closer to the river that would widen their markets and access to trade routes.
But he could see in their stubborn round faces a determination to argue, and he mentally sighed in frustration. After talking and asking them to consider well the decision, he sent them off for a mid-day meal and gave the constable his orders. Only then did he seek a few quiet moments with his own bowl of soup and bread, alone in his chambers.
It wasn't fair to toy with Warna's heart and life. As short lived as humans were, she deserved more than that. The honorable action would be to pull back gently, so as not to hurt her. Remembering the look in her eyes, the taste of her mouth, a pang of regret arced through his chest, but Verice shook his head at his own stupidity.
Unfair to her, heartbreak for him. It had to be done.
He returned to his tasks, after reassurance from the constable that his message had been delivered. The men of Birch Cove gathered once again and Verice was surprised to find that they seemed more open to the idea of resettling. The maps returned, but this time with a sense of hope in the future.
Then the scouts reported with fresh news and more information and once again his chambers rang with the going and comings of his warriors, all bearing reports. He listened carefully to their words, watching their hands on the maps, pointing out where and what they'd seen.
"So, no massing of troops. A probe perhaps, but one with no real force behind it."
Nods all around.
He stood, satisfied. "Then we've done what we can for now, to see the border secure. Seek your beds, all of you, with my thanks."
They filed out, and he stretched his back, tired. It had gone well enough, given Narthing's absence. He missed having the man at his side. There'd been no word all day as to his injuries, but Verice was inclined to think that no news was good news. But he'd see the man himself before he sought his bed.
Which brought him up short. He'd have to talk to Warna tonight as well. He couldn't let that issue linger any longer. It would be painful enough as it was.
The night sky was clear as he stepped out into the courtyard; it was later than he'd thought. A few steps brought him to the door of the Healers Hall; a quick question told him where Narthing was to be found. But first he went among the wounded, going from bed to bed, taking the time to ask after them and listen to their responses.
Finally, he came to Narthing's door, and after a light tap, he entered the room. "How goes it, my friend?"
Narthing's pale face lit in a smile.
Warna was sitting at his bedside.
Chapter Thirty-Seven
"Narthing," Verice moved into the room, conscious of Warna's gaze. He took a chair from the far wall and moved it to the bedside. The sharp scents of medicines and mixtures tickled his nose. "How do you fare?"
"Well enough." Narthing's voice was breathy and thin.
"Pain?" Verice frowned.
"Some," Narthing said slowly. "When I take too deep a breath. As long as I move slowly, and don't laugh, it's tolerable."
"They haven't dosed you?" Verice asked.
Narthing shook his head, but Warna answered. "He wouldn't take it," she said quietly. "He put them off, told them he wanted to talk to you."
"Wanted to know," Narthing put his hand over his wound, as if to brace it. "You've reports, Lord?"
"Ah," Verice nodded his understanding. "Then lay there and listen, Captain."
Verice summarized what he knew briefly, but with enough detail that Narthing seemed satisfied.
"So, if it was a probe, it wasn't a serious effort," Narthing breathed out. "That's good. Better than I'd hoped." He let his head sink into the pillow, staring at the ceiling for a moment.
Verice waited, watching his face, letting Narthing mull over the information. "But what of Birch Cove?" Narthing finally asked, his eyes narrowing.
"The town's a loss," Verice said. "I'm sending warriors with the menfolk to see what can be retrieved of personal belongings, and to round up what they can of the livestock."
Narthing gave the slightest shake of his head. "That river ford—" he said and then winced.
"We think alike," Verice said. "I talked to them about building there. They seem amenable to the idea."
Narthing cast him a doubtful look. "Really? Humans can be stubborn, m'lord." He blinked owlishly at Warna. "No offense," he said.
"I'm fetching that healer," Warna said. "It's past time you slept." She slipped out the door.
"You must have a care," Verice said. "That was a mean slice you took."
"No fear," Narthing said. "Dominic stood here and told me all the complications I risk unless I follow orders. His description of a bowel rupture was graphic enough that I fear to cough, much less anything else."
Warna returned with healers in tow, who gently shooed them both out of the room. "He needs his rest, m'lord." The one said as she closed the door in Verice's face.
Warna was on the stairs, leading up to the room tucked under the eaves. It seemed his orders had been carried out then. She had a place to sleep.
She paused, and turned to look at him, her face closed and warded. "Goodnight, m'lord."
"Warna," he said firmly.
She paused on the stairs, one hand on the railing. There was the slightest trembling in her fingers as they rested on the wood.
"We should talk," Verice said softly. "Walk with me. In the gardens."
The night air was cool on Warna's flushed cheeks, a slight breeze played with her hair as Verice lead her out of the Healing Hall. The dogs gathered around them, tails slowly wagging as they walked.
The courtyard had emptied of all but the watch and a few souls. Light spilled from the buildings around them, which thrummed with life. As tired as she was, as confused as she was about the man next to her, Warna smiled at the visible proof of her labors.
Except for the keep, of course. It lay at the center, dark, still, and daunting.
Much like its Lord High Baron.
"All are settled, it would seem," Verice said quietly, standing next to her.
"Yes," Warna said, just as softly.
"And you've your room back," Verice said.
"Yes, but only for tonight," Warna said. "Dominic was called to Church duties, and he will return tomorrow. I'll need to find another place." Verice scowled, and opened his mouth to speak, but she hurried on. "It's only right that he be with his patients. It's not as if he will sleep on a cot in the dining hall."
"But where will you—" Verice cut off his own words.
Warna glanced away, not willing to look at him.
Verice cleared his throat. "This way," he said softly as the dogs rose to join them.
"I didn't know there were gardens here," Warna said, wincing as it sounded more like an accusation than a question.
"The moat between the inner and outer castle walls was foul and disgusting when I arrived," Verice's face was mostly in shadow, but she could hear the pride in his words. "They were using it for all matter of waste and garbage. The reek was thick. So, I ordered it drained."
"The area between the outer and inner walls?" Warna blinked, frowning as she thought back to the ride through the gates. That area had been big. Really big. "How long did that take?"
"Not long," Verice said absently as he led her around the Healing Hall, to a heavy wooden door set into the wall. "Four, maybe five years."
"Five...years?" Warna said.
"Ten more after that to really get the soil ready, and get the plantings established." Verice chuckled softly. "There was some protest from the warriors, about the need for a moat for protection. But I planted rantha bushes and that put an end to the protests."
"Rantha?" Warna asked.
"Take twenty years to mature," Verice explained. "But well worth it. The flowers are sweet smelling but the vines are thick with thorns that are wicked sharp and as long as a man's hand."
Thirty years? Warna added it up in her head. Thirty years to plan such a thing, and Verice thought nothing of it?
Between the Healing Hall and the next building was a small, heavy wooden door, barred and locked. Verice removed the bar, and began to free the various latches. The dogs milled around their legs, tails wagging.
"This area is more the herbs and medicinal plants," Verice said as the door swung open. Warna peered inside. There was just enough light to see a path, and a garden stretched out beyond. The breeze touched her face, carrying the sweet scents of flowers and herbs.
"After you," Verice gestured.
Warna stepped forward, through the door—
And smacked into an invisible barrier.
Chapter Thirty-Eight
Verice froze, not understanding for a heartbeat, then understanding all too well. The warding. He had released it temporarily when they'd left for Wolfe's Tower, but he hadn't taken it down.
Warna stepped back, frowning, staring at the doorway. Before he could move, she reached out, her fingers stopped by the invisible resistance.
Sand and Gray slipped past her and into the gardens, their nails clicking on the stones. Gray returned, coming back to Warna, whining in his throat as if he sensed something was wrong.
"I," Verice's stomach sank. "For your own protection, I—"
"That's what Kalynn was talking about, wasn't it?" Warna's expression was guarded, her eyes shuttered. "When she said 'caged'?"
"Warna—" Verice wasn't even sure what he could say, how he could tell her—
"Lord Verice, perhaps we could discuss this later." Warna took a step back from the door, her gaze cast down, the perfect image of proper deference, but with an edge to her voice. "The day has been a long one, for both of us."
"Warna." He couldn't leave it like this, couldn't let her go without trying to explain. Yet, what really could he say?
"Good night, m'lord." Warna turned away.
"I'm sorry," Verice said. For so much. For leading you on, for the pain I've caused you. But he kept those words in his heart.
She paused but didn't look at him. "I'm sure you acted as you saw fit, m'lord."
He watched as she walked away, followed by Sand and Gray.
Brindle whined and pushed his head against his leg. Verice reached down to stroke her ears. He whistled the rest of the pack to his side, and then, with an odd sense of relief, regret, and utter defeat, he swung the door shut and dropped the bar into place.
"It's been days since they've shared a meal?" Narthing asked.
Those clustered around his bed all nodded glumly.
Narthing sighed.
They'd all gathered in his room at mid-day, supposedly to share a meal and keep Narthing informed as to events.
Honestly, what he wanted to hear was the gossip.
"They've not eaten together, they've barely spoken," Ersal said, staring at the chicken leg in his hand. "And when they do speak it's of laundry supplies and cooking oil."
"And painful to watch," Janella added, poking at her own plate. "As if each is afraid of pricking the other if they get too close."
"What happened?" Narthing asked. The healers still had him on a soft diet, and he eyed Ersal's chicken leg with longing, then picked up his mug of broth.
"Don't know," Ricard sighed. "They went for a walk the night the Chaosreaver appeared."
Narthing jerked, almost spilling his broth. A jolt of pain went through him at the movement.
"Narthing," Janella scolded.
"She came back alone," Ricard continued. "He followed after a while, looking morose. Well, more morose than normal."
"When was the Chaosreaver here?" Narthing demanded. His stomach clenched
against the tightness in his chest, and he set the broth back down.
That got him surprised looks all around. "The day after you were wounded," Ersal said. "Didn't the Lord mention it?"
"He did not." Narthing closed his eyes and breathed through the pain.
"You're hurting," Ersal said. "Let me fetch Dominic and—"
"He's gone to Edenrich for the day," Narthing said. "He's being considered for a position in the Church."
"Good riddance," the constable muttered.
"He's a skilled healer," Janella said.
"He's an arrogant prick," Ersal replied.
"And I'm to eat something before I can take more for the pain," Narthing said. "How long was he here? The Chaosreaver?"
"Never left the courtyard, and gone just that quickly." Ricard reassured him.
"Thank be to the Lord of Light," Narthing offered up a heartfelt prayer. "But why did he come?"
"Lord Verice didn't say," Ersal said.
Narthing sighed, and picked up his broth again. "There's nothing good at hand when that one roams the world."
"The seer was with him," Janella offered.
"That's no cause for comfort," Narthing managed a sip. The broth was warm and flavorful, but it was still just broth.
"Lord Verice must have done something, said something to her," Ersal said. "You should talk to him."
Janella rolled her eyes. "He didn't listen to any of us for months after the attack. Warna is here for what? A week? Ten days? And she's got things returning back to normal."
"Except for the keep," Ricard pointed out.
"Except for the keep," Janella agreed. "But it's only a matter of time."
"Do you think it was the humans? From the village that was destroyed?" Ersal asked. "Did they say something to upset her?"
"I don't know," Ricard shrugged. "But she seemed odd after she talked to them."
"Now she's humming sad songs under her breath," Janella said. "All the time."
"The Festival's in just a few weeks," Ersal said. "What are we going to do?"
"Nothing," Narthing said firmly.
"Nothing?" Janella stared at him. "But—"
"Lord Verice's relationship with Lady Warna is none of our concern," Narthing said, only to be cut off by Janella's glare.
"I think she'd be good for him," she declared, as others agreed.
"Even so," Narthing said. "That's between the two of them, and I can promise you that our meddling will not aid that process. There's nothing to do but wait and see. Something will give, one way or another. M'lord has enough on his shoulders without us raising this issue. Let them be." Narthing lifted his cup and gave them all a look as he finished his broth.
"Aye," came the chorus of reluctant agreement.
"But to my way of thinking," Ricard said. "We owe a debt to Lady Warna for all that she has done for us. If naught comes of this or them, we'll still see her safe."
The 'ayes' to that statement showed they were all in agreement.
Chapter Thirty-Nine
Thwack, Thwack.
Warna woke in the darkness of her room above the bakery, warm under her blankets, and blinked at the dawn just starting to spill through her window. Verice was back at weapons-practice again.
No. She couldn't call him that anymore. Lord High Baron Verice was back to his normal routine, now that matters had settled down. He'd rise early, eat, then take to the pells and practice grounds until the sun rose. He'd fallen back into his old habits, now that they
weren't...doing what they had been doing.
Whatever that was.
He'd done the same before she'd arrived, and likely be the same after she left.
But now she could also hear the workers in the bakery below and smell the faint scent of kav in the air. The castle's Lord may have fallen back into old ways out of frustration, but the castle was returning to its old routine with intent. Warna smiled into her pillow wearily. At least in that aspect she'd done well.
Thwack, Thwack.
She stretched, then curled onto her side, hugged her pillow, and closed her eyes. If she lingered until he was done, he'd be gone before she finished her morning kav.
But the noises continued, and in her mind's eye she could see him, wielding his sword, face so focused and intent...which was not conducive to sleep.
Warmth flooded through her, and she shifted in the bed, trying to still the ache in her chest. Damn the mael. Damn his kiss, for awakening something in her that she put aside as lost to her. Something she didn't want to have to think about. For all that she had tried to avoid Verice - Lord High Baron Verice - it was impossible not to be conscious of his every move, every action. Even if she didn't see him, she heard of him from the people around her.
Thwack, Thwack.
Warna rolled over and buried her head in the pillows. Her emotions churned. Angry, hurt, bewildered, she wasn't sure what she was feeling.
At least, Verice - Warna gritted her teeth - Lord Verice had named a new Seneschal. Ersal was very nervous, but determined to do well. He'd come to her at once, asking questions and she'd aided him in the organizing of the castle's needs. They'd been going over the lists of supplies when Mayth had come to ask if she'd wish to settle with the humans of Birch Cove. Ersal's eyes had gone wide. "But she's not yet done here," he'd blurted out. "The keep...the Festival..."
Before Warna could say a word, Mayth had nodded his agreement. "But after," he said. "Just something to think on. We'd be glad to have you."
Ersal had opened his mouth, then closed it with a snap.
It was all well and good for everyone to look to her to continue, but no one was much help with the 'how'. And now that she and...Lord Verice were no longer...well, whatever they had been, they weren't it now.
Confusingly, that hurt. She flipped her pillow again, and punched it with her fist.
She didn't have any real idea of how she was to open the keep. Return the castle to working order.
Warna reached out and plucked at a bit of fuzz on the hem of the blanket, seeing again the Great Hall, with its shattered window, the stains on the floor, the spilled tables and broken dishes. Verice's face, as he stood within, holding out his hand to her. So much pain.
The silence from outside finally cut through her thoughts. Lord Verice would have started to summon his men, and would be opening the portal soon for his regular patrols.
Warna sighed, threw back the covers, and shivered in the cooler air. She'd promised to aid Ersal with his accounts; she'd best be about her day.
But that ache was still in her chest as she washed. An ache that had settled there as soon as she'd left Lord Verice standing at the garden door. An ache for something she'd lost, or something she was in the process of losing, if that made any sense. A wistful dream, a hope, a desire, slipping away like the mist in the full light of the sun.
Warna huffed at herself as she dried her face. Foolish thoughts.
At least this room at the top floor of the bakery had a few of the niceties. A privy of its own, and a large comfortable bed. Even a dressing table, with a mirror. Clouded with age, but still a mirror. And she'd acquired a few more clothes in the past few days. Dresses and tunics and skirts, underthings, and new shoes. All sturdy and well made. Although there'd been bright colors available, she'd stuck with muted grays, and browns. Both her parents had frowned on full formal mourning, but Warna hadn't the heart to wear the jeweled colors she'd been offered.
She'd combs now too, and hair pins, and a brush. Some cream for her face and hands. Moonpads, and by her reckoning she'd have a need for those soon. Little things, true enough, but it meant so much to have them in her small lidded-basket.
She dug out what she'd wear, and paused when she heard the crinkle of paper within. She couldn't help herself really. She pulled out the note and read it again, as she had done a thousand times since she'd received it.
Warna,
The barrier has been removed. You are free to move about as you will.
Verice
Short, succinct, to the point. But in his own hand. Warna carefully folded the note, and returned it to the trunk.
She settled herself at the dressing table, and started combing her hair, working the tangles out. The noises below were louder now, the scent of kav and bread stronger. She would see to Ersal, then talk with Janella about the keep. Perhaps she would have some ideas. It promised to be a full day, full of things that needed doing.
She started to pin up her hair, humming under her breath.
All it would take to open the keep would be one legitimate reason. Something that was a need, not a want. A meeting that needed a large space, or the visit of a dignitary. Warna frowned, pins in her mouth. Weren't there foodstuffs stored in the keep, in case of siege? Or the mice she'd seen. That might be reason enough. Mice led to rats, and that wasn't healthy. If they could use that to open just one door, Warna was certain the rest would flow naturally. The keep would be open to all, and her work here done.
What will it look like, she wondered, not for the first time. All lit up, with candles and mage lights, those colored windows all aglow, the shattered window restored to its glory. Verice seated in the high seat, herself at his side, a feast before them and friends all around. Laughing and dancing, with his arm around her waist, twirling about—
With a cold, sick feeling, Warna looked at her hair in the mirror and realized she was trying to cover the tops of her ears.
Her hands dropped to her lap, letting the pain wash through her. Tears came unbidden, and for long moments she didn't bother to wipe them from her face.
But after a time, she took a deep breath and removed the pins, letting her hair fall around her shoulders. She'd wear it loose today, tucked behind her ears.
Then she washed her face again, to remove the evidence of her tears.
"Narthing."
Narthing looked up from his breakfast tray, startled to see Lord Verice standing there, fully armed and armored, his face grim. The mael had just been out at the pells, Narthing had heard him. What had brought him to the Healing Hall this early? "M'lord?" he asked.
Verice crossed to his bedside. "Look at this."
Narthing took the open scroll, careful to keep it out of his porridge and frowned at the seal. "A message from Valltera?" he asked, working his way through the formal elven wording.
"Worse," Verice growled. "A politely worded summons from the Coeval. And see whose attendance is required?"
"Yourself, of course," Narthing hazarded the safe guess, then sucked in a breath as he read the words. "Lady Warna?"
Verice's face was grim. "I've sent messages out, summoning my most trusted political advisors. If you're up to it, I will see if Dominic will allow us to carry you to my chambers. If not, we will meet here to determine our response. This needs consideration." Verice turned to go.
"And Warna?" Narthing asked. "You'll summon her as well?"
Verice paused, his eyes hooded. "We'll see."
Chapter Forty
By mid-day, Warna was still wrestling with the accounts, determined to slay the beast, but Ersal was far more curious about the activities outside his office window.
"Well, something is certainly happening," Ersal said, gazing out toward the Healing Hall. "Portals opening and closing, and messengers coming and going all morning. What could it be about?"
"Ersal," Warna said, keeping her voice patient and kind. "These accounts will not balance themselves." Her head was down, her eyes focused on the figures on front of her, for all that she wanted to jump up and run to the window.
"Something's happening," Ersal said.
"Yes," Warna said. "Your accounts don't balance for the last three days and they need tending." She continued to compare the tiny numbers.
"But don't you want to know?" Ersal asked, crossing over to plant himself back on his stool.
"Yes, of course." Warna turned the page of the ledger. Of course she wanted to know why Lord Verice hadn't left this morning, and why his advisors were being summoned and escorted to Narthing's room. Lord of Light, the entire castle was abuzz with curiosity. "I am sure we'll be told what we need to know when we need to know it." She strived to sound aloof and above idle curiosity. "Now, is this entry accurate? Did you really order this many candles?"
He examined the lines she was pointing to. "That can't be right," Ersal scowled and started digging through the pile of documents at his side of the table.
"You're going to need help keeping this organized, Ersal." Warna said. "A clerk of your own, maybe two."
Ersal gave her a sharp look as he pulled forth the chandler's statement. "You won't be staying?" he asked. "I'd thought perhaps—"
"Here's the correct figure," Warna interrupted, not wanting to talk about her staying or going. "See?"
Ersal whooshed out a relieved breath. "I knew it couldn't be right—"
A cough had them both looking up, startled.
The constable stood in the doorway. "Lord Verice asks that you both attend him."
Narthing's room was crowded with people and chairs. Warna hesitated in the doorway, recognizing many faces in the crowd as Ersal pushed his way in. Even Dominic had managed to squeeze himself into the room.
From his bed, now moved into the corner, Narthing caught Warna's eye. "Here, Lady Warna," he said loudly, and gestured to a chair placed next to the headboard.
Heads turned to stare at her. Warna felt her cheek grow hot as people stood and shifted to allow her to pass. Warna threaded her way through with soft apologies. "Narthing, what's happening?" she asked urgently as she took her seat.
Narthing opened his mouth, but a sharp knocking silenced the room.
Verice stood in the center of one wall, and commanded everyone's attention. "Now that Seneschal Ersal and Lady Warna have joined us, let's review the situation."
Warna drew a breath. She hadn't been this close to him for some time. His face was set, hard as granite and yet he appeared tired to her eyes. Weary, even. She swallowed hard, and looked away.
"You've all had a chance to read the missive from King Barathiel of Valltera. We can all agree that the wording—"
"Warna has not," Narthing said firmly.
Verice seemed to catch himself, as if forcing himself to slow down.
"It would not be bad, to review what we know," Lord Mayor Pernard said mildly.
Verice nodded. "To summarize then. This morning, when I finished with the pells, a message from King Barathiel awaited me on my desk." He nodded to the parchment on Narthing's lap. "It contains a polite but strongly worded summons to attend upon his Majesty today 'to discuss the welfare of my person and Tassinic'." Verice's blue eyes drilled into hers. "The Lady Warna is also included in the summons."
"What?" Warna couldn't quite take that all in. "Me? But—"
Narthing had pushed the parchment into her lap, and she stared down to where he pointed. She could see her name clear as day in one of the lines of spidery, thin script.
"The document extends me the privilege of opening a portal to the Royal Household this noon, and implies that the visit will be a short one, given that it fails to mention servants or retainers." Verice grimaced. "Our worries stem more from what it doesn't say, than what it does."
"So, the question becomes," Narthing said. "do you accept this invitation?"
"Observations?" Verice said. "We've little time to debate, and no doubt that is by intent as well." He paused, then gave them all a rueful expression. "You've advised me well in the past. Give me the gift of your wisdom now."
Pernard rose from his chair. "M'lord, King Barathiel has not once contacted you since the troubles began within Palins, has he?"
"He has not," Verice confirmed.
Ersal gestured to Warna, and she passed him the invitation to read.
Pernard frowned. "Yet he has brought up troops to our border. Not of a strength that we would fear invasion, but enough to cause concern. I do not know what that portends, but I say do not go. Exchange messages, yes. Use scrying bowls, yes. But do not go."
An older woman rose, someone Warna didn't know. "And I would argue that point. We do not know the intent of this. King Barathiel has not been openly hostile and the borders remain open for trade and travel. They know that if Tassinic falls, they will have to deal with the Usurper, and they don't want that."
There were many nods at that.
"Still, I do not like this," Ersal next rose. "The summons is almost worded as if to a vassal, and you are not a vassal of the Elven King."
"True," Verice nodded. "I was released from my oaths and allegiance to Valltera before I swore fealty to Palins and Tassinic. King Barathiel has no claim on me."
"Yet still, he summons you," Ersal said. "Don't go, m'lord. Send another in your place. Plead illness, plead necessity, plead the coming Festival. Do not place yourself in his hands."
"Any excuse given must be legitimate," Dominic protested. "Lest they discover otherwise and take offense."
Verice raised an eyebrow. "I am not without my own abilities."
"True enough, m'lord," Dominic bowed his head. "But the Royal Court is quick to take offense at any violation of protocol or etiquette. Once there, you must dance to their tune or risk their wrath."
"Well I remember," Verice snorted. "My mother ever feared suffering the consequences of my actions."
That was met with chuckles and nods all around the room.
"It's not just you, m'lord," Narthing shifted in his bed. "All of Tassinic goes with you through that portal. Not to mention Lady Warna."
"Lady Warna is not going," Verice said.
Warna glanced at Verice, then at Narthing.
"M'lord, I hesitate to say this," one of the older maels spoke slowly. "But she is included in the invitation. Her presence will be expected and—"
"No," Verice said. He stood there, considering, his arms crossed over his chest. "Everything you've said to me is true, and I understand your concerns. What we need is information, and its better if it's exchanged face-to-face. King Barathiel can be difficult, but he is honorable. I have no reason to believe this is other than an exchange of information. I will go. Warna will remain here."
"Is that a command?" Warna asked.
"What?" Verice stopped, stunned. "Of course it's a command."
"Why?" Warna asked. "My name is on the invitation. Isn't it my choice?"
The room went silent.
Verice glared. "It's not safe."
"If it's not safe for me, how is it safe for you?" she countered. "And if I do not appear at your side, that could be offensive, correct?"
Heads nodded in agreement around the room, but Verice had a counter. "You've not the wardrobe to visit the Royal Court," he said.
"I'm in mourning," Warna replied. "Plain garments are expected."
"Which excuses her from any formal parities, and those intricate dances," Janella piped up from a corner.
"The fact that they've pulled a young woman from her home during a time of mourning will not be viewed favorably," Pernard said with a helpful tone.
"She does not know elven ways, or proper behavior," Verice snapped. "You'll cause more problems than—"
"Speak only in response," Warna threw his weaponsmaster's words back in his face. "Answer, but never ask. And never make the first move."
"That will serve," Narthing chuckled.
Verice shot him a glare. "She doesn't speak elvish." he said.
"Please," Dominic spoke up from his corner. "That's a simple spell for you, one that allows her to speak and understand. And a decision must be made quickly. My patient needs his rest."
"I'm fine," Narthing protested.
"Bowel ruptures," Dominic said.
Narthing sank back onto the pillows with a mutter.
"The decision is yours, of course m'lord," Warna said, standing and brushing off her dress. "And I will abide by your command. But this summons seems to me both threat and promise, to you and your people." Something fiercely protective rose in her chest for him and Tassinic. "If we both go, we may discover their intent easily. If I am not there, you may waste precious time dealing with the consequences."
She lifted her chin, and waited to see if she was pawn, possession, or person in his eyes.
Chapter Forty-One
Verice eyed her cooly for a long moment, but the determination in her lovely face just grew. When had he lost control over the situation? Over her?
She'd made her choice, and his heart swelled at the idea that she would put the interests of Tassinic over her own. But that pride also bore a tang of fear. Fear for her stepping into the unknown.
He shook his head in surrender, acknowledging the truth of her words. "Very well. We leave at noon."
Warna gave a sharp nod. "There's not much time then." She started to weave her way towards the door.
"For discussion?" Pernard asked.
"To look presentable," Warna retorted.
"Just be certain to be ready on time," Verice said.
She halted just at the door, and gave Verice a look, raking him from head to toe. "Look to your own self, m'lord."
With a flash of blonde hair, she was gone, running down the stairs, calling for some of the female healers to check and make sure the bathhouse was ready.
"You've been given your orders, m'lord," Narthing said with a wan smile.
"It would seem I have," Verice snorted softly as the others started to file from the room.
Dominic stood by the bed, eyeing his patient. "That took more out of you than you'd care to admit," he observed. "You'll sleep now." Narthing nodded weakly, submitting to Dominic's ministrations.
"I needed his advice," Verice said.
"The Royal Court of Valltera places high values on appearances, m'lord," Dominic said. "Appropriate attire and a certain level of grooming would be in your best interests. Think of it as armor for the coming battle, if you must."
"So, Warna is right?" Narthing asked.
"Not that I'd admit to," Dominic said.
Narthing laughed, then groaned, holding his stomach.
The women's bathhouse was ready, thankfully, and Warna plunged in, refusing all offers of oils and unguents, except for the plainest of creams for her face and hands. Black dress, with black shoes, and someone found a black cloak that fit her well. Her hair didn't need washing, and there was no time to dry it anyway, so she braided it tight and wound it up on her head, making certain this time that her ears were exposed. She'd not cover up what she was, not ever again.
There was a tingle of excitement deep in her stomach. Valltera, the palace of the Elven King and Queen. She read so many stories as a child, she couldn't help wondering if it would be like the tales.
It was only when the women were chattering around her and she was putting on the cloak that Lottie entered, hesitating at the door. "M'lady?"
"Lottie." Warna took her hands and drew her into the room filled with faellas. "I'm about to depart with Lord Verice, but is there something you need?"
"I know, we heard, Lady." Lottie had a bundle in her hands. "Mayth managed to pull some things from our home. I thought perhaps—" She lifted her hands, and a black lace veil spilled from the bundle, with a pattern of roses woven within.
"Lottie," Warna breathed as the others ooh'd and ah'd. "You made this?"
"Aye. There's no scent of smoke on it," Lottie assured her. "I thought perhaps...given that you're dressed in mourning..."
"It's perfect. Thank you," Warna took the soft veil from her hands and draped it over her head, winding the ends around her neck. "How do I look?"
Lottie reached out, and adjusted the drape with pride. "Like a perfect lost soul, overcome with grief." She stepped back. "You watch over yourself and our lord now, you hear?"
"I will," Warna said. "I promise."
The women, human and faelle, all curtsied as she turned to leave. Warna flushed and made for the door.
She walked quickly across the courtyard where she could see Ricard standing. He greeted her and gave a nod over her shoulder. "He's just coming now."
She looked behind, and her eyes went wide.
Verice had taken the time to bathe, and his fine white hair was long and flowing outside its normal braid. He was wearing black leathers with a silver chain shirt, belted at the waist with his sword and dagger at his side. He looked like the very picture of an elven prince, down to the black boots and black leather gloves. He wore a black cape, but the chain ran across his chest, and its hem touched the back of his boot.
"I take it I have 'looked to my own self'," he said with a quirk of his lips.
"You'll do," Warna said.
Ricard looked up. "Almost time, m'lord."
"But first there's one thing I must take care of." Verice stripped off one glove. "Warna," he said softly, lifting his hand to her face. "If you would allow?"
Warna tilted her head slightly, feeling Verice ease his fingers under the veil and brush the delicate skin behind her ear. She shivered at his touch.
He whispered something she couldn't quite make out, and a tingle went through her, down to the tips of her toes.
"Lady, can you understand me?" His breath touched her cheek as he whispered strange words.
"Lord, I understand what you are saying," she whispered back, but the sounds were odd on her tongue.
He withdrew his hand, brushing her ear again, looking satisfied as he put his glove back on. "It will not last much more than a day, but it should suffice."
A chime sounded in the air, ringing a perfect tone.
"It's time," Verice said, and a portal opened before them. "Constable, you have the watch, but defer to Narthing in all things."
"Aye, m'lord," Ricard said. "Travel well, and return safe."
"M'lady." Verice extended his arm.
"M'lord." Warna placed her fingers on the back of his wrist and allowed him to lead her through the glowing white curtains of the portal.
Verice grimaced mentally as he and Warna emerged into the sunlight dappled grove in the palace gardens of Valltera.
"Oh my," Warna breathed, and he knew she was taking in the tall spires that rose above the gardens.
How long had it been since he walked these halls? Hundreds of years was his best guess. Yet it looked the same, even down to the vines and flowers. The more the world may change, the more elves remained the same, that was certain.
Verice had no idea how they endured it. It was one of the reasons he'd left these lands.
One of many.
"Verice, Bearer of the Blood of Tethnar, I offer you greetings." A royal herald stood before them in stately robes, holding his staff of office, looking as welcoming as an offended cat. "I am Mathonalar, and I am to escort you to the royal presence."
"Mathonalar, I accept your greetings, and extend my own in return." Verice gave a formal bow. "But I must correct you in your choice of title. I am of Palins now, Lord High Baron of Tassinic."
Mathonalar bowed formally in return, as slow and stately as one could wish. "I offered greetings as I was commanded."
"I see," Verice would have spat the words, if that were permitted. "May I introduce my ward, Lady Warna of Farentell."
Warna curtsied, and Mathonalar bowed, offering his formal greetings yet again. Verice had forgotten the elaborate slowness of ritual welcomes. It made him grit his teeth.
"Once the guard has peace-bonded your weapons, I am instructed to bring you to Their Majesties' presence," Mathonalar continued.
Which was another way of saying 'show up and wait your turn,' Verice thought, but let no hint of it show on his face. He turned to the guard, and they started the ritual of binding each blade in its scabbard with ribbons and wax seals.
This promised to be a very long afternoon.
Mathonalar set a slow pace through the gardens and halls as he escorted them to the King and Queen. Warna was quiet at his side, but a glance told him that her eyes were wide with delight, drinking in the sights.
He could hardly blame her. Elves moved about them, graceful and serene in their bright robes that shimmered as if woven of moonlight and shadow, their ears decorated with the traditional piercings along the edges, glittering with jewels and precious metals. They walked down corridors of glowing white marble, with thick carpets patterned with leaves and birds in patterns that never seemed to repeat.
And the air was sweet with perfume and soft music floated through every window. Perfect, unblemished, unchanged. As it had been for centuries.
"It's lovely," Warna dared whisper.
It's stifling, was Verice's thought.
But at last they turned down a short hall, and at Mathonalar's gesture, the guard drew open the double doors. As they stepped through into the large chamber filled with courtiers, Verice could see King Barathiel on his throne at the other end of the room, with Queen Blesenthala beside him.
Mathonalar led them straight up to the throne at his slow, regal pace to give those present time to study and assess them, Verice was certain of that.
Mathonalar stopped before the throne, and tapped his staff three times upon the floor. "Verice, Bearer of the Blood of Tethnar, and his ward, Warna of Farentell."
Verice narrowed his eyes at the lack of title for Warna, wondering who had instructed that little detail. But the room had gone silent, and King Barathiel was rising to his feet, a smile on his face.
"Welcome, cousin!"
Chapter Forty-Two
It was all Warna could do not to let her mouth gape open like a dying fish. Cousin?
Verice took a step forward as the King approached them. The courtiers were all bowing, and moving to the side, creating a path for the King.
"Your Majesty," Verice gave a formal bow. "I offer thee greetings."
"So formal." King Barathiel waited until Verice rose, and then grasped Verice in a hug that seemed to catch him by surprise. Before Verice could react, the King released him, and faced Warna directly. "And this is Warna? Your ward, I believe."
Warna sank down as gracefully as she could and bowed her head.
"So lovely," King Barathiel murmured. "We've heard much of your gifts, Warna."
That brought her head up, to stare into eyes more cruel, rather than kind. A frisson of fear ran down her spine, but Warna remembered herself enough to lower her gaze. "My thanks, your Majesty," she whispered.
"So shy," King Barathiel said. "And so sorrowful. We are saddened to hear of your loss, Warna. The actions of the Usurper of Palins are a threat to us all."
The waters here were deeper than Verice had anticipated, and rapidly rising over his head. "Your Majesty?" he asked, careful to leave his question open-ended. He'd forgotten the layers within layers of the simplest of words spoken in the royal court of Valltera.
"Come, cousin," Barathiel took his arm, and guided him towards the dais. "Charrin has told us much of your ward, and the situation you are facing. We've had many long talks with him."
That came as a shock. Charrin was seated on a stool one step down from the throne. A signal honor. He sat, face turned toward Verice, his harp in his hands.
"We, Your Majesty?" Verice asked.
"Our advisors, the Queen and myself." The King left his side and mounted the steps to his throne. Verice glanced back to see that Warna had followed him, standing one step behind him, a single black rose in a mass of colorful dresses. "We've discussed it for some time, and have reached the only conclusion possible. The Usurper threatens your barony, cousin."
"There is tension within Palins, Your Majesty," Verice agreed cautiously. "But to my knowledge it has yet to reach the borders of Valltera."
"It is only a matter of time." Barathiel settled back on his throne with a confident air. "Tassinic must come under our protection, Verice. And you must be restored to your rightful place in our society."
A political pit yawned wide at Verice's feet. "Your Majesty, I was released from my oaths to yourself and this land many years ago. I have sworn my allegiance to Palins and—"
"To a dead human king, and a lost bloodline," Barathiel said sharply. "That means little now, wouldn't you agree?"
"No." Verice replied and etiquette be damned. He wasn't being pushed into this. "I am bound by those oaths."
"A simple matter, really." Queen Blesenthala's eyes glittered, her voice low and lovely. "In all honor, you will be brought back within the Royal family. Blood binds tighter than any oath. And to that end, we have had a thought to bind you even tighter to us. A marriage."
"Marriage?" Verice gaped at her, as the pit became a chasm. "Your Majesty, I—"
"Too long you have been without companionship, Verice." Barathiel leaned forward. "It's not healthy to live alone without the love of a faella." He paused. "Unless you prefer a mael?"
"No, Your Majesty," Verice said. "But—"
"Then there is no impediment," Barathiel said. "We would see you wed to a faella of a Blood that will bring you all honors."
"Your Majesty—" Verice tried to gather his wits. "My oaths—"
King Barathiel would have none of it. He cut through Verice's protests. "Tassinic is best brought within the protection of our throne and power."
"Your Majesty—"
"Your blood is of the highest, Verice. It's time for you to stop wasting time with these—" his eyes flicked to Warna and away. "These amusements. Take up the duties and responsibilities imposed on you by virtue of your birth. There's really no reason you cannot be wed, is there?"
Verice's mouth was as dry as his brain. "Your Majesty—"
"Actually, there is," Warna's voice came over his shoulder as she advanced to his side. "He has pledged his troth to me."
Warna watched with a great deal of satisfaction as her words wiped the smug looks off the faces of the King and Queen.
The Queen recovered first, her face serene, her eyes enraged. "We'd no word of this," she said icily, shooting a glance at Charrin.
"Your Majesty." Warna gave her best deep bow, more to give Verice time to find his voice than to honor the Queen. She rose to her feet as slow as grace would allow. "Our vows were only recently exchanged. I'd asked my lord to keep this between the two of us, in hopes that my family might be located and permission given."
Verice seemed to recover, and lifted his wrist, extending it to Warna, who placed her fingers on it gratefully. "I honored my lady's request." He bowed to both the King and Queen. "Please forgive our delay in informing you of our intentions," Verice focused on Warna, and she glowed at the warmth in his eyes. "We'd love to have you for the ceremony."
The silence was icy, but the look in Verice's eyes was enough to protect Warna from the chill.
Verice turned back. "If that was all, Your Majesty, we would return to Tassinic. I offer assurances that I will keep my borders secure, and honor the treaties between Palins and Valltera."
"No." Barathiel stood abruptly. "This warrants private discussions between you and I. But at this time, other petitioners await our attention. Perhaps you wish to show your...intended...the gardens? We will summon you to our side shortly."
Verice inclined his head. "Our thanks to your gracious majesties." Before Warna could start her curtsey, he led her off through tall doors on the other side of the room, and into the gardens.
Verice didn't stop until he was sure they were well out of the range of any listeners. He took Warna's hand and urged her through the rows of hedges and flowers, all perfectly trimmed without a leaf or branch out of place.
Finally, he found a bench surrounded by a field of knee-high lavender, where he had a clear field of vision. He stopped, and checked their surroundings.
Warna sank down onto the bench as if all the energy had drained from her. "Verice, I am so sorry," she started.
"You have nothing to be sorry for." Verice started to pace in the area before her, still keeping watch.
"I've all but trapped you into a marriage," Warna said. "But I didn't see any other way. They both seemed so smug, so sure they'd trapped you—"
"They may have," Verice said. "And please believe my anger is for myself, not you. I should have seen this coming."
"I don't see how," Warna said.
"Barathiel has always resented Palins," Verice said. "And that his father, my uncle, consented to releasing me so that I could swear fealty to King Jeverard."
"So, he is your cousin?" Warna asked, her eyes going wide.
"Only when he deems fit to acknowledge that fact," Verice growled. "Now, to find a way out of here without offending their delicate sensibilities."
"You will find a way," Warna said.
"I appreciate your faith in me," Verice paused in his pacing. "Since I have no idea of how I am going to do that." He stared down at her. "But one thing is clear. We are being watched."
Warna's eyes went wide. "But you said—"
"They can't hear us," Verice assured her. "But they can see us. And it would appear that we have been arguing." He shook his head. "So, we need to address this issue," he knelt before her, and reached for her hand, pressing it to his chest. "I will ask forgiveness, as a proud elven warrior should when he has offended his lady."
"And as a gentle human lass, I will forgive." Warna smiled. "This isn't your fault."
"Nor is it yours," he replied.
"I never intended—" Warna started.
"I know," Verice murmured. "We'll discuss this at another time. But in order to hold true to our story, there's another thing we must do."
Warna blinked. "Yes?"
He leaned in, his lips hovering over hers. "With your permission?" he asked.
"Yes," Warna whispered and pressed her lips to his.
Chapter Forty-Three
Warna melted into his body, bringing her arms up to wrap around his neck. His mouth felt so good on hers. When his tongue danced over her upper lip, she parted them and let him in.
They kissed for long moments, until Verice pulled back slightly. "Not sure we've convinced them," he whispered in her ear.
"I agree," she said solemnly, and captured his mouth again, eager for more.
A clearing of a throat came from behind them. "Forgive me, Verice, Bearer of the Blood of Tethnar, but I've been sent to escort you to the King."
Verice broke the kiss, breathing heavily. "Give us a moment, if you would."
"But of course."
Verice helped Warna with her veil. "They will separate us," he said into her ear as he helped her to rearrange her veil. "Remember the three rules. And if it comes to that, seek out my old weaponsmaster. His name is Arthrano. He would aid you."
"How would he know who I am?"
Verice's chest rumbled in a deep, quiet chuckle. "After our little announcement? I suspect the entire Elven Kingdom knows who you are."
Warna took a deep breath to still her shakiness. "Once we are free of this place, we will discuss this further," she said. "And in more detail."
Verice's face stilled, all humor gone. "You have my word, m'lady." With that he rose to his feet. "We are ready now."
The guard advanced and bowed to Verice. "This way, Bearer of the Blood. There is a small sitting room where your ward can wait. You and the King are to have words."
"We will indeed," Verice said mildly.
"You always were the unconventional one," Barathiel said in the privacy of his chambers. "Wine?"
"No, thank you." Verice followed Barathiel into the room. He'd been forced to leave Warna in the care of one of the handmaidens down a distant hall. He chafed at the separation.
"Charrin has told us that you were attracted to the human woman." Barathiel poured himself a glass. "Polluting your blood line even further than it already is."
Verice stiffened.
"Have her if you will," Barathiel continued. "For the time she has left. But no children, Verice."
Verice gave the man a cold look.
"Seal the borders to Palins, and the taint will dissipate from your lands over time. Tassinic can become one with our land. We would honor your boundaries and welcome you into our confidences."
"They aren't chess pieces, Barathiel."
"Take the long view, Verice," Barathiel gestured with his glass. "Sooner or later, there will be war with the Usurper. You and Tassinic will be caught in the middle. Ally with us and we—"
"As in the royal we?" Verice asked. "Is Blesenthala behind this offer?"
Barathiel paused, swirling the liquid in his glass slowly. He finally lifted his gaze to Verice. "She's a lovely thing, your human," he said. "If you like that sort of thing. But at best she's good for what, another fifty years? Your interest will wane, or she will."
"We'll be leaving." Verice stood.
"No," Barathiel said. "You'll stay until this is settled. Attempt to open a portal without permission, and my mage-guards will see to it that small chunks of your flesh rain down on your precious castle."
"I find this hard to believe, cousin," Verice said coldly. "That your sense of hospitality suffers so."
"Nonsense," Barathiel said as he strode to the door, opening it to reveal an escort. "I'd honor you, cousin, by assigning you a role in the afternoon ceremonies. It's rare that one such as yourself is afforded the honor of smoothing the royal pillows."
"What of Warna?" Verice growled.
"Another reason you should consider your position," Barathiel said. "But have no fear, cousin. We will see to her comforts."
A handmaiden escorted Warna into a small room with paintings on the walls, and windows overlooking the gardens. There was no other way out beside the one door, and she was fairly certain there was at least one guard in the hall.
She settled on one of the chairs by the windows, and resigned to wait patiently.
She had to smile in spite of herself. Her picture books of elves and their lands hadn't done justice to the beauty and elegance of these people. And hadn't prepared her for their arrogance either.
The Lady of Laughter alone knew where she'd gotten the courage to claim Verice before the King and Queen. Warna had to admit to herself that part of her motivation was simply anger at their smug faces, certain that they'd caught Verice in their snares.
She hadn't thought of rumors, or that the word of their engagement might travel as swift as flight, but she should have known. Even elves weren't above a good gossip, it would appear. Something none of her childhood story books had mentioned. And wasn't that a disappointment, to find out that elves were human?
Her stomach rumbled a bit, reminding her that it had been some time since her morning meal. Had it only been half a day since she'd awakened to the sound of Verice's sword against the pells? If felt like forever...
With any luck, they'd feed her at some point.
The door opened, and Charrin walked in.
He really hadn't changed since she'd seen him in Bode's tower. Tall, elegant, with that horrible slash over his eyes, puckered and red. He was carrying his harp and wearing formal robes embroidered with flames.
"Warna," he said.
"Bard Charrin." Warna rose and curtsied.
"You needn't bother," he said, moving unerringly to the chair opposite her. "It's not like I can see your courtesies."
"Still I offer them," Warna said. "Out of respect."
"I don't see why," he said. "It's not like I have any respect for you or your kind."
To the hells with the three rules. "Then why are you here?" Warna demanded.
"To tell you that I heard the note of surprise in his voice," Charrin said. "That I know that you are no more betrothed to Verice than I am able to fly." Charrin placed a hand on the back of the chair. "Retract your lies before the court, so that Verice can take his true place in society."
"That which lies between Verice and I is a private matter," Warna said. "And his surprise was in the announcement, not the betrothal."
"He pollutes his bloodline again if he goes forward with this," Charrin spat. "Tassinic needs to be cleansed of its human taint, and brought within the Kingdom."
Again? Warna wasn't going to ask, because a deep chill ran down her spine at his words, his lovely voice filled with hate. Recalling Kalynn's words at the tower, she didn't hold back. "Does your hatred of humans," Warna paused. "Does your hatred of us truly add value to the memories of your Lady Summer?"
Charrin reared back. "How dare you speak her name," he hissed. "What do you know of loss, of pain? You, who have barely seen twenty years, if that? I have underthings older than you."
Warna wrinkled her nose at that, but then answered him honestly. "In the last year, I've lost everything. My family, my home." She looked down at her hands, pale against the black of her skirts. "A degree of belief in the goodness of people, human as well as elven. I am not sure that the number of years matter. We share these things, Charrin. Elf and human alike."
"How dare you," Charrin spat, his face contorted in rage.
"It's easier to hate than to mourn, isn't it?" Warna continued on. "Easier to dwell on the grief than live."
"You miserable, hateful—"
A knock on the door brought Charrin to a stop, trembling as he stood there.
"Forgive the intrusion," it was the handmaiden, peeking in through the open door.
"Enter," Warna said. "Please."
The handmaiden advanced, her flowery skirts rustling on the carpet, and curtsied before Warna. "Please forgive the delay. Queen Blesenthala invites you to take tea with her."
Warna didn't think twice. "I'd be delighted."
Charrin watched the human flee.
How dare she compare her squalid feelings to his. How dare she claim that they shared anything.
Verice had to be made to see his error, his folly, and no amount of song or poetry would convince him, Charrin was certain of that. Only actions would suffice to bring that stubborn Lord around.
Charrin took a deep breath, composing himself. There would be a time and place.
And then he would act.
Chapter Forty-Four
Warm sun streamed through the windows as Verice watched the nobles strip the bedding from the King's bed with slow, careful movements.
It was probably for the best that he had been 'invited' to participate in this ceremony. It gave him time - lots of time - to consider his position.
Barathiel had caught him flat-footed and off-guard with his proposal that Verice abandon Palins, and marry to bring Tassinic into Valltera. Thank the Ancestors that Warna had stepped forward with her declaration. Verice's only other course would have been to try to stall, and Barathiel had seemed fully determined to force the issue then and there.
The mattress had been stripped, and turned. They all stood waiting patiently as the fresh bedding was carried into the room.
King Barathiel was an absolute ruler, Verice knew that well enough. But he had a council of Earls who held a great deal of power. Not all of them would be pleased with Barathiel's heavy-handed manner, for what force he brought to bear on Verice could easily be turned on them.
Verice cursed himself for his lapse in not knowing what was happening in Valltera much beyond the borders. He was an idiot, a thrice-times idiot, and he'd pay for that lack now. It would take time to locate the Earls, time to seek out their positions, and in the meantime Barathiel seemed determined to keep him here, a prisoner in the court.
Or Verice could risk the offense, open a portal, and defend himself from whatever happened next. But Tassinic could not stand against the concentrated might of Valltera.
And he couldn't risk Warna.
Barathiel knew that, damn him.
They were spreading the first sheet now. Verice sighed stoically, and girded himself for a long afternoon.
Warna felt like a black stain in a sea of flowery dresses. The hallway that the handmaiden led her down was filled with elven maidens in their finery. But the handmaiden walked serenely on, and Warna followed dutifully as she wove a path through them.
One of the faella leaned forward as Warna passed. "Your veil, so lovely," she whispered.
"Where did you find such quality?"
Warna's merchant soul rose up within her. "Its maker resides in Tassinic," she whispered. "Send word to me there, and I'll pass on her name."
The faella gave her a grateful look, and Warna continued on, following the handmaiden through large double doors. Only to find herself in a large room, as large as any ballroom she'd ever seen in her picture books.
At the far wall was a single throne, capped with a cloth of gold that shimmered under the light of a thousand candles. Before the throne, spread out in a fan pattern, were delicate white chairs, each with a tiny table beside it, each set with a white cup and saucer.
"Private tea?" Warna muttered under her breath.
The handmaiden led the way to the chair facing the throne, almost isolated from its neighbors. "I bid you welcome in Queen Blesenthala's name."
"I thank you," Warna replied, settling carefully in her chair. All she could do was fold her hands in her lap and wait.
The room filled, each faella taking her chair, sitting with perfect posture and composure, looking more like perfect painted dolls than living beings.
The cup and saucer caught Warna's eye, startling in their whiteness, of porcelain so fine she swore she could see through it. She'd love to own such a pretty thing, but right now she had but one thought: Lord of Light, Lady of Laughter, don't let me drop it.
The stir behind her finally stopped and a hush fell over the room as the doors were closed. Once all was silent, with each lady facing the throne, the doors opened again, and Queen Blesenthala swept in, and to her throne.
Warna rose with the others, and curtsied, careful not to let her skirts knock over the tiny table.
"Ladies, and Warna of Farentell, you are most welcome," Queen Blesenthala cooed, settling herself on her throne. Her dress was a vivid pink, making her the rose in the garden. "Let us refresh ourselves with tea and conversation.
"Warna, you are a delightful surprise this day, and we extend our greetings to you," the Queen continued. "Verice has been invited by the King to the Ceremonies of the Bedchamber. He is to place the pillows on the King's bed. A singular honor."
"Your Majesties are both so kind," Warna murmured, after it seemed that the Queen was expecting a response.
The Queen tilted her head gracefully to a footman off to the side, and servers flooded into the room, each carrying pots of tea held in towels.
"Verice is held in high regard here," Queen Blesenthala responded. "And we honor his choice of betrothal." She watched as her tea was poured, steaming, into the cup.
"An odd choice, of course," the Queen continued. "Humans are like flowers that bloom only to wither away so quickly. A brief moment in time."
"But, Your Majesty," Warna sent a mental apology toward Verice. "While it blooms, it is cherished all the more for the briefness of its beauty." She watched as the servant poured her cup of tea. "One treasures the time one is given."
Queen Blesenthala had lifted her saucer, her cup poised before her lips. "Well spoken," she said with a lift of her cup. "Shall we drink?"
Everyone else had claimed their cup and saucer. Warna lifted hers as well. She paused as the steam brought a flowery scent to her nostrils. "May I ask, what flavor is this?"
"Hibiscus," Queen Blesenthala hid her smile behind her cup. "My favorite."
No, it wasn't. Warna recognized the scent. It was gwenwyth tea.
'Your pardon, lady," Aeric had said. "but me mum was full human, and while she liked the taste, it gave her the flux something fierce.'
The cup poised, Warna froze, staring at the Queen as the Queen stared back. The steam rose, the cup warm beneath her fingers, and yes, she could see them through the thin white porcelain.
Warna narrowed her eyes, hoping against hope that her thoughts were reflected in her eyes. 'You think humans are delicate little flowers in your garden, don't you?' Warna thought. 'Well, guess what, bitch—'
She drank the entire cup, setting it softly back on its saucer.
'We are not.'
Chapter Forty-Five
Verice had the honor of placing the first pillow, and was smoothing the top when there was a flurry of movement and raised voices at the door to the King's Bedchamber.
It would never do to have the ceremony disrupted, so Verice finished his task, and stepped back to allow the next ridiculous step to occur in this foolish ceremony.
Until he heard Warna's name in the talk.
He bowed to the bed, backed from the room, then turned on his heel to face the guards and the clearly agitated handmaiden. "What's this?" he demanded.
"Verice, Bearer of the Blood of Tethnar," the faella was wringing her hands. "Your betrothed has taken ill. Violently ill. She drank her tea, and suddenly—"
"Take me to her," Verice snapped, pushing through the guards. "Now."
The handmaiden turned, and actually ran, telling Verice more than she ever could verbalize. He ran behind her, ignoring shocked looks and quiet protests of outrage as the serenity of the palace was broken.
It wasn't far. Verice charged through the doors, and slid to a stop.
Faellas lined the side of the room, chairs and small tables abandoned. Queen Blesenthala was on her throne, her face pinched and tight. And Warna, his Warna—
—was on the floor, on her hands and knees, heaving violently. Evidence of her illness lay before her, stretching all the way to the tips of the Queen's slippers.
"Warna," Verice breathed.
She turned her head, giving him a miserable blank stare. Then her eyes focused, and she smiled weakly. "Verice." She grimaced as he strode to her side. "No, Verice, don't—"
The retching caught her again, and she turned away as her body was wracked with pain.
"Here, now," Verice knelt down, heedless of the mess. He rubbed her back, offering what comfort he could. "What's happened?"
"Your betrothed has taken ill," Queen Blesenthala spoke, her face pinched. "Healers have been sent for and they will attend her." She glanced at the doorway. "There was no need to send for you."
"There was every need," Verice said mildly, hoped that for her sake, the handmaiden had
disappeared into the crowd. "Warna, let me get you off the floor."
"No," she panted, letting her head hang down. She grabbed his wrist as if to prevent him and tapped the back of his hand three times with her finger.
Verice held his face still, keeping his anger behind a wall. Something then, something the Queen had done. He tapped his finger on Warna's back, so she knew he understood. There were shards of teacups all around them, but no evidence of foodstuffs. The tea? His mind was working even as Warna succumbed to another round of horrible vomiting, her skirts now stained with urine and...his heart stopped.
There was blood seeping through her skirts.
Rage colored his vision red.
Warna spat to clear her mouth, then glanced at him, her eyes tinged red, her face covered in broken blood vessels. Her grip tightened on his wrist. "Verice," she moaned. "Take me home."
That startled him out of his anger.
Running footsteps, and a small cadre of mael and faella healers burst into the room. The foremost ran forward, reaching for Warna.
Warna reared back, seeking shelter in Verice's arms. "No," she warded off the healer's hands. "Do not touch me."
"Our healers are the finest," Queen Blesenthala declared, but the healer only withdrew her hand, and knelt, seeming to take no offense.
"Lady, I am gifted in magical healing. Let me see to—"
"Have you ever healed a human?" Warna demanded, her voice hoarse and thick with pain. She pressed herself closer to Verice, and he tightened his arms around her.
"No, lady, but—"
"My lord and I anticipated our wedding vows," Warna lied as loudly as her throat would let her. "I may bear his heir. Would you risk us both?"
No longer surprised by anything Warna said, Verice moved his hands, making sure the healer caught sight of the blood on Warna's skirts.
The healer's eyes widened, and she lowered her hand. "Your Majesty, it would be for the best if—"
"No," Queen Blesenthala declared.
Verice banked his rage, tamping it down, barely maintaining control.
Another commotion at the door, and King Barathiel arrived. "What is this? What has happened?"
Warna groaned, turned away from Verice and retched.
Barathiel stopped a few feet away, his nose wrinkled in disgust. But then his eyes narrowed. "Blesenthala, what have you done?"
"Nothing," the Queen said quietly, lifting her chin. "Warna has had a bad reaction to the tea, that is all."
"There's a chance she is pregnant," the healer rose to her feet. "It would be best if she is seen to by those who have tended humans and half-elven before."
"Is this true, Verice?' Barathiel demanded.
"Would you take that risk?" Verice demanded in return. "For the sake of any potential child, Barathiel, let me take her home."
Barathiel stood frozen for an instant, then shook his head. "Go. We grant permission—"
"No," Blesenthala rose from her throne.
Verice didn't wait another moment. He stood, and cast the spell, summoning a portal to Tassinic.
"Don't think we are done," Barathiel called out. "We will speak again, and soon."
Verice ignored him. As soon as the oval opened, the white curtains flowing in a non-existent breeze, he swept Warna and her sodden skirts into his arms, and stepped through—
Into a bed-chamber covered in dust from months of dis-use.
His bedchamber. The one at the top of the keep.
Verice stood, paralyzed for a moment, as memories rose up before his eyes. But then Warna moaned in his arms, and he moved to place her on the bed.
"No," she groaned, plucking at his arm. "Privy."
He got her through the door and propped against the hole just as she started to heave again.
"Warna," he rubbed her back, pulling the hair away from her face. "How do you fare?"
She cast her eyes up, giving him a look. "Fine, just fine," she coughed and spat into the hole. "Where are we?"
"Home," Verice stood. "Just give me a moment," he strode out into the bedchamber. Warna muttered something after him, but he was intent on his task. With a word and a gesture, he threw open every window in the room. "Constable," he bellowed, using his powers to amplify his voice so it shook the stones around him.
"M'lord?" came the faint response from somewhere below.
"Warna's ill," Verice shouted, trying not to let his fear echo with his voice. With another gesture he slammed open every outer door to the keep. "Come to her aid."
Chapter Forty-Six
Everyone came running, healers, warriors, dogs, all thundering through the keep, calling for Verice and Warna. "Here," Verice called from the doorway, and stepped aside to allow the healers through. "She's—"
But the sound of her retching was clear and the healers disappeared into the privy.
"Constable," Verice said to the man huffing and puffing by the door. "Keep them back for now. But have runners ready for whatever the healers might need."
Ricard had a million questions on his face, but all he said was, "Aye, sir."
Verice caught Brindle trying to squeeze through the door. "And try to keep the dogs back as well."
Verice returned to the doorway, watching as Warna, supported by the healers, retched helplessly.
"We'll get you out of these clothes first," Dominic said, his voice holding a rare note of gentleness. "Then we'll see to this."
"There's blood," Verice said sharply. "On her skirts."
"Blood?" Dominic asked sharply. "Warna—"
"Lord and Lady, can this day possibly get worse?" Warna moaned. "It's my monthlies, I think. On top of everything else."
The knot in Verice's chest released, and it felt a bit easier to breath. Not a wound then. Or something worse.
"We'll check you out to be sure," Dominic said, leaning forward to seemingly peer at the vomit. "What brought this on?" he asked. "Was there fever? Pain? Did you eat—"
"Queen Blesenthala said it was hibiscus tea," Verice offered.
Warna muttered a few pithy phrases about the Queen. "It was gwenwyth," she panted, after her strength ran down.
"Gwenwyth?" Dominic frowned. "That can cause illness in a human, yes, but not this violent a reaction. At least, not usually."
"I drank the entire cup," Warna admitted.
Verice jerked in shock. Dominic sputtered. "An entire cup?"
"Why?" Verice asked. "If you knew—"
"Because she knew," Warna sagged against the wall. "Because she knew I knew she knew." She sighed. "Maybe just to spite her."
"Warna," Verice whispered, half in admiration, half in dismay.
"We're home, aren't we?" Warna closed her eyes, looking sick and weary.
Verice reached out, and gently placed his hand on her head. "We are," he admitted.
Warna swallowed, then grimaced. "But drinking the entire cup," she sighed. "May have been a mistake."
"How long ago?" Dominic asked.
"I don't know," Warna said wearily. "We sat there, staring at one another until...it seemed like forever." She coughed, glaring at the jakes. "It was violent when it hit."
"You vomited on the Queen's slippers," Verice said, thinking on the room.
"I was aiming for her lap." Her disappointment was clear. "No more than an hour, I think."
"Well, now I know what I'm dealing with," Dominic said firmly. "We'll need water," he glanced at Verice. "Fresh clothes, and clean cloths. I'll send one of my apprentices for medicines. There's no sense in moving her—"
Warna heaved, bringing up little more than spit and bile.
"At least until that stops," Dominic added. He raised an eyebrow at Verice. "My lord, give us some time to see to her."
"I—" Verice hesitated. "Warna—"
She gave him a wan smile. "Go," she said. "I'll be fine."
Verice stepped back, reluctantly, then returned to the main doors, to find Ricard waiting with Ersal and a half-dozen of the staff. "Dominic needs water, hot and cold," Verice said.
One of the men in the back darted off.
"Some fresh clothes for Warna, and clean cloths and towels—"
Two more disappeared.
"And I want runners waiting here if he needs anything else," Verice added. "Ersal," he hesitated, glancing back at the bed behind him. Pain rose in his chest, memories of that horrible night—
The sound of Warna being sick again echoed from the privy.
"Ersal, see to it that this room is cleaned and restored." Verice ordered. "Do everything possible for Warna's comfort."
Ersal's face was solemn. "M'lord, I will see it done. It would be easier though, if we could use the hot springs below, and the smaller hearths."
Verice's throat closed. For a moment the pain threatened to overwhelm him. But he didn't let it stop him. "Whatever you need, Ersal. Except the Great Hall. Let no one enter there."
"On my honor," Ersal bowed his head. "It will be done as you command."
"My thanks," Verice said. "Ricard, send word to the commanders along the border with Valltera to watch for trouble." Verice said grimly. "Then join me at Narthing's bedside."
"M'lord," Ricard acknowledged the command. He hesitated for a moment. "You might want to clean up first."
Verice looked down at his stained and fouled leathers. "I will. We'll need to send word to my advisors as well," he started off down the dimly lit and dusty corridor, Ricard at his side. "There is much to discuss."
The stars were out that night by the time Verice returned to the keep. He entered through the main doors, taking the steps two at a time. Painful memories lingered in the shadows, but he ignored them. His thoughts were of Warna. He'd received hourly reports from Dominic, all of which boiled down to 'no change'.
The keep was alive with light and movement as the work of cleaning progressed. Ersal's voice was coming from the Seneschal's office, but Verice didn't pause to inquire. He continued on.
The main corridors were being scrubbed, the carpets removed to be aired and beaten. Verice acknowledge the staff's quiet nods and 'm'lords' as he strode on, climbing the stairs and walking the halls to his chambers.
He tapped on the door, and one of the apprentices opened it and bowed him in.
This room shone, having been cleaned to a fare-thee-well. The smell of fresh soap and linens filled the air, but there was an underlying scent of medicines and sickness.
Warna was lying in bed, almost dwarfed by the bedding and pillows. She gave him a weak smile. Verice crossed to the bed and took her hand. "You look terrible," he blurted out.
"Trust me," she said wryly. "I'm not feeling much like a delicate flower right now."
Verice sat on the side of the bed, looked over to where Dominic was conferring with the other healers. Dominic caught his look, and motioned for him to wait.
"What's been happening?" Warna rasped. "Anything?"
"Yes," Verice hesitated. "Barathiel has sent messages of concern for your health and assurances of the sanctity of our mutual border."
"What does that mean?" Warna said.
"We're not sure," Verice admitted, enfolding her cold hand in both of his. "There have also been messages from the Regent of Palins, inquiring as to the health of my betrothed and offering assurances of his readiness to defend my borders."
Warna's eyes went wide. "But how would they know? So fast?"
Verice shrugged. "Spies, no doubt. In both courts, probably. Here, even. News flies on the wind."
Warna's fingers tightened weakly around his. "I've made a mess of things, haven't I? I was lying my fool head off to get us out of there, and never thought through the consequences."
"Hush," Verice said. He reached out to push a strand of her hair back off her face. Her skin felt flushed. "Are you cold?"
Warna pulled at the blanket. "Can't seem to get warm."
Dominic and the others approached the bed. "Well, let's see to you," the healer said.
Verice rose, and released Warna's hand slowly, making way for the healers.
"Open," Dominic ordered, and Warna obeyed. "Let this melt under your tongue. That will ease the pain, and let you sleep."
Warna grimaced. "Bitter," she complained.
"Let us help you to the privy before the drug takes effect," Dominic said, and Warna grimaced, but nodded weakly. Dominic pulled Verice away as she was aided out of bed.
"Well?" Verice asked softly.
"She hasn't been able to keep anything down, even water." Dominic said. "I've never seen this violent a reaction to gwenwyth before, but then I've never known any human to drink a full cup of the stuff. We're hoping that a night's rest will settle her stomach. We'll try a bit of broth in the morning, and see what happens. We'll stay with her tonight."
The implication being that Verice was in the way. Verice sighed as Warna walked slowly back to the bed, and was tucked under the covers.
"I'll have warming stones brought—" Dominic started.
"Yes, do that. But for now..." Verice stepped forward. Warna gave him a puzzled glance as he put his hands on the bed. "Allow me," he said softly, then cast a warming spell on the bed.
Warna sighed as the heat enveloped her, some of the lines in her face easing.
"That feels lovely," she whispered.
Verice sat on the side of the bed. "Would that my gifts included healing," he said ruefully. He glanced over his should to see that Dominic and the others were giving them a bit of privacy.
"So sorry," Warna said softly. "Never thought it through." She fumbled her hand out from under the blanket, and reached for Verice. He took hers in his, pleased that her fingers were warmer. "Trapped you in a marriage," she whispered, struggling to keep her eyes open. "Didn't mean to...I'm sorry."
"I am not," Verice whispered, but she was already fast asleep.
Chapter Forty-Seven
"Well, that explains quite a bit," Verice said, as he studied the map of Tassinic, and the neighboring baronies laid out on the floor of Narthing's room in the Healing Hall. The day had been a blur. Between fears for Warna, and fears for the border, Verice wasn't sure where the hours had flown.
"I can't believe that the Baroness of the Black Hills attacked Wyethe and Athelbryght at the same time." Narthing said. He was seated on the edge of the bed, trying to keep his toes out of Palins. "She had to know that Summerford would rise in response."
"King Barathiel has pulled his troops back from our border," Verice said.
"Not far enough," Ricard growled.
"Far enough to show his intent," Verice said.
"Aye, sit back and wait for a weakness," Ricard grumbled.
"True enough," Verice said. "I've let my sources of information lapse there, Pernard."
"Easily remedied," Pernard replied. "Leave it to me, m'lord."
"And the Usurper," Ricard consulted some notes. "His forces have pulled back as well."
"Thanks to Elanore's mistake. With the Black Hills fighting a war on two borders, he can't count on her support." Verice said with no little satisfaction.
"Warring on two separate borders at once?" Narthing said. "She's mad."
"Well, if she's taken to raising odium then even if she's not now crazed, she soon will be." Verice said grimly.
Pernard shook his head "Has she turned to blood magic?"
"I can't confirm it," Verice said. "And I will not risk scouts to learn if it's true. But what Elanore forgot is that while the High Baron of Summerford and the High Baroness of Wyethe despise each other, they each leap to the other's defense at the slightest hint of a threat. They've joined forces against her, and even if she's using odium, she cannot stand against them."
"Stalemate," Narthing said. "Your enemies afraid to come against you. Exactly as you'd hoped for."
Verice sighed. "True enough," he said. But at what price, he asked himself.
Almost as if Pernard had read his thoughts, he cast him a glance. "How is your lady?"
"Not well," Verice sighed. "In fact, if we're done here?" He rose from his chair.
The others rose as well.
"My thanks, Pernard, for coming. Your wisdom is appreciated," Verice said. "Narthing, get some rest. Ersal, continue to draft bland messages of meaningless diplomatic phrases to our 'ally' Valltera." There were chuckles as Ersal nodded. "I'll be with Warna if more news arrives. Gentlemen." He nodded to his advisors, and slipped from the room and headed to her bedchamber.
The keep was quieter now. The work was still going on, and Verice could see that Ersal and others had moved back into their old chambers and offices. But the mood was dampened by the growing awareness that Warna was ill...seriously ill.
Still the work continued on all the rooms and chambers. Except the Great Hall, as he had ordered.
He opened the door slowly, hoping not to disturb Warna if she was sleeping. And she was, curled around a warming stone, buried under the blankets.
The room was lined with cots and pallets; the healers were keeping a constant vigil. He noticed Warna's lidded basket against the one wall. Someone had made sure her things had been brought to the room.
Not that she was in any shape to enjoy them.
He went to the other side of the bed, and sat so that he could see her face. She looked so tired and listless. Her hair had lost its luster, and someone had pulled it back in a loose braid. He doubted she'd had the strength.
Her eyes fluttered open, and after a moment she focused on him and tried to give him a smile. "Verice," she whispered.
"Lady," he said. "How are you?"
"Thirsty," she grimaced. "But when I drink, it starts again. I don't want that," she closed her eyes.
"I should let you—" Verice started to excuse himself.
"No," she complained. "All I do is rest. Tell me the news."
"Barathiel has pulled his forces back," Verice said. "I think he was trying to take Tassinic so fast that no one would have a chance to respond before he had it under his control. But now that word has leaked out, I think he's decided to wait and see what happens." Verice hesitated. "I don't think he knew what Blesenthala was up to," he continued. "I don't think Barathiel would have countenanced it, if he'd have known."
Warna frowned, thinking it through. "But why would she do it?" she asked. "Does she hate humans that much?" She took a shaky breath. "I doubt she was really trying to kill me. More of a cruel prank, don't you think?"
"Blesenthala and I have a bit of a history," Verice said softly.
Warna gave him as much of a glare as she could. "One of these days, you are going to sit down and tell me every day of every year of your life," she whispered.
"What makes you think I remember with that level of detail?" Verice quirked his mouth, and leaned closer.
Warna reached out and captured a lock of his hair between her fingers. "Every detail," she whispered.
"My parents offered marriage for myself and Blesenthala," Verice said. "Many, many years ago. But the offer was refused, and she was given in marriage to Barathiel, next in line for the throne."
"She wanted you," Warna said. "She still wants you." She tugged on his hair. "Charrin said something about a taint in your blood. Was that why—"
"Yes," Verice said softly. "Five generations back, the eldest male of my line married a human woman."
"Five generations?" Warna rasped, licking her lips. "Five elven generations? That's ridiculous."
"That's yet another reason I left," Verice said.
"Thick as posts, those people are," Warna closed her eyes and sighed.
"M'lord?" Dominic approached. "A word?'
Dominic drew him out into the hallway and down a ways from the door. "It would be best if Lady Warna does not hear us, m'lord."
"Dominic?" Verice felt the fear leap in his throat.
"M'lord," Dominic looked him in the eye and there was none of his normal haughtiness in his expression. "Lady Warna is critically ill, and I fear for her life."
"Tell me," Verice said.
"She has kept nothing down these past days," Dominic said simply. "And that includes our herbs and potions. Items that normally end nausea only seem to worsen the problem. She retches up everything we give her. Her urine output is decreased, she complains of thirst, her hair and skin are dry, and her cycle is upon her, which only adds to her misery." He took a deep breath "M'lord, she will die if she cannot drink."
Fear lanced through him, clutching at his heart. This could not be possible, and yet Dominic's face told him otherwise.
"I mean no offense," Verice said, "but perhaps another healer...?"
Dominic gave him a look that managed to combine sympathy and arrogance all at once. "M'lord, I am your foremost healer."
"I—" Verice wasn't sure how to reply to that. True enough, Dominic was skilled but there had to be someone—
Dominic wasn't done. "I met a woman when I was in Edenrich. A mage, but also a priestess with the gift of magical healing." His face was tight, as if with pain. "Evelyn."
Verice frowned. "Lady High Priestess Evelyn?" At Dominic's nod his frown deepened. "She's human, Dominic. And bound to the Church of Palins, which supports the Usurper. I daren't be beholden to—"
"Evelyn is not like that," Dominic said. "She heals all and sundry, even ministering to the poor when she was told to attend only those of the highest rank." Dominic shook his head as if he could hardly believe it. "She'd come, m'lord. And she may be Lady Warna's only hope."
Verice drew a breath, seeing what it cost the proud mael before him to utter those words.
But it was only a breath of hesitation. His heart reflected the fear in Dominic's eyes.
"Contact her," Verice said. "See if she will aid us."
Chapter Forty-Eight
Lady High Priestess Evelyn was both mage and priest. After she agreed to come, she offered to open her own portal. But Verice insisted on controlling access. He opened a portal for her right in the bedchamber after excusing all but Dominic.
Dominic stepped within the glowing oval, and returned with a woman wearing the formal hooded cloak and embroidered white and gold robes of a priestess of the Lord of Light. She was short in stature to Verice's surprise, and her smile was serene and kind.
"Lord Verice," she said softly, her attention focused on Warna, who lay in the bed just beyond. "This is Warna?" she asked, moving to her side. "Dominic has told me of the problem." She threw back her hood, and removed her cloak, tossing it aside. "Let me see what I can do for her."
"My thanks, Lady High Priestess. I owe you-" Verice started.
"Nothing," Evelyn interrupted. Verice hesitated, expecting more talk. He blinked in amazement as power started to gather in the priestess's hands. Wasting no time, she leaned over and placed her hands on Warna's breast.
Warna roused, opening dazed eyes, but not seeming to really see. Verice swallowed hard.
Evelyn's eyes were closed. It might have been the effect of her robes and the candlelight, but Verice could have sworn that the woman seemed to glow with divine light as she ran her hands down, moving the bedding aside to get access to Warna's body. Warna shivered for just a moment, then closed her eyes and seemed to relax into Evelyn's touch.
Dominic stood beside Verice, his hands tucked into the sleeves of his robes, and watched Evelyn work. There was a look in his eyes...and Verice was almost sure it was envy, for the power Evelyn wielded. But after another glance, he knew it wasn't jealousy.
It was desire for the human woman.
'Poor mael,' was all he had time to think before Evelyn started talking.
"Gwenwyth, correct?" Evelyn said, holding her hands over Warna's stomach.
"Yes," Dominic said. "An elven tea, but humans sometimes cannot tolerate it. I've never seen this severe of a reaction before."
Evelyn nodded, her eyes still closed. "Yes, I can see it, lingering in her stomach and bowels. Poor thing, no wonder she's so weak. She can't rid herself of it with fluids, and it won't dissipate on its own." Evelyn wrinkled her nose. "I'm afraid this is going to be unpleasant."
"Unpleasant?" Verice demanded.
"Once we wake her, we'll get her to drink as much as she can. I'll aid to help cleanse the gwenwyth from her body, but it must come out, and she's already exhausted from vomiting. I'll strengthen her as much as I can before we purge her." Evelyn said calmly, ignoring Verice's reaction. "And we'll carry her into the jakes before we start. Dominic and I can handle the details." She focused calm blue eyes on him. "You might want to leave, m'lord."
"No," Verice started to remove his leather tunic. "I'm staying."
Evelyn raised an eyebrow at that, but she merely glanced at Dominic, who shrugged. "Very well," she said, and leaned over her patient. "Warna? I need you to wake."
Warna blinked at her, rousing with some difficulty. "Are you an Angel of Light?" she asked drowsily.
"No," Evelyn said, putting her hands on Warna's chest. Once again Verice saw her hands glow. "I am Evelyn, a healer. Dominic and I are going to help you."
"Oh no," Warna looked so pitiful. "Evelyn, no more vomiting," she begged.
"Call me Evie," Evelyn gave her a rueful smile. "And no more vomiting. I promise."
Verice resisted when they made him leave at dawn.
"The worst of it is over," Evelyn pointed out as they settled Warna back on the bed. "Dominic and his staff can handle it from here. I must return to the Church for the dawn service, but I would like to return later to make sure that the gwenwyth is out of her body. You can open a portal at—"
"I give you leave to open your own, Lady High Priestess," Verice said wearily. "I will seek my own bed, I swear. I don't know how you will have the strength to perform your duties."
"Long years as a healer." She smiled.
Verice looked down at Warna, who hadn't stirred as they'd covered her with blankets. "Lady High Priestess, you have my heartfelt and undying gratitude. She's—"
"Hush." Evelyn turned him, and pushed him towards the door. "Before you promise me all sorts of impossible things." She opened the door and forced him through. "But Lord Verice?"
He paused just outside the door. "Yes?"
She wrinkled her nose at him impishly, and gestured toward his stained tunic and trous. "You might want to bathe before you take to your bed."
Verice slept longer than he intended, and woke to a mid-day sun streaming through his windows. The dogs weren't about; he couldn't remember when he saw them last. He dressed quickly, threw water on his face, and started for the keep, not pausing for food or drink.
It might have been his imagination, but the sun seemed brighter this day, and the folk that greeted him seemed lighter of heart. A fancy, surely, but Verice took the steps to the keep two at a time, barely nodding at anyone he saw. The door to her bedchamber was closed, and he almost feared to open it when he heard—
Verice stopped, the knot deep in his chest unwinding from around his heart. He leaned against the wall and did something he rarely did. He offered his deep and sincere thanks to his Ancestors.
Warna was singing.
Chapter Forty-Nine
Kalynn stood at the center of the Heart of the Plains and breathed in the air of home.
The sky above was a bowl of blue, darkening to the east as the sun set. The stars were starting to dance along the horizon.
The breeze was soft; the heat of summer fading from the air. She'd toed off her boots, and the Heart was warm beneath her feet. Warm from the sun, but lifeless otherwise.
Wolfe was removing the airion's harnesses, freeing them to hunt. Of course, they had to roll in the grasses as soon as they were free. It made her laugh to see their joy.
Wolfe walked toward her, his wispy white hair floating in the breeze. He carried one of the saddle bags and a blanket. He paused at the rim of the stone.
Kalynn waited.
He shook his head, shrugged, and stepped on to the surface.
Nothing happened.
"Do you remember?" She asked as he walked closer. "When it pulsed with life? When all the Tribes gathered around, and the Heart beat with their energy?"
"Yes, of course," he spread out the blanket, and pulled her down to sit beside him. "Let's see what we have. There's those hard crackers you like, and cheese and—"
"Regrets?" She asked.
Wolfe stilled, and then looked out into the distance. "I regret that they would not listen. I regret that they would not honor your choice. They dragged you from me, screaming your outrage and fear, and I lost my mind in that instant."
Kalynn rose on her knees, and hugged him, pressing his head to her breast.
He continued, his voice muffled. "I regret that I lost all control, tore the magic from the lands in my rage. It fled, from me, from them, from the very Plains around us."
He pulled back, and looked up at her. "But I would do it all again, tear the world asunder to be at your side."
She cupped his face with both hands and kissed him, pouring her love into him.
He broke the kiss, and took a breath. "Now, dried cherries?"
She laughed and settled beside him. The airions took flight, spiraling up into the sky.
"Will they be all right?"
"I'm cloaking them," Wolfe said absently, pulling out wrapped bundles. "I've enough reserves to hide them and us from any wandering eyes."
"Is anyone about?"
"Some thea camps, and one group of Singers, but they are far enough not to be a problem."
"The Ancients?" Kalynn asked.
"Pfft, those little dried turds?" Wolfe popped a cherry in her mouth. "Do not worry. Once the airions have fed, we'll fly north." He grimaced, and she knew it wasn't the taste, it was the destination.
"She may have mellowed," she offered as she bit into the tart fruit, bitter and sweet on her tongue.
Wolfe grunted. "And ehats might fly." He pulled out a loaf of bread. "But you are right. She needs to know."
"Will you have enough power to hide us?" she asked.
"So long as you don't have your mount do any more loop-de-loops." He raised a chiding eyebrow at her.
Kalynn just smiled. "It felt so good to be flying." She reached for the crackers, but then she looked up and off to the west. The tug on her heart came again.
"Seeing?" Wolfe asked softly.
Kalynn nodded absently, lost in the sensation. They needed to be there, at a certain time, a certain place—
"Eat," Wolfe nudged her shoulder with his. "Time enough to do what must be done."
"We did something in the name of our love that reached far beyond us," Kalynn was still lost in the possibilities. "It echos still. This is our chance to make amends."
"Kalynn," Wolfe said, his voice heavy with sorrow. "We can't fix this."
"No," Kalynn whispered as the possibilities faded from around her. She smiled at Wolfe. "But we can set other feet on the path."
Chapter Fifty
"Is there any lingering soreness when you move your bowels?"
Warna wrinkled her nose at that. Healers asked the most uncomfortable questions sometimes, and Evelyn was no exception. "No," she answered.
"And your bowel movements are regular? Solid?"
"Yes, and yes," she said patiently.
"And the color?"
"Evie!" Warna sputtered.
Evelyn laughed. "Sorry, it's just that the expression on your face—" she laughed again, looking more mischievous than any priestess Warna had ever met. "Here, let me examine you one last time."
Warna lay flat on the bed, and let Evie have her way. She admired the high ceilings and the sunlight streaming through the windows. Verice's chambers were lovely, but she'd been cooped up in here for days.
"And your cycles?" Evie asked as she moved her hand inches from Warna's stomach.
"Over, thank the Lady," Warna sighed.
That brought another chuckle, but then Evie went silent, her face intent as she invoked her powers. Warna felt a tingle as her hands moved around her mid-section. "That's amazing, you know," she whispered.
"It's a gift of the Lord of Light," Evie said just as softly. "But it has its limits. Dominic can treat an entire village dying of sickness; at best I could treat a limited number before my own life was at risk."
Warna's eyes went wide at that thought, but she stayed quiet, letting Evie do her work.
Finally, Evie breathed a sigh and opened her eyes, pleased. "Gone. Not a trace of gwenwyth that I can find."
Warna sat up, breathless with hope. "Dominic said that if you released me from care, he would lift his restrictions as well."
"Then consider yourself free," Evelyn said. "But bear in mind that it will be a while before your true strength returns. Rest when you are tired," she warned. "Listen to your body."
"I promise," Warna said and on impulse swept the priestess into a hug. "Evie, thank you!"
To her delight, the hug was returned. Warna tightened her arms again, and then released, feeling absurdly happy. "Evie, please, visit as a friend in the future."
Evie smiled back, but then her face dimmed. "I'd like that, Warna, truly. But the times are...difficult."
"I know," Warna sighed. "But if Dominic's assigned to the Church in Palins, perhaps they'd assign you here?"
Evie wrinkled her nose. "As much as I'd like that, it's doubtful. They like to reserve my powers for the nobles at Court." She flashed a grin again. "Not that I let that stop me."
"Dominic's social climbing skills will be most welcome then," Warna snorted.
"He's very skilled, both as a healer and apparently in moving among the ranks of power. Not one of my abilities, I'm afraid," Evie said. "But they won't remove Dominic from his position here until they've found a qualified healer to replace him."
"Use that as an excuse to visit," Warna suggested.
"Lord Verice has said that I might call on him at any time."
"I hope you take him up on that offer," Warna said.
Evelyn gave her an odd look. "I will think on it," she said. Then she smiled, her face once again calm and serene. She stood, reaching for her cloak. "For now, I've promised Dominic I'd look in on one of his patients to see if I can speed his healing. Apparently, the man is such a horrible patient that Dominic wants him healed and on his way before Dominic's own bowels rupture in pure frustration."
"Before you go," Warna took a deep breath. "I wanted to talk to you about—"
"Yes?"
Warna made her decision. "I want to talk about babies. Well, not having babies." She blushed scarlet, trying to find the right words. "Preventing babies."
Evie gave her a direct look. "Warna, I've scanned you. I've heard the rumors, but I know that you have not had relations with a male."
"Yet," Warna said.
I'd like to talk. Please come.
Warna.
Verice stared at the note, and felt an odd flutter in his chest.
"She first asked for hot kav, and a bath," Ricard spoke with satisfaction, having delivered the note himself. "Dominic and Priestess have both given her their blessing. The Priestess even saw to Narthing. Nice of her," he sniffed. "Unlike some healers we know."
"Warna wants to talk," Verice said, and felt that flutter again. It wasn't as if they hadn't talked since her recovery. But there's always been healers or servants in the room, seeing to Warna's care and comfort. There'd been no privacy.
Verice had felt oddly relieved at that when he'd visited. He wasn't certain what to say to her, or how to express so many things. His admiration for her manipulation of the situation. His horror that she would drink gwenwyth and sacrifice herself. His terror at the knowledge that she'd do something so fundamentally stupid as to drink the entire cup without knowing what it would do to her, just to spite her foe.
Ricard interrupted his thoughts. "If the Lady Warna wants to talk," he said, "best be about it."
Verice nodded, and rose from his table. But not before he tucked the note into safe-keeping.
He schooled himself on the walk from the barracks, nodding greetings to all. There were many knowledgeable looks and smiles, so the word must have spread that the healers had released Warna from their care.
He entered the keep from one of the smaller doors, not really ready to trod the main staircase, but the lit hallways and buzz from the various rooms and offices didn't cause any pain. Maybe because he was more intent on seeing Warna, than anything else.
He allowed himself to mount the steps two at a time, and paused at the door just long enough to catch his breath.
He knocked.
"Come in.," Warna's voice was strong.
The room was flooded with morning sunlight. Flowers in vases sat on every open surface. Even though there were chairs by the hearth, Warna sat at the end of the bed, her hair flowing down her back, dressed in one of her light gray dresses. She was smiling, her brown eyes clear and bright.
She was alone.
Verice closed the door. "Good morning," he said.
"Good morning," Warna answered. "Dominic and Evelyn have released me from their care. I'm free."
"That's well, then," Verice stood there, feeling awkward and rather stupid.
"Verice," Warna caught his gaze, her eyes warm and intent, "I know what I want now." She lifted her head, glowing with confidence and strength. "With my life, I mean. At least, for the next month or so."
His mouth went suddenly dry. "What?"
"I'll tell you," she said abruptly. "But right now, I want the sun on my face and the wind in my hair. Let's go walk in the gardens."
Chapter Fifty-One
To Warna's delight, Verice extended his hand without hesitation. "As you wish," he said. "But you may not find it as easy as you think to get to the gardens."
"Why so?" she asked.
Her answer came when he opened the door. "Because I will have competition for your attentions," he whispered. The corridor was filled with people cleaning, all turning towards them with smiles on their faces.
"Oh." She hesitated, feeling the heat on her cheeks. "I don't suppose—"
"No." Verice escorted her through the door, and extended his arm again. He lowered his head to her ear. "We can't go another way."
Warna sighed, and returned all the smiles and greetings as they walked along the corridors and down the various staircases.
Out in the courtyard, it wasn't so bad. Most people hung from windows, waving kerchiefs, but those in the yard itself didn't crowd all around them. Warna felt warmed by the greetings, and by the sun on her face. It felt good to be up and about.
The constable crossed the yard to greet her, along with Verice's dogs. "It's good to see your smile, m'lady."
"Thank you. Ricard." Warna smiled back. "I'm going to walk in the gardens for a bit," she explained as the dogs milled about their legs, looking for attention.
"Mind the rantha thorns," Ricard warned. "There's been no gardeners out there, m'lord, and they've probably overrun the paths."
"We'll have a care," Verice said. "I'm not going to let her go far, trust me."
Ricard stepped to the small door in the castle wall, throwing back the locks and releasing the latches.
"You might have Ersal send word to the gardeners," Warna said innocently. "So that they can get to work trimming things back."
"They're already at work in the kitchen gardens." Verice gave her a wry look. "Apparently when I opened the keep, that was interpreted as a general invitation for everyone to return." He gave Ricard a raised eyebrow. "I wonder where my people learned that ploy."
"Hard to say, m'lord," the constable said as he opened the door. The dogs pushed past him, snuffling the air with anticipation.
"Warna," Verice gestured to her to go first.
Warna didn't hesitate as she stepped through the doorway and into the garden beyond.
If this had been a moat, it must have been a wide one, deep and dangerous. The area between the walls was large and spacious and the ramparts towered over her. She could see guards along the outer wall, pacing out their watches.
But the land between the walls was lush and green, and filled with the wildness of over-grown rose bushes, with large pink roses, their blooms as big as cabbages. The plants sagged under their weight, and petals littered the stone walk that angled away from them.
Warna took a deep breath of the flower-scented air, and lifted her face to the sky. She could hear Verice walking up behind her, and the dogs running around through the bushes, stirring up birds in pursuit of a rabbit.
"I should not have neglected it for so long," Verice said. The sorrow was thick in his eyes. On impulse Warna reached for his hand, taking it in hers. Verice squeezed once, and kept hold as he continued. "It didn't take long for this place to turn into a wilderness. Watch out for the rantha vines."
"It's not that bad," Warna said. "I like it better than the palace gardens in Valltera. Those plants were groomed to within an inch of their lives." She tugged once, and they started walking down the paths, Verice reaching to clear the branches out of the way. It wasn't really practical to remain hand in hand. But he didn't release hers, and she wasn't going to pull away.
"Everything perfect, nothing out of its place," Verice said. "Not so much as a fallen petal."
"I never got the chance to ask." Warna laughed. "They told me you'd been invited to make the king's bedchamber for the ceremony. Did you get to smooth the king's pillow?"
Verice snorted. "I was just positioning it on the bed when word came you'd taken ill." He stopped for a moment, lifting his head. "You might want to hold your breath for a moment," he said wryly. At her puzzled glance, he nodded to a bush off to the side. "Gwenwyth."
She wrinkled her nose as she got a faint whiff.
He hurried her past, leading the way. "If I remember correctly, off to the side here..."
He released her hand and thrust aside more branches, revealing a bower under a trellis of large purple flowers, with two stone benches opposite each other. He cleared the leaves and twigs from one. "Here," he gestured. "Sit for a while."
"Tell me about the ceremony." Warna sank onto the bench. The stone was warm from the sun that dappled through the leaves. "And what did Barathiel say to you?"
Verice brushed the other bench clear, then sat opposite her, adjusting his sword as he took his seat. Something flashed through his eyes, but he spoke easily, explaining King Barathiel's position, describing their conversation. There was something he wasn't telling her, but Warna could imagine enough not to need details.
"What of you?" he asked finally. "What happened while I was apart from you?"
So Warna told him about Charrin, and the Queen's invitation to a private tea. "I couldn't think of a way to refuse," she said. "And once I was there, and the tea was poured, she was so superior, so smug—"
"You drank the entire cup," Verice finished.
"I wish I could claim that I thought it all through," she admitted. "That I had this grand plan. But really I just...improvised."
"I find that at once admirable," Verice quirked the corner of his mouth. "And terrifying."
Warna laughed.
"But you need to know what's happened as a result," Verice said. He told her the situation, from the Usurper's notes to the pull-back of Barathiel's armies.
Warna frowned. "Why would he do that?"
"Warna, elven faella do not conceive easily. Elven children are rare, and as such, are considered precious above all things," Verice said. "Any threat to a child, or an expectant mother, human or faella is unpardonable."
"Oh," Warna thought it through. "So, my lies—"
"I've had several unofficial communications," Verice said. "From elven nobles, from Barathiel, from Blesenthala, even from the Usurper, all delicately inquiring as to the fate of your unborn child."
"Lord and Lady." Warna bit her lip. "It never occurred to me—" She stopped. "But you and I, and my healers know the truth."
"Still, when you don't give birth in the next year, it will be assumed that you miscarried the non-existent child." Verice looked away. "On one hand, you've provided the perfect diplomatic weapon against Barathiel. But on the other, your reputation has suffered, and for that—"
Warna snorted. "Reputation? What reputation? Verice, I'd been fleeing the Usurper's army for months, sleeping in ditches, fields, and sheep lofts before you rescued me. Not to mention sleeping in a barracks full of men once I arrived here. No need to be concerned for what is already broken."
"I fault myself for that," Verice said. "I should have had a chaperone, a handmaiden or—"
"I don't fault you," Warna said. "And I don't regret a moment of it, either." She let her gaze fall to her lap. "I do feel bad that Blesenthala thinks she killed a child," she started, but then in her mind's eye she saw the Queen's expression as she stared over her teacup. "But she knew exactly what she was doing, didn't she? She may not have thought I might be pregnant, but she certainly meant me ill."
"You certainly caught her off guard," Verice said. "What with the vomit on her shoes."
"But not on her lap," Warna admitted with a smile.
Verice looked at her, the laughter in his eyes slowly fading. "So that is where it stands now. Stalemate. Hopefully, a peaceful stalemate. Not that I will relax my guard just yet."
"So that just leaves us," Warna blurted out.
Verice jerked his head in a nod.
Gathering her nerve, Warna sat up straight on the bench. "Verice," she started, her words catching in her throat.
He raised an eyebrow, and waited for her to continue.
"Verice," Warna said. "I know what I want."
Chapter Fifty-Two
Verice's heart leaped with a sudden, irrational fear that she'd ask to leave. She'd every right to ask to go, but he—
He swallowed, and chose the honorable path, as much as it choked him to do so. "Whatever you want, Warna."
"Hear me out," she chided. She breathed deep, and he took a moment to just look at her, lovely in the scattered sunlight. She seemed to glow against the greenery that sheltered them.
"I want to celebrate the Festival of Light and Laughter with you in the Great Hall." She raised a hand to forestall any protest. "You and I have been dancing around the central issue of the castle and your keep since I've arrived. We've - your staff and I - we've used subterfuge, dissembling, shams and deceit." She gave him a solemn look. "As conspiracies go, it's been a fairly quiet one."
Verice couldn't help but snort, and at Warna's questioning look, he raised an eyebrow of his own. "Isn't that the very nature of conspiracies?" he asked.
That got him a soft smile but it didn't reach Warna's eyes. "And you've let us. Turned a blind eye to our doings; ignored what was happening around you."
Verice said nothing, kept his face as still as stone. But Warna wasn't fooled. She rose, pushed through the dogs, and sat next to him, taking his hand.
He felt the warmth of her skin, took in the soft scent of her hair and the band around his chest tightened.
"That was fine," she assured him. "It worked, in fact. For both you and those around you. But now, going forward, there should be only truth between us. No more lies, no more coy maneuvering. What I want is for us to be honest with each other."
"Very well—" Verice began
"I want to open the Great Hall, bring the business of the keep to its full operations as the heart of your power," Warna said. "We'll honor the dead, I promise you, and then celebrate the full Festival in all its glory."
"Then, after-" she faltered slightly. "After the Festival is concluded, after a week or so, we will quietly break our troth. I'll go to my great-uncle's and rebuild my life."
"This is what you want?" Verice asked, staring at her hand in his.
"Well, there's one more thing," Warna said, and now he felt her fingers tremble in his. She didn't continue, and he glanced at her to see her eyes downcast as well.
"Warna?" he asked in the barest of whispers.
She took a trembling breath, leaned closer, and kissed him.
Her heart was going to beat its way out of her chest. Warna took her failing courage into her hands and kissed Verice.
His lips were smooth and dry against hers, and when he didn't respond she felt all her hope die a long agonizing death. She missed the warmth of his mouth even before she pulled away.
She felt his hand on the back of her neck, and his warmth returned as he kissed her with a power that stole the breath from her body. Warm, wet, inviting, his mouth was all that and more. Somehow, without her even realizing it, she was wrapped in his arms.
She broke the kiss, trying to catch her breath. "I want you," she half-sobbed, half-laughed. "I want this, whatever this is, for as long as I remain." Words failed her now as she plunged along, trying to explain. "I want to explore you, to touch you, to know you, to have you know me. Please, Verice." She was more than willing to plead for this. "I know I won't be more than a flower in your garden, but please—"
He kissed her again, cutting off her words, and she moaned against him, sensations swirling around her like a tempest. Only one real thought remained. She'd be a brief moment of pleasure to him, that was certain.
But she'd love him for a lifetime, and beyond.
It meant separation, it meant having him, and losing him. So be it.
Even those thoughts scattered as his hands stroked her through her dress, and rational thought fled. She was lost in the wonders of his mouth, his touch, and a burning craving that flushed her skin.
He broke the kiss, his voice hoarse in her ear. "Warna, are you certain? Because—"
Warna rested her head against his, and nodded. "I talked to Evie, and asked her to make certain that I can't get pregnant. She's taken care of that with her magic." Warna swallowed hard, leaning back to catch his eye. "Verice," she whispered "Please."
A shadow crossed over him then, but it was gone in an instant, and something else burned there. She caught her breath.
"It would be my honor," Verice said, and the tightness in her chest eased.
"Here?" She trembled with longing, and a touch of fear. "Now?"
"No." Verice closed his eyes. "If you don't think there are more eyes on us now than there ever were at the elven court, you are mistaken." He darted in for a kiss, startling her as his tongue flicked out to lick her mouth. But he rose just as fast, and pulled her to her feet.
"Come," Verice said. "Let's see about getting you what you want."
Narthing stared at the ceiling of his small, clean prison and sighed. "Ersal," he said patiently. "You have many skills. Chess is not one of them."
Ersal sat opposite him, staring at the board and its pieces. "Just give me a moment," he said.
He'd appeared with lunch, bearing the set, and challenged Narthing to a game. Narthing had welcomed the lunch, his first real, solid food, and the company. But after one game it was fairly clear there wasn't going to be much of a challenge involved.
Ersal continued to study the board.
Narthing huffed out a breath. "It's mate in three moves," he pointed out.
"It can't be," Ersal said. "How so?"
Narthing reached over, and showed him.
Ersal shook his head in defeat. "Another," he said, setting up the board.
"Fine. But talk to me," Narthing said, waiting for Ersal's first move. "What's the word on m'lord and m'lady?"
"How can I talk and play at the same time?" Ersal said, reaching out to place a finger on his pawn and hesitated. Then he slid it along the board and sat back in satisfaction.
Narthing folded his arms over his chest.
Ersal rolled his eyes. "Lady Warna has been released by the healers, and I believe she's asked to speak to m'lord."
"Ah," Narthing said. "I wonder what that means."
"Nothing." Dominic breezed in with a tray. "Drink this," he commanded.
Narthing took the cup, eyeing it with trepidation. Dominic's medicines were as sweet as his personality. "Must I?"
"No, of course not," Dominic said. "As an adult, intelligent mael, you're free to ignore all of my treatments and advice and endure the consequences as you see fit. Or take my advice, drink the tea, and perhaps be released from my care as early as tomorrow."
"When you put it that way." Narthing rolled his eyes and drank the cup down in three quick swallows. The bitterness almost closed his throat. "Why do you say 'nothing'?" he forced out.
"Please." Dominic sniffed as he took the cup. "She's too common for a lord high baron. If there's any interest on his part, it's for a fling, surely. Nothing serious—"
Ersal coughed.
Verice and Warna were in the doorway, Ricard standing just behind looking appalled.
To Narthing's horror, there was a slight flush on Warna's cheeks, but Lord Verice's face was set in stone. They must have heard—
"M'lord," Dominic said. "I am pleased to be able to say that Captain Narthing can be released from our care once he's had a successful bowel movement. Possibly as soon as tomorrow morning."
Narthing covered his eyes as Ersal turned slightly purple with what had to be suppressed laughter.
"That's good to know," Verice said.
"Healers." Warna looked a little strained, but she chuckled. "I understand Evie saw to you, Narthing."
"She did," Narthing smiled. "She said she was just supplementing Dominic's fine work but I think it helped."
"I would point out," Dominic was looking down his nose. "That the Lady High Priestess is gifted by the Lord of Light. Any endowment of her power is to be treasured, honored, and respected."
"Oh yes." Narthing managed a straight face. "Especially if it improves bowel function."
Dominic curled his lip.
Lord Verice gave a slight cough. "This is excellent news. Captain Narthing, once you are free of this place, move back into your old chambers. The constable will see to it that my gear is moved back into my old room." Verice paused. "In the keep."
"M'lord." Narthing nodded his head to acknowledge the command.
"Seneschal Ersal," Lord Verice glanced at Warna. "Our troth is fairly common knowledge at this point. I would make it official unto my people. No ceremony, however, so as to honor her period of mourning."
Ersal beamed. "I would be honored to send out word, m'lord."
Verice continued. "Lady Warna is in charge of the planning for the Festival."
Narthing felt his throat close; so many bloody memories.
Lord Verice must have caught his thought. "I trust her to get us through this." He and Warna exchanged a long glance.
Narthing nodded.
"She'll need assistance sending invitations and organizing events. See to it, Ersal."
Ersal rose to his feet and bowed. "Of course, m'lord."
"My thanks." Lord Verice turned and gestured Warna out the door. But just in the doorway, he looked over his shoulder. "Priest Dominic," he said.
"M'lord," Dominic bowed.
"The Church of Palins has informed me that you are to be assigned to Edenrich on a permanent basis. When the summons comes to you, you have our leave to depart without any ceremony." His voice was hard. "They will make full use of your particular skills there, I am certain."
Dominic opened his mouth in surprise, but Lord Verice was already gone.
Chapter Fifty-Three
"He's right, you know," Warna said.
A scowl passed over Verice's face as they crossed the courtyard side-by-side.
"I am not a noble," Warna continued, taking a deep breath as she tried to match his angry pace. "Father was a spice merchant and Mother was—"
"Dominic is an arrogant bastard," Verice growled. He glanced at her, and then slowed to a walk. "Edenrich and the church are welcome to him."
"As long as they replace him with someone just as competent," Warna said, suddenly realizing that the keep seemed farther away than it had before. She hated to admit it, but she was tiring.
There was a sudden warmth as Verice put his hand on her lower back. She glanced up to find that he was giving her a serious look. "We did too much for your first outing."
"No, no," she protested. Odd. It wasn't that he was pushing, but that warmth at her back seemed to strengthen her steps. "I'm fine," she insisted, afraid that he'd use that as an excuse to put her off. Delay...other things. She didn't want to delay, didn't want to wait one more moment for—
"We'll eat," Verice said firmly as he led her into the keep.
Warna opened her mouth to protest, but then her stomach grumbled. The corner of Verice's mouth quirked and she had to laugh at herself.
"I'll have it brought to our room," Verice said. "Head that way. I'll be right behind you."
His hand lifted from her back, but Warna could still feel its warmth as she started up the stairs, feeling light of heart. Which may or may not have had anything to do with 'our room'.
She managed to slowly climb to the second landing before Verice caught up with her and swept her up into his arms.
"Verice," she protested even as she wrapped her arms around his neck.
"Save your energy for other things," he mock-growled.
Warna laughed, but a soft tendril of warmth wrapped around her that had nothing to do with the heat of his skin, and the strength of the arms that held her.
Nothing at all.
They hadn't been in their chambers for more than a brief moment before there was a knock at the door. Verice noticed that Warna's hands trembled while the servers set out their meal.
He was confident that it was anticipation. Or nervousness. So, he kept the talk light as their food was served, and the servants excused themselves. Nothing too serious; observations about the dogs, and the gardens. The dangers of working around rantha thorns.
Warna responded, and relaxed as they ate and talked.
He owed her a boon for so many things; that much was certain. If she wished to have him as a lover for the duration of the Festival, it was his duty to oblige. That she was inexperienced put an even greater responsibility upon him.
He'd slept with inexperienced women before. Never a human; but from what he understood human women were no different from faella. He wasn't concerned about that. What he wanted more than anything else was to make sure Warna experienced nothing but pleasure at his hands. She deserved nothing less.
He'd teach her all the pleasures he knew. It wouldn't touch him the way it would touch her, but he'd take the utmost care of her body and her heart.
As soon as she'd finished eating, he pushed back his own plate, stood and stretched, enjoying her wide-eyed attraction.
"Food's improved since the kitchens reopened," he observed as he reached for the side buckle on his armor.
"Far easier to cook on-site," Warna said. She stacked their plates, and was frowning at him, watching him as he fumbled with the buckle. "What's wrong?" she asked.
"Stuck," Verice muttered, as he tried to work the strap free. "Not sure what's—"
"Here," Warna huffed a breath. "I'll do it."
She moved closer, bending her head as she reached for the leather strap. Verice held his arm up high, letting her do the work.
"There," she said as she unfastened the buckle. "That wasn't so hard—"
Verice leaned in. "My thanks," he said softly.
She lifted her head, startled.
"Help me with the rest," Verice lowered his arm, brushing her hair back off her face and tucking it behind her round ear. "There's another," he pointed to the next buckle.
Warna blushed, her cheeks pink. "I see," she said, and started to work on the next strap.
Verice turned to give her better access, but he used the movement to his advantage. He lowered his head, so that his breath mingled with hers, and gently stroked the soft skin of her neck.
She shivered, but concentrated on her task. "So many buckles," she said as she tackled the next one.
"It needs to be tight," he explained. He curled his hand around her neck, letting his thumb stroke the soft flesh behind her ear and his fingers sheltered in the warmth of her hair. "Tight enough to keep me safe, flexible enough to let me move."
"You wore elven chain to the court," she said as she freed the last strap.
"True enough," Verice agreed. "But that's hardly for daily usage."
"Ah," she lifted her hands to his collar clasp, but he shook his head.
"The bracers first. Would you mind?" he asked, lifting his arm about her, ensuring that she stayed close. "Just the two clasps."
She turned in his arms, her back against his chest as he presented his forearm to her. She reached for the clasps.
"Careful," he cautioned.
The clasps snapped open. "Oh," she jerked her head slightly at the blade hidden within.
Verice leaned in, and nuzzled her ear. "I never like to be without a blade or two," he whispered. He breathed on her soft skin, and felt her shiver in response.
She tilted her head, giving him a glance over her shoulder as she pulled off the bracer, careful to set it, and the concealed blade, on the table. Verice raised his other arm, letting her work on those clasps. He slowly moved closer, bringing his free hand to her hip, then sliding it over her stomach with a firm pressure.
Her breathing quickened. She removed the other bracer, this time expressing no surprise at the second hidden blade.
She turned back then, in the circle of his arms. The sweet scent of her skin warmed him as she reached for his collar clasp. He lifted his chin, waiting...a soft kiss pressed to his jaw.
He murmured his approval, pulling her close, nuzzling her face until she lifted her mouth to him and he could claim it with a kiss.
Gently, he reminded himself, as much as he wanted to plunge within its depths. She tasted salty and sweet. He went slow, with a gentle firm pressure, as she leaned in closer, and of her own volition opened her mouth to him.
Even then, he just nipped at her lower lip, darting his tongue within to tease, before retreating back. Warna buried her hands in his hair, holding his head, and he returned the favor, one hand buried in her hair, the other at her lower black, pressing her against him.
They broke off when breath became an issue. Still he held her close, unwilling to release her.
She swallowed with a shudder and a sigh. "Verice," she breathed into his ear.
"The clasp?" he whispered.
With a chuckle, she fumbled with the metal, then eased her hands into the opening, pushing the armored tunic open.
Once the leather parted, he rolled his shoulders. Without any further encouragement, she eased the leather back, displaying the linen tunic beneath.
"Careful," he warned again.
She lifted an eyebrow at the blade concealed at the neck. "One or two?"
"Or three," he said, taking the armor from her hands and tossing it on the table.
With a soft stroke, Warna smoothed the linen tunic over his chest. Her hands left a trail of warmth through the cloth as they traced down and around to his waistband. There, she hesitated, and glanced at him.
He waited, keeping his own hands on her hips, and simply lowered his nose into her hair and took in her sweet scent.
There was no need to hurry. Discovery of a new lover, and a first lover, only happened once. They could take their time feeling, touching, tasting, exploring. Slow was preferable.
But he couldn't help a rumble of pleasure when her hands slid along his belt, slipped around his back and started to tug his tunic free.
Followed by a clatter as his throwing knife fell to the floor behind him.
Warna's head jerked back, her eyes wide, then narrowing. "Or four?" she asked.
"Sorry," Verice shrugged. "I was...distracted."
She pulled the shirt up. He cooperated, sliding the cloth over his head and easing his hair free. She laughed as she tugged it off his arms. She caught her breath as her gaze lingered on his chest.
He took the shirt from her hands, and threw it on the floor before drawing her in closer. She rested her hands on his bare chest.
"Are there any other surprises?" she inquired with an impish look as her fingers brushed his belt.
"There might be," he whispered, nuzzling her ear. "Feel free to explore, if you wish."
Chapter Fifty-Four
If she wished? She wished for nothing more, and yet...
Warna took a breath, hesitating, letting her fingers rest on the leather of the belt. She dared, but she also didn't dare. She felt like she was trembling on the brink of something amazing and delightful, and terrifying all at the same time.
Verice stood, unmoving, like a rock. His chest rose and fell almost imperceptibly. His skin was dusted with silver hairs that trailed down his chest, narrowing as they reached his waist. She licked her dry lips. Her fingers seemed to take on a life of their own, loosening the belt, untying the laces, slipping her fingers around and back and down to slide the leather over his hips and—
Verice must have helped, because it seemed that he was suddenly, gloriously naked, stepping out of the trous as they fell to the floor with a grace she was certain no human could achieve.
"Do I please you?" he rumbled and she could forgive the lilt of arrogance in his voice. He was certainly entitled. She glanced up to see the glint of humor in his eye, with a touch of something else.
She wanted nothing more than to touch, to explore further, but instead she put her hands up to splay them over his chest, went up on tiptoe, and kissed him. He caught her mouth and returned the kiss.
She didn't resist when he stepped back, following his lead as they kissed. She was slightly shocked when he sat abruptly on the edge of the huge bed, and pulled her down next to him. It was the logical next step of course, but she felt scandalous.
"You're seducing me," she whispered as she tingled with excited realization.
"If so, I'm not very good at it," he chuffed. "I'm the one who's naked."
Warna laughed at that, for it was only the truth. She pushed him down, suddenly greedy to touch every inch of his skin, explore every aspect of his body. He offered no resistance, letting her hands trail down, drinking in the sight of all that he—
What caught her eye was the horrid scar that laced his thigh, running from the outside of his hip inwards at an angle.
"Verice," she whispered, reaching to trace its length.
His leg twitched and he caught her fingers half-way along the scar. He grimaced an apology. "It's still sensitive," he said.
"From the Festival night," she said. "You almost died."
"I healed," he said with a shrug. He kept her hand in his, turning it over palm-up. "It will fade, given time. Fifty years or so."
Fifty years. As if it was nothing. As if it wasn't a lifetime.
He seemed to sense the way her thoughts were tending, because he lifted her hand and kissed her palm, letting his tongue brush the skin. Keeping his eyes on hers, he breathed on the damp patch, sending shivers down her spine. "What matters is that I am here now, and healthy." He took her hand and pressed it against his length. She blushed hotly as she felt him beneath her hand. "And I believe you wanted to explore."
Warna couldn't have made a sound if she'd tried. Her throat closed up, her mouth dry. It was what she wanted, and the thought brought a warmth to her body and loins that swept over her like a fire.
She just wasn't sure where to start.
Verice moved then, keeping his hand over hers, and reached out to cup her neck, pulling her in for a kiss. Her hand tightened, and his body moved in response, and suddenly her reservations were gone.
He was a song, a perfect song, with endless lyrics she'd sing the rest of her life, and a melody she'd never be able to quantify.
And beautiful, so beautiful. Like a marble statue, made even more perfect by the fact that he lived and breathed and had calluses on his hands and scars on his body.
His long silver hair cascaded over her hands as she dared to trace the points of his ears, stroke his neck, place kisses along his collarbone. The silver hairs on his legs were coarse on his calves and thighs, but seemed to turn to silk as she neared his core. He didn't resist, didn't stop her explorations. Just stretched out before her and let her have her way. It was only the trembling of his body, the shortness of his breaths that made her think she'd erred somehow.
"Verice?" she whispered, sprawled next to him.
The intensity of his silver eyes caught her. "I'm roused, that's all," he said tightly. "Do not stop."
"Oh," Warna glanced at him, realizing what she'd done. "I've never done this before. I'm sorry—"
"I'm not," Verice said.
"What can I—" Warna started, but Verice reached for her hand before she said another word.
"Finish what you've started," he growled.
And to her amazement, she did, watching as he threw back his head to expose that long, elegant neck. Watching, as his strong warrior body quivered and succumbed to her touch. Watching as he shattered in her hands.
Verice regained his senses to find Warna curled up in his arms, the fabric of her skirts covering his legs. For a moment he enjoyed the pleasant sensation of being sated and relaxed. But then guilt rose up. He tightened his arms around her. "Warna?"
"Verice," she said against his chest, her breath warm on his skin.
He couldn't see her eyes, and didn't know what she was thinking. He cleared his throat to offer his apology. "Warna, forgive me—"
"For what?" she asked.
He frowned. "I meant to see to your pleasure first. Not take my own before you'd had a chance to experience—"
"It was amazing," she whispered. "That I could do that to you...make you feel that way." She lifted her head, her eyes glowing in satisfaction. "And there's more to it, isn't there?"
"Yes," Verice couldn't keep his amusement out of his voice. "A lot more. But we've no hurry, Warna."
She frowned. "No more waiting."
"Impetuous humans," he teased.
"Staid elves," she sat up and considered her dress. "It was messier than I anticipated."
He laughed, letting it shake his entire body. Warna gave him a delighted look.
"Well, there's a remedy for that," he said, reaching out to trace her collar around her neck. "You are overdressed for the occasion." He hooked his finger on the fabric and gave a tug. "Besides, is it not my turn to explore?"
Chapter Fifty-Five
Warna felt the tug of the fabric against her neck, and the heat of his hand through the cloth. As much as she wanted to, as much as she wanted his hands on her skin, she hesitated.
Verice knew it in an instant. "What's wrong?" he asked, releasing her collar.
She looked away, licking dry lips. "It's just...in your lifetime, you've been with thousands of faelles and—"
His snort was explosive. "Thousands?" Verice choked, clearly amused until he saw her face. "Ah, Warna," he said, and sat up enough to reach for the bedding that had piled at the end of the bed. With swift movements he pulled her down beside him, and covered them both in warmth.
Warna didn't resist his tugging. He waited until she'd settled beside him before he spoke. "I admit I am experienced," Verice's voice was warm in her ear. "And in my early days when I was a hundred or so, I was fairly wild. But thousands?"
She shrugged, hiding her face within the covers. "I just don't see how I can compare. Elven women are lovely, and seemingly so perfect."
"The important word being 'seemingly'," Verice said. "Don't be taken in by appearances, Warna."
"But how do human women compare?" She rose, letting the blanket slide off her shoulders.
"I wouldn't know," Verice said. "You are my first."
"Oh," Warna blinked in surprise.
"I have to say," Verice pulled her back down into his arms. "You are amazing."
He turned on his side to face her, pulling her close. "Not that I've seen much, mind, except when you were—" he stopped himself.
"When I was vomiting," Warna said ruefully.
"Well, yes," Verice said, his tone dry and serious. "But even that you did in your own special way."
Warna couldn't help laughing.
Verice reached up, and ran his fingers through her hair, tracing over the tops of her ears.
"Would you like to know what I have learned over all the years? That what really matters isn't the physical attributes or the skills of a lover. The size, the shape, the appearance...that's secondary. It's important to find your lover pleasing, but what really matters is the person you are with, and the depth of the feeling you have for them."
She reached then, to smooth back his hair, and trace the tips of his pointed ears. "Do I please you?"
"Oh yes," Verice whispered. "And I believe it's my turn."
He threw back the blanket, so gloriously naked underneath, and reached for her.
She couldn't have said where her clothing went. But once it was gone, she reveled in the touch of skin on skin from her head to his toes. Her body couldn't contain all of these sensations another moment. She reached for him, looking for an anchor in the wildness. Her hands wandered over him, stroking and gliding over every lovely inch.
And his hands, his wonderful hands, caressed every curve of her breasts, her hips, her thighs, lingering between her folds until she writhed beneath him, begging with soundless pleas for so much more.
He held her close, his hand relentless within her depths, and put his lips to her ear. "It's all right, Warna. Let go. Explore your pleasure for me."
Her entire body seized, every muscle tight with the pleasure of it all. She cried out, and for long, lovely moments, was lost in white heat and light.
Half-asleep, she felt him move, felt him cleaning her with a soft cloth. She murmured in pleasure as he pulled the blankets over their rapidly cooling bodies.
He settled into her arms, pulling her close, entwining their arms and legs deep in the comfort of the bed. "There's more?" she whispered, almost half-afraid of the possibility.
"There is," he chuckled into her hair. "But the delay of pleasure is a pleasure in and of itself."
"Any more, and I'll die," Warna whispered back.
If Verice said anything more, it was lost as she drifted off to sleep.
Verice awoke first, to the hints of dawn coming through the windows, and Warna in his arms.
She radiated warmth, her head on his shoulder and her blonde hair spilling over the pillow. Verice reached and tucked the hair behind her ear, his fingers lingering against the soft skin of her neck. Her pulse was warm and steady under his fingers.
She was beyond anything he'd experienced before. He'd though he was gifting her a boon, but in truth she'd given him far, far more.
Amazing in her passion, in her willingness to let him lead, and then in her eagerness to show what she had learned. There was a playfulness to her loving that he'd never encountered before. Maybe it was the fact that she was human.
Or maybe it was just because she was Warna.
He'd not taken her, and he wasn't going to until he was certain that she was ready. This he could gift to her, and he was determined that they'd take their time.
He pulled himself out of her embrace, and left the warmth of their bed. Warna made a small sound of protest, but didn't awaken.
Pulling on trous, he went to the outer chamber. The dogs were all sprawled on the hearth rugs. Brindle sat up from the midst of the pack, yawning and blinking at him.
A servant appeared almost immediately. Verice sent a message to Narthing cancelling his normal routine for the morning. It could wait for a while. He also gave instructions not to be disturbed. They couldn't shut out the world forever; there was too much work to be done. But they could steal a few hours.
As he headed back into the bedchamber, Brindle curled back down with a sigh.
Verice closed the door, and padded back to bed, discarding his trous along the way. He crawled into the warmth of the covers.
Warna was blinking at him sleepily. "All's well?"
"Very well," Verice murmured. He stretched out, pulling her warm, unresisting body to his, and claimed her lips in a gentle kiss.
She smiled against his mouth. "Not time to get up yet, is it?"
"Not in the sense you mean," Verice said, tracing a line of kisses along her neck.
Warna laughed, then matched his every demand with one of her own.
Later, much later, Warna stared down at the account books, her eyes half-closed as she remembered the previous night. And awakening this morning. Remembering Verice's touch, his skin, his mouth—
Ersal coughed.
She brought herself up with a jerk. "Ersal? Did you say something?"
"Well," Ersal was looking at his own accounting, trying to hide his amusement and failing. "I did ask a question a few moments ago. Did Janella include new napkins in the order for the table linens?"
Warna blinked. "Did we place that order yet? I didn't think we had."
"I'll check," Ersal said.
Warna returned to her accounts. But honestly, how was she supposed to be able to work? How was she supposed to focus on anything except how Verice made her feel?
Somehow, she felt like she'd been let in on a huge secret, one that made the entire world feel bigger than she'd ever dreamed. She wanted to sing of it, but she'd never be able to find the words to communicate the experience.
Or that she'd be able to sing in public.
But in private, now. In the privacy of their room, with just she and Verice, she could sing to him, of her feelings, her longings.
She hesitated at that thought.
No, that wasn't fair. She wouldn't burden him with those things. She wouldn't cling. She'd made a bargain and she'd live with the terms. She'd keep her songs to herself, to be sung...later. When the troth was broken. When she'd left this place. After Verice had shared all the physical aspects of lovemaking with her.
Because she did want to know all of it. Verice had awakened her with kisses and touches, and brought her to shuddering pleasure with just his hands. He'd promised more of the same tonight, leaving her sated and gasping in their bed.
He might be determined to move slowly, but Warna had her own feelings on the issue. Her skin tingled at the thought.
She fought to bring her mind back to the task at hand. There were two weeks before the Festival started, and so many decisions had to be made. She needed to be thinking about the work before her, and not about enjoying the time she'd have with Verice.
And wonder what else Verice had to share with her.
"Then there's the matter of the ale to be ordered," Ersal's voice cut through her thoughts. "Given the crowds, I'd thought perhaps two duns, but maybe we should consider three."
Warna sighed. "Three would probably be best."
Narthing was pleased to be back in his regular chambers in the barracks. But he was even more pleased to see Lord Verice looking more relaxed.
Not to the degree that he was laughing or smiling. But his shoulders were looser under his brigandine, and his eyes warmer.
At least until he started talking about the security for the Festival with himself and Constable Ricard.
"I want everyone trained," Verice stood, his arms crossed over his chest. The maps of the barony had been replaced with the schematics of the castle and keep. "I want everyone drilled in responses in case of attack. Everyone, from the clerks to the stable boys. Where to go, what to do." Verice leaned on the table, his eyes now sharp as daggers. "I'll not be caught again. Not ever again."
"Agreed," Narthing said.
Ricard nodded. "Easy enough to do, Lord Verice. We can see to it over the next few weeks."
"The Lady Warna, as well," Verice said. "I'll train her myself."
"If they attack, they'll rue it," Narthing said.
"It's not 'if', Narthing," Verice said grimly. "It's 'when'."
Chapter Fifty-Six
It was three days before Warna had a glimmer of a rational thought in her brain.
Yes, she worked with Ersal and the others. Yes, she'd started making decisions about the celebrations. Hopefully, good ones; it wasn't like she could remember them. Yes, she'd some semblance of sanity, but that was all it was. For in truth, it was the nights in Verice's arms that seemed the center of her existence.
It wasn't just the physical aspects, although just the thought of what they'd done, and what they'd do, and what they hadn't done yet was enough to turn her body into a heated lump of pure desire. Verice was still insisting that they move slowly, pox take the mael. Each night she'd argued, he'd touch her and the argument was over, for all intents and purposes.
No, it wasn't just that. It was the closeness. The feel of his leg against hers, or the smell of them in the bedding. Or arguing over whether the dogs would sleep in the bed with them.
She'd won. The dogs slept on the floor.
But as glorious as it was, Warna was suddenly counting the days until the Festival of Light and Laughter started. She began to feel a flutter of panic.
Verice was relying on her to find a way to open the Great Hall of the keep, and for the life of her she hadn't any ideas. She remembered what she'd seen when she'd explored inside, the broken furniture, the dried blood. There had to be a way to honor the dead and yet bring the place back to life, but she wasn't sure quite how to accomplish that.
The Festival lasted seven nights. Back home, most holidays were a few days at best.
In Tassinic, they'd combined the elven and human traditions into a seven-day long party, and while she applauded the idea, it made her task just that much more overwhelming.
Warna frowned. Hadn't Ersal said something about a Priest of the Lady at the church in the city? He might have an idea or two, or at least be someone she could talk to about it without fear of raising old sorrows. She wasn't above asking for help. This was just too important.
Verice entered her sitting room, lifting an eyebrow at the vases spread around the room.
"The gardeners have started on the flowers, trimming some things back," Warna explained. "I didn't want the blooms to be wasted."
"I'll have to check their work," Verice said, coming closer, careful not to let his sword hit any of the vases. "I was wondering if you were free, m'lady?" He leaned on the arms of her chair and kissed her. Warna caught her breath at his touch and taste, and returned the kiss with joy.
Verice was breathing deeply when she finally broke away to take in air. "For lunch?" she asked, licking her lips.
"Or other things," Verice growled.
She reached up, tangled her fingers in his hair and pulled him down for a kiss that left no doubt as to her answer.
Or availability.
Later, when they sprawled on their bed, sated, and breathless, she asked. "When will you show me the rest? Teach me more?"
"Impetuous human," he said softly.
"Staid elf," she whispered back. She curled up, her head on his chest. "Could we make a trip into town? There's someone I need to talk to."
"No," Verice rolled over onto his side, and pulled her close.
"Ersal tells me there is a Priest of the Lady at the church," Warna placed a kiss on Verice's collarbone. His skin tasted salty, and she blew a breath over the moist spot.
"Summon him here," Verice murmured, cupping her breast.
"Verice," she pushed at him back far enough to look into his eyes. "You don't summon a Priest of the Lady. You go the church and you approach them with respect and humility," she started to laugh as he raised an eyebrow. "Well, that's what we poor humans do."
"Unnecessary and far too dangerous," Verice said firmly. "I refuse to authorize any trips into Octara."
They left at dawn.
"Stubborn woman," Verice grumbled under his breath as he mounted. Warna was already up on her horse. Her smile was soft, but he could see the triumphant gleam in her eye.
Once she'd won his concession to this little outing, she'd decided on five other tasks that could only be taken care of in the city.
She'd also sent word to the church, asking when it would be convenient to call upon Priest Dorne, who it seemed, kept early hours.
At least he'd managed to set the size of the escort. With any luck, they'd be done with their errands and out of the city before the crowds developed.
"You have the watch, Constable." he gave a nod to Ricard.
"Aye, m'lord." Ricard responded, and Verice set his heels to his horse, leading the way. They started off with a clatter of hooves on cobblestones.
As they approached the gate, Warna slowed her horse. Verice shot her a glance. She lifted both eyebrows and tilted her head toward the gate.
He snorted.
She laughed, a lovely light sound in the morning air, and urged her horse through the gates.
The ride down was quick. Verice set a fast pace, and with the streets barely awake, he could keep that pace as they made their way to the church.
They were greeted by a faelle acolyte.
"Priest Dorne?" Verice asked as he dismounted, and went to assist Warna.
The acolyte smiled. "He's in the bakery, m'lord," she said with obvious delight.
"Ah," Verice said. "We can wait until—"
"Nay, m'lord." The acolyte's smile grew even wider. "He'll be some time. I'm to take you to him."
To Verice's surprise, Dorne wasn't supervising the bakers.
He was baking.
"Welcome, Lord High Baron, Lady Warna." Dorne was a small, dark human with olive skin and a bit of a paunch. He was dressed in the traditional black robes of a Priest of the Lady, but with an apron over top, and a dusting of flour overall. "May I offer you kav?"
On the table before him was a huge lump of dough. Dorne was shaping loaves, making shallow slices across the tops, basting them with egg, then sliding them in the huge ovens behind him with a large wooden paddle. His hands never stopped as he gestured for them to take seats on a long bench opposite him.
"Please, be seated," Dorne said.
The brick ovens behind him radiated heat, and the room smelled of yeast and bread. Along the length of the room, other bakers were working, taking out the finished loaves. Verice settled on the bench, adjusting his scabbards, trying to keep them out from underfoot.
"Please," Warna said as she settled beside him. She took a deep breath. "It smells wonderful," she said.
"My thanks," Dorne said. "But I can scarce take credit for a bit of flour, water, yeast and heat." He chuckled. "Still, a few warm slices might not go amiss, eh?"
"We already ate," Warna made a token protest.
"What does that have to do with anything?" Dorne asked.
Verice found himself with a warm, buttered slice in one hand, and kav in the other. Warna had the same, a bemused look on her face.
"Eat first," Dorne said. "Then tell me how I can be of assistance."
Warna bit into hers with obvious enjoyment. Verice followed her lead. The bread was good, slightly sweetened with honey. The crust was crisp and chewy but the bread itself seemed to melt in his mouth.
Dorne nodded, seemingly pleased with their enjoyment. He continued his work, preparing the loaves for the oven. "So, you have something you wished to ask me?"
Warna glanced at Verice, drew a breath, and started to explain the situation.
Verice had dreaded this. Dreaded trying to explain to someone how he'd reacted, reliving the pain and grief all over again as they explained the situation. To tell the tale was to relive it, and his stomach had clenched at the thought of talking to anyone about the problem.
But as Warna described the wreckage in the Great Hall, Dorne just kept working, his hands busy constantly as he nodded his understanding. Maybe it was the heat, maybe the warm bread in his belly, maybe the quiet repetition of Dorne's task, or maybe just Dorne's quiet acceptance that made it easier to discuss.
"So, we need to find a way to honor the dead, and yet restore the Hall," Dorne said quietly.
"Yes," Warna said. "I'm not really sure how to do that, and I was hoping that you might know, or have some ideas."
Dorne shook his head ruefully, his hands pausing for just a moment. "I have a few ideas," he said. "Give me a day or two to think on it. I'll come to the keep so we can discuss it in detail."
"Thank you," Warna sighed, giving Verice a questioning smile.
Warmth washed over him that had nothing to do with the heat of the kitchens. She was worried about him, concerned that he'd been upset by the re-telling. "All's well," he murmured, if only to reassure her.
But to his surprise, he found he'd finished his bread and kav. He felt lighter somehow, as if he'd taken off plate armor after a long battle. Something in his shoulders eased as he found it easier to breath.
Warna's relief was clear as her smile widened.
Verice found his voice, "My thanks, Priest Dorne. For the food, and the assistance."
"You are most welcome, m'lord." Dorne turned to shove another loaf in the oven.
"We've other errands," Warna said. "But if there's no hurry," she touched Verice's arm. "I'd like to pay my respects in the Sanctuary. It won't take a moment."
"Of course," Verice said and rose with Warna.
Dorne gestured to one of the cooks. "Show Lady Warna to the Sanctuary," he ordered.
"I'll meet you at the horses," Warna whispered, and was gone.
Verice hesitated then settled back down on the bench. He watched Dorne work for a while, and the other man seemed content with the silence.
"You're different from Dominic," Verice finally said.
"In that I am not a pompous ass?" Dorne paused in the act of slicing a loaf. His dark eyes pierced Verice. "Or that I am human?"
Chapter Fifty-Seven
"Both," Verice said, meeting Dorne stare for stare. "It seems odd to me that you are appointed to replace Dominic when the hierarchy of your church is well aware of my preferences."
"No odder than Lady Warna appearing at your side," Dorne said dryly.
Verice bristled.
"Peace." Dorne set down the loaf in his hand. "Lord High Baron, I know full well that while you do not follow our faith, you are not ignorant of its tenets."
"True enough," Verice said.
"I cannot replace Dominic," Dorne continued. "I have no skill at healing, first off, and second, Priests of the Lady are wanderers. We do not take administrative posts within the church. As you are well aware."
"Yet here you are," Verice growled.
"Yet here I am," Dorne said calmly. "Taking up the loaf and the knife. Word came of a need, and I am here to serve until such time as a permanent replacement can be found. Someone half-elven, as per your requirements." He paused, a flash of sorrow in his eyes. "As it is, I have some experience with planning mourning ceremonies."
"I'd offer thanks again, for your willingness to aid Warna," Verice said.
"But no apology for your obvious hypocrisy?" Dorne asked.
"Watch your tongue," Verice rose to his full height, the bench clattering the floor behind him. His hand went to the hilt of his sword.
"Who else will confront you?" Dorne demanded, standing there, covered in flour and not backing down an inch. "Who else will make you look at your own actions?" The smaller man snorted. "Not to mention the fact that seeing you both together, it seems to me that you fear the pain you are already suffering. Can't you see that—"
"Lord High Baron!" one of his men ran into the kitchen with the cook that had escorted Warna at his side. "M'lord, there's trouble in the courtyard. Lady Warna—"
Verice took off running.
"You idiots are going to get yourself killed!" Warna called out as she tried to stay calm.
They had waited until she'd emerged from the church and mounted to swarm into the courtyard, trying to separate her from her escort, banging drums and shouting, demanding tribute for the Lady of Laughter. She'd recognized the company of actors from before. Especially their leader, the one with the kitchen pot on his head and some sort of serving dish as a shield.
Verice's lieutenant had acted quickly. Ustov and his men cut between the mob and her, forcing them back, away from Warna and her horse. The actors re-grouped to the outer gates of the church's courtyard, blocking the exit.
"Stand and deliver," Master Zester shouted as the crowd swirled around behind him. "Tribute is owed to the Lady of Laughter!"
More drums, trumpets, and voices sounded. Warna's horse threw up its head and pranced a bit at the noise, but it seemed more annoyed than frightened. She kept her seat easily enough but one of her guards took the precaution of grabbing the bridle.
"Dismount, Lady," Ustov urged. "In case—"
"Cease that racket," Warna called to Zester. "And Ustov, sheath your weapons. There's no need for bloodshed over something this foolish."
Ustov had his sword out, his men were lined up with their shields and naked swords. In another moment something incredibly stupid was going to happen to someone...
"What is the meaning of this?"
All movement ceased, all heads turned to the speaker. Verice was standing on the steps to the main church doors, looking every inch the warrior. His blade was out, and Warna knew full well that he'd not sheathe it at her request.
He also looked very, very angry.
"M'lord," Master Zester, stepped forward, his pot rattling on his head. The noise rose in the air as the drums, rattles and horns were brought into play. Zester raised his voice to be heard. "We hold your lady hostage for—"
Verice started toward him. "You threaten my lady?" his voice cut through the air. The noise and the crowd behind Zester melted away as he advanced.
Zester squeaked, but stood his ground. "M'lord, I can explain—"
Verice ignored him as he moved to Warna's side. He paused by her knee. "Are you well?" he asked quietly as his warriors moved up beside them.
"I'm fine," Warna reassured him. "I think they just wanted your attention—"
"They have it," Verice growled, swiveling to stare at Zester.
"M'lord," the actor removed his pot and clutched it to his chest as his men clustered around behind him. "We meant no offense," he said, nervously eyeing Verice's sword. "We'd only meant to ask permission to perform for the castle at the Festival. A tribute is owed to the Lady of Laughter, after all, and we've not been permitted within those walls for almost a year." Zester straightened. "It was a poor joke on the part of our company, m'lord. I beg the Lady Warna's forgiveness and your own."
Verice stared at the man. "Warna?"
"Idiots and fools," Warna scanned the crowd. "It's only by Ustov's good sense that they weren't cut down or trampled. Still no one is hurt," she continued. "One can only hope they are better actors then one might think."
"M'lady," Zester protested.
Verice sheathed his sword. "Very well," he said, and gestured for his horse. The warriors all mounted as well, with Ustov giving the actors a very grim look.
"Lord High Baron," Zester persisted. "About the Festival..."
Verice stiffened in his saddle. Warna glanced over and saw Dorne in the doorway of the church, wiping his hands on his apron. Verice was staring at him, an odd look on his face.
"Very well, Zester," Verice turned in his saddle. "You may set up your stage for one day and night during the Festival. Contact my seneschal for the details."
"My thanks, Lord Verice," Zester said.
"And Master Zester," Verice paused as Ustov lead the others on. "Present a comedy. We've had overmuch tragedy of late."
Verice forbade Warna to dismount in the markets, and for once his stubborn woman listened.
He knew full well that this was a breach of trade custom. One usually walked through a market, leaving horses on the outskirts. But custom could go hang from the battlements. He wanted her up high, where he and his men could scan any that approached her.
And they all approached her. Word must have spread that she was in charge of planning the festivities at the castle. Every merchant with a slice of cheese, mug of wine, pastry, sausage or fruit wanted her attention. And that was just the food merchants. They'd the entire length of the market to go yet. Verice had the men surround Warna, but not close enough to hinder the merchants from drawing near.
Close enough to keep a watchful eye on them, though.
He'd have brushed them aside, or referred them to Ersal, but Warna...she seemed in her element, talking, laughing, eyeing the items and asking prices. No tasting - he'd put stop to that fast enough. Still. She was enjoying herself.
Verice huffed out a breath. It was a pleasure to see, but it was going to take forever.
"M'lord," Ustov moved to his side, scanning the crowd as they walked the horses along. "M'lord, I ask forgiveness. That incident, back in the churchyard, it should never have happened. It was under my command, and I take full responsibility for—"
"Rest easy, Ustov," Verice said. "You did well."
"My thanks, m'lord." Ustov frowned. "They moved fast, m'lord, swarming in and trying to cut her out and away from us. Almost as if they were...more than actors. I am not sure I trust those humans."
And there it was, from the mouth of one of his own men.
"Master Zester has had a troupe here for many years," Verice said. "I've no reason to doubt him. Still, we'll mention this to Captain Narthing. Forewarned is forearmed."
Ustov nodded and drifted back toward the rear, leaving Verice to his own, uncomfortable thoughts.
Dorne's words pricked at his conscence. In the past, he'd striven to be fair to all his people, human, elven, mixed. But now, especially since the attack, he wondered if that was true. How much of his suspicion of the actors was because the majority of the company was human?
He'd been about to deny Zester, until he'd seen Dorne standing there. True, it paid to keep one's friends close, and one's enemies closer, but he'd seen no wisdom in inviting a troupe of humans into the walls. But was that more because they were humans than anything else?
He'd tried to ensure equal justice in his courts for all and sundry, but he hadn't allowed a human within the walls of his castle for many years. Not until he'd carried Warna within the gate in his arms. That was an ugliness within him that he truly did not wish to see, and could not ignore.
They'd passed through the food merchants, and were entering the cloth and leather-workers. People were running into the street with bolts of cloth, and waving lace and ribbons. Warna's horse shied a bit, but she got her under control. "Here, now," Warna called out. "Mind yourselves around the horses."
Verice moved up then, to ride beside her, frowning at the various men and women. They backed off a bit, still trying to get Warna's attention. One in particular had a bolt of velvet, as blue as the sky itself. "A new dress for the dancing, m'lady! I can have it done in a trice!"
Warna just laughed, and shook her head.
Verice frowned as they moved past the man. "You should have new dresses, for the festivities," he was thinking out loud. "Not to mention jewelry. I've some diamonds that you could wear, but you may wish to buy something—"
"No," Warna said.
"But," Verice was startled at the look on her face.
"I'll take nothing from you but what I need," Warna said firmly. "And nothing more than what my lidded basket contains when I leave."
Verice's heart turned to stone.
Chapter Fifty-Eight
Her words and her tone struck like a knife, but he kept his face blank. "I meant no offense," he said quietly.
"None taken," Warna had stopped her horse to take up a spool of ribbon, running it through her fingers. She appeared to be inspecting it closely, but Verice saw her glance his way. She smiled at the merchant and handed it back. "Please be sure to approach the seneschal, and tell him that Warna asked to see your wares."
The faelle's face lit with delight. "Bless you, m'lady," she called as she retreated from the crowd.
Warna started her horse forward, giving him another glance. "But when I leave—"
"We can discuss that another time," Verice said, casting a glance around them before he looked at her again.
Warna nodded her understanding.
"As my betrothed, you represent Tassinic when you sit beside me on the high seat," Verice continued, keeping his voice low. "It would be a topic of discussion if you were not suitably clothed."
They continued on in silence, with Warna outwardly admiring the items being shown to her. "I hadn't thought of that," she finally admitted.
"There's jewelry in the vaults," Verice said. "If it is your wish, it can be returned to the vaults after the festivities." He rolled his eyes at her. "And a few dresses will not beggar me or the barony, m'lady."
Warna laughed, then shrugged. "Very well, m'lord."
Verice raised an eyebrow. "That blue cloth was fetching," he coaxed. "I could go back—"
"Velvet?" Warna snorted. "At that price? Think again, m'lord."
"I defer to your wisdom in the matter," Verice said, pleased when Warna laughed again.
But she also gave him a piercing look.
"I'm still not taking anything with me when I leave, Verice."
"A topic for another time," Verice said as pain rose in his chest. This was not a conversation he wished to have in the streets. Seeking to change the subject, he rose in his stirrups, then settled back down in his saddle. "It would appear that the furniture makers' lane is ahead. Perhaps we could pick up the pace after this corner?" Verice raised an eyebrow at Warna. "Before they start coming out carrying chairs and tables?"
Narthing was pleased to find that the stairs to Warna's office didn't wind him. At this rate of healing, he might even be able to dance at the Festival.
Constable Ricard had accompanied him, keeping a weather eye, but even he gave a nod of satisfaction as they approached the door. "I'll leave you to it, then," Ricard paused outside the door. "I'm off to drill some of the young'uns."
"You're just avoiding the desk work," Narthing said.
"Leaving such things to you and the Lady Warna," Ricard said innocently. "Fine, capable hands."
Narthing muttered something rude under his breath as Ricard strode off. Then he squared his shoulders, took a deep breath, and knocked.
"Enter," Warna called.
As he'd expected, the room was filled with a chaos of people and paper. The people were pulling chairs close; the papers were spread over every surface of the room, fighting with the vases of flowers for space.
Warna laughed. "Just move these out of the way," she said, placing a vase on the floor.
Ersal was there, along with two of his assistants. Warna had recruited Farnor, the quartermaster and his clerk. Janella had four people with her, because of the demands on the housekeeping staff. Dominic's replacement, Priest Dorne was already seated at the side of Warna's desk. Even Lord Mayor Pernard had come.
Lady Warna took the chair behind her desk, and seemed in complete command. "Narthing," her face lit up. "We've three days left to get this chaos under control."
"Might as well try to organize mayflies," Janella sighed. "For all the good it will do."
"No plan survives the first encounter with the enemy." Narthing smiled as he took a seat.
"But we need review our plans, none the less," Warna said firmly. "So, let's start with the First Night."
Narthing caught his breath as a sudden stillness filled the room. His own pain caught him off guard, with a sudden swift clutching of his heart. The faces around him all reflected the same. They'd all known it was coming, known that it had to be done. Now it was here, and no easier.
Warna looked stricken by her own words. For a moment, he thought she might start crying, but she took a deep breath and continued. "Priest Dorne and I have talked. We'd like to share our thoughts on how we should proceed." She dropped her eyes to the scroll that was set out before her. "I want you all to aid us in this; to honor the dead, and re-open the Great Hall. So, if you have anything to offer, please do so."
Narthing moved to the chair she gestured him to, glad of a chance to cover his emotions with movement. The others organized themselves around Warna's desk.
"We'll start with a call to prayer," Priest Dorne started. "And then—"
Narthing concentrated, not wanting to miss a word.
Surprisingly, with Dorne's calm demeanor, they managed to review the plan for the entire First Night fairly quickly. Everyone had contributed, and the final plan met with general approval.
Warna handed off the last scroll to one of the assistants for copying, and heaved a huge sigh. Her brown eyes were warm as she surveyed them all. "I think the hardest part is behind us. Let's get some hot kav, and then continue."
The others relaxed as well, and the tension in the room eased.
What a Baroness she'd make, Narthing thought as he took a mug of kav from a servant. She'd the deportment and skills, that was certain. With this Festival, she'd have restored the castle to working order, and restored Lord Verice as well.
Narthing knew, hells, the entire castle knew that she and Verice were sharing a bedchamber. Admittedly, it wasn't proper, but given all that had happened, no one was pointing fingers.
The fact that Warna was human, well, that had raised a few eyebrows. Narthing hadn't heard much talk on that topic, but then he didn't move within the social circles. He glanced at Pernard and wondered. Although from Pernard's expression, he need not have concerns on that aspect. Pernard clearly approved of Warna, and why not? Practical, smart, and lovely as humans go.
Warna caught him staring, and gave him a questioning look. Covering his embarrassment, Narthing gestured to the piles of scrolls on her desk.
It was Warna's turn to be embarrassed. "The morning's delivery. I haven't gotten through it all yet. Mostly responses to our invitations, but I do need to sort them out this morning."
"There's one there with the Valltera royal seal," Narthing noted.
"Probably Verice's, then," Warna said matter-of-factly. "If everyone's been served, let's move on to the Second Day—"
They continued on, covering all seven nights and the days within faster now that the subject matter had lightened in tone.
"You've made arrangements for the actors?" Warna asked Ersal.
"Aye," Ersal said. "They know when and where to place their stage in the courtyard."
Narthing said nothing. He and Lord Verice had already discussed the actors. Nothing seemed out of place, and everyone had vouched for Master Zester. Still, they'd be confined to the courtyard, under the watchful eyes of his men.
"I won't bore you all with the orders for ribbons, banners, flags, and flowers," Warna laughed. "Trust me when I say that the castle will be decorated to a fare-thee-well." She looked at her desk, and then at each of them. "I think we've covered everything. Does anyone have anything to—"
Alarm horns sounded from the battlements.
Chapter Fifty-Nine
Verice stood on the inner wall and scanned the courtyard as the alarm horns were sounding. He watched in satisfaction as everyone turned away from their tasks and responded to the drill. Some ran for designated shelters where warriors already guarded the doors. Others pulled their weapons, and moved to locations where they'd been told to gather. All acted quickly, quietly, and with deadly seriousness.
He knew it was disruptive and difficult. No one complained. His people remembered all too well the betrayal, and the deaths that had resulted. Drills, repetition, knowing what to do, that would make a difference when the next attack occurred.
"Give me time to check the keep," Verice commanded. "Then sound the 'all's well'."
"Aye, m'lord," was the response, but Verice was already headed down the stairs.
Captain Narthing was by the main gates, and he raised a hand to show that his people were in place. Constable Ricard was over by the kitchens and bakery. Verice couldn't see him, but he knew well that he'd be making sure that all was as it should be. He'd receive detailed reports later, but his goal now was the keep, and to make sure that everyone had obeyed their orders.
Ersal was barricaded in his office, with most of his staff and two armed guards. Verice lifted an eyebrow to see Priest Dorne in the room with them, but he didn't stop to talk.
He'd finished checking three floors when he heard the horns calling the 'all's well'. Everything had been in order so far, with everyone barricaded in their rooms, armed with whatever weapons they could bring to bear, knowing what was expected of them. Satisfied, he went to check on the very last occupant of the keep.
Warna's office was empty, as it should be, with a few papers scattered on the floor. He checked the bedchamber, just in case, but it was empty as well.
So, he returned to the outer chamber, locked the outer door, then stepped to the wall, and pressed his hand to the corner. With a soft rumble, the marble wall shifted aside.
Warna was seated within the bolt-hole cross-legged, her lap covered with scrolls and letters.
"You are supposed to leave your tasks," Verice said pointedly. "Stop what you are doing and get to safety."
She looked out at him in exasperation. "This is the fourth drill in three days," she said. "Some of us have work to do," she waved one of the scrolls at him.
Verice folded himself in next to her. She slid over to give him a bit of room.
"If you'd dropped one of those letters or scrolls it could have given your position away," Verice said.
"But I didn't," she pointed out. "I grabbed a handful, waited until the others left, and crawled into the first available of your little cubby-holes, and closed the door behind me." She rolled her eyes at him. "I sat quietly, waiting for you. I didn't leave when I heard the 'all clear'. I waited for you to come."
"And if I hadn't come?" Verice asked.
Warna gestured to the corner. "Then I've food and water for two people to last three days, along with a pallet and a chamber pot." She wrinkled her nose as she recited her instructions. "At the end of three days, I'm to wait until dark, leave the cubby hole, and seek to learn more. Although I have to say that if two people were to hide in here, they had better like each other."
"It was meant for family," Verice said shortly.
"I know," Warna said. She fingered the edges of one of the envelopes. "How did the rest of the castle perform?"
"Well," Verice said. "I've no reports yet, but I am satisfied that everyone knows what to do. Which doesn't mean I won't drill them again, if time allows." He frowned. Warna was staring at the pile of letters in her lap, but she wasn't really seeing them "Warna?"
She lifted her head, blinked at him then bit her lip. "Verice...this letter was addressed to me," She handed him the stiff paper, and he scowled at the royal crest at the top of the page. "It's from Charrin."
Verice took it from her. Warna leaned her head against his shoulder as he read.
Lady Warna,
I have thought on our last conversation and have considered your words carefully. As hard as they were to hear, I have heard them.
I would request that I be permitted to attend your Festival of Light and Laughter, at least on the First Night, to add my voices to the others.
Bard Charrin
Verice let out a long, slow breath he hadn't realized he was holding. "Well," he said. "This is...unexpected."
Warna took his hand in hers, but didn't say anything.
"Charrin has harbored his hate for so long," Verice continued. "I wouldn't expect that mael to change."
"He's harbored his hate as long as you harbored your grief," Warna whispered.
Verice nodded absently, lost in thought, studying the words of the letter. "What do you think?" he asked.
"I wish I could spare you this pain," Warna said. "But we both know that it must be faced. Charrin wants to face his, here with us, in the place that his love died. I do not want to deny him that, but—"
"I don't want him to lash out at you," Verice growled.
"He may," Warna acknowledged. "If we warn Dorne, and Narthing, they can be ready to deal with him gently. With understanding."
Verice snorted as he folded the letter away. "Fair enough." He leaned over and nuzzled her ear. "How goes the planning?"
"Three days left," she said, her voice softening at the touch of his lips. "Really, we are down to tiny details, and sudden crises."
"And is there anything in that pile of paper that can't wait a while?"
"Well..." Warna tilted her head. Her skin shivered under his lips. "There's a lace order for the women of Birch Cove that I want to forward on. From one of the faellas at the Valltera Court."
"That won't take long," Verice said. "I need to check in with Ersal and Narthing to make sure that all went well with the drill, but after that..." he paused, nipping at her neck.
"Why, m'lord," Warna gasped as he dragged his teeth over her skin. "What did you have in mind?"
"More," Verice growled.
Warna jerked her head back, her eyes wide, sparks flying in their brown depths. "I'll meet you back here," she scrambled up and out of the cubby-hole, gathering her letters as she moved.
Verice was right behind her. He took the steps two at a time, trying to rush with some degree of dignity befitting a Lord High Baron.
Ersal, Narthing, and Ricard were waiting for him, all with pleased looks on their faces. "It went well, then?" Verice asked.
There were nods all around. "Although the cooks ask that you time future drills for a moment when they are not spitting carcasses," Ersal said. "But they obeyed orders, m'lord."
"Excellent," Verice said. "I will be conferring with Lady Warna about the details of the Festival this afternoon."
Their well-trained faces were professionally blank, although there was a distinct look of approval in Ricard's eyes.
"Just one thing, m'lord," Ersal spoke up as Verice turned to go. "Lady Warna has written a letter to her great-uncle in the Barony of Summerford. Should I find a special messenger, or send it along the regular trade routes?"
Chapter Sixty
Verice's first thought was to rip the letter from Ersal's hand and tear it to shreds.
"The trade routes are slow and uncertain," Ersal frowned at the letter. "The city of Alsmeda lies along the border with Summerford. We could probably find a messenger there, but there's a cost involved."
Warna had been honest with him. She'd told him what she wanted, and she'd laid out what would happen. Why was he so angry that she was keeping her commitments to him?
Yet, he didn't want that message to go.
"M'lord?" Ersal waited for an answer.
"Special messenger," he managed to croak, but it wasn't what he wanted to say. He wanted the damn thing in the fire, or on the oldest, slowest, fattest pony that ever walked a caravan route.
"As you wish, m'lord," Ersal said.
Not really, Verice thought, but he managed to keep his mouth shut as he left the room. With the door shut, he took a calming breath, and then headed for their chambers.
He was rounding the last flight when he saw her. Warna appeared down the hall, her errands done, heading for their chambers. There was a flush to her cheeks, and a twinkle in her eye as she stopped and stared at him.
His heart started racing.
Warna laughed, and she backed up a few steps, as if daring him to—
With a laugh, a twist of her skirts, and a flash of a lovely ankle, she was gone.
Verice gave chase.
Warna caught her breath at the look of desire in Verice's eyes. She couldn't help laughing in pure delight, and then with an impish leap of her heart, she turned and run down the corridor.
She had spent enough time in the keep to know its twists and turns. She darted up the next staircase, hearing the sound of Verice's footsteps behind her. She flew down the next corridor, avoiding some of the staff scrubbing the floor. With a frantic motion, she shushed them as she ran past. She could hear their stifled laughter as she disappeared around the next corner, and pressed herself against the wall.
Verice ran by, his surprise clear as he sailed past her, sliding to a halt. She fled back the way she'd come, running by the servants who were smiling and giggling. Warna rushed for the stairs, daring a quick glance behind.
Verice was running, gaining on her.
She laughed, picked up her skirts and bolted up the stairs, taking them two at a time. Breathless with excitement, she headed for the farthest door, and dashed through it, onto a balcony of white marble that shone bright in the noon sun.
Verice bolted through the door, and his heart almost stopped in his chest. For an instant, he saw Warna in her tattered clothes, fleeing from him, about to leap out into—
Warna turned, her hair flying free, her laughter ringing out, and the memory was wiped away in the next instant. She launched herself into his arms, and he swept her up, twirling her in a circle that left her even more breathless.
"Verice—" but he cut off her words by claiming her mouth.
She moaned, returning the kiss with passion, wrapping her arms around his waist. It was only when the need for air was overwhelming that he broke away, burying his face in her hair as they both struggled to breathe.
"Bed," Warna whispered in his ear.
He nodded, sweeping her up into his arms. "Bed."
She wanted to preserve every moment in her memory, remember every detail humanly possible. Every touch, every soft sound of pleasure.
Verice's gaze seared her skin. Intent, hungry, focused on her and her alone. It was terrifying, yet she wasn't afraid. There was no fear in her heart as they came together, grasping at clasps and fumbling with buttons and laces. No, the tingles on her skin, the feelings in her chest, those weren't fear.
She reached for him, comfortable now with touching and stroking. She knew the places, the ways to touch him. Verice responded, and reached for her as well.
His kisses were sweet, not just on her mouth, but along her neck and over her shoulders, and her breasts. Warna leaned back, giving him access, confident in the strength of his hands to hold her upright even as she melted against him.
The bed was cold, but the heat of their bodies warmed it quickly. With the bedding thrown back they were free to sprawl together, arms and legs entwined as they kissed and stroked each other.
At first Warna was content to follow Verice's lead, but as her need grew her patience faded. "Verice," she moaned into his mouth, trying to push his fingers deeper within her folds.
"Wait," Verice said.
"Verice," she pleaded, but he stayed her questing hands with his own, pinning her to the bed and distracting her with his mouth.
She arched her body, wanting more. There was no fear, only need when he urged her legs open, rose up over her and slid within. She gasped at the hot, heavy pressure.
More. It was so much more.
Verice released her wrists, bracing himself over her, studying her face intently. He held perfectly still, waiting. "Warna?"
"It's just so-" she shifted and drew a sharp breath at the pleasure that spiked through her.
"Verice, please—" she sobbed, not sure exactly what she was pleading for.
Verice kissed her jaw, just below her ear. He shifted and she cried out as the burning heat crashed over her, carrying her further and further up. Faster, faster, and she moved as well, meeting and matching him as she laughed and cried at the sheer wonder of it all.
Until the heat built white hot and exploded, blocking out all the world, except the sound of Verice reaching his own heights, crying out her name.
The world faded back slowly, sweetly. Warna was cradled against Verice, the cooler air delicious against the heat of her skin.
Verice was stroking her hair, his movements slow. Warna murmured her pleasure, shifting just enough to reach his mouth for a long, slow kiss.
"Warna?" he asked softly. "All's well?"
"Perfect," she whispered.
His chuckle rumbled in his chest. "I'd agree," he said quietly. "Shall we sleep for a bit? Tell me what you wish."
Warna hugged him tighter. 'I wish it could be like this forever,' She thought silently. 'I wish I could spare you the pain of the Festival. I wish joy wasn't so fleeting.'
She raised her head to look into his silver eyes, and reached up to rub the very tips of his ears. "More," she said simply, hiding her true desires, taking what was offered.
"As you wish, m'lady," Verice said and pulled her into his arms.
Chapter Sixty-One
The airions spotted the entrance to the old eyrie, even thought the trees had grown up in front, blocking it from Kalynn's sight. They back-winged into the tunnel entrance, Wolfe's going in first. The clatter of their claws against the stone was an old and comforting sound. Kalynn had to fight the familiar urge to duck her head as they entered its cool depths. Going from sun to shadow in the stone tunnel brought back a rush of memories.
The solid stone wall at the back did not.
"Are they behind there?" Kalynn asked as she dismounted. Her airion danced toward the wall, clawing at it and clacking its beak.
"They're there," Wolfe said shortly. He started to unsaddle his mount, grunting with the effort as he dragged off the saddle bags. "She locked them safe away, sleeping, awaiting the call to awaken. Awaiting the day."
"A day which comes," Kalynn said. "The trees have grown up." She went to the edge, peering out. "The path has certainly deteriorated."
"Kalynn," Wolfe added her saddle and gear to the pile. "It's been a hundred years, give or take. Trees grow," he added. "Rocks fall."
"Do you suppose the rabbit hutches are still there?" She craned her neck out, looking off to the side. "You can still see a faint trace of the path."
"The hutches are sure to be gone, but the great-great-who-knows-how-many-great grand-offspring are probably still there." Wolfe chirped at the airions. They settled down along the back wall, curling into balls, tucking their wings in tight.
"I guess," Kalynn hugged herself. "I guess I thought it would be the same forever."
Wolfe came up behind her, and wrapped his arms around her. "Everything changes."
She cast a glance back at the airions. "You put them to sleep?"
"You saw the herd below us, probably the descendants of the feeder herds." Wolfe rolled his eyes. "She's not going to be pleased to see us, and even more so if they kill any of those cows."
"True," Kalynn sighed, leaning back against his warmth. "Do you suppose she is there?"
"She's there," Wolfe said confidently. "She'd not stray far from her charges. But let me check," he closed his eyes. "Yes. With two others, both male." He frowned. "They are at the old storage cave, loading a wagon with something. We should wait until she is alone."
Kalynn nodded.
"We should be ready," Wolfe said. "I'm sure her temper has not improved. She might launch a mage attack as soon as she catches sight of us." He snorted. "Well, catches sight of me," he added gruffly.
"She wouldn't," Kalynn insisted, suddenly fearful. She turned in his arms to look at him.
"She might," Wolfe said. His face was calm and resigned. "I have to assume that she will lash out."
"Wolfe," she put her hands on his chest, felt the steady beat of his heart through the leathers.
"Kalynn," Wolfe took her hands in his. His fingers warmed hers. "You're right, we need to talk to her. But we should be prepared for the worst, yes? If she attacks, stay close. I'll shield us, and then portal us out." Wolfe looked down toward the cave. "The men and wagon are leaving. She's alone."
"You are not going to make me walk down that path, are you?"
Wolfe chuckled. "No."
He opened a portal, and they stepped through. Kalynn looked around, recognizing the large boulder that sat by the path, but not much else. The trees had grown up, and the underbrush allowed to thicken. She could hear the cows in the fields beyond. She looked at Wolfe, and he nodded, and gestured for her to proceed.
The cave entrance had been covered by large wooden barn doors, now closed. There was a small door off to the side. The wagon, and its drivers were gone. Kalynn strode up to the smaller door, Wolfe followed. Kalynn took a breath, and knocked.
"Who's there?" came an old, quavering female voice.
"That's not—" Wolfe said, but then the door was thrown open.
An aged, wrinkled woman confronted them, her white hair piled on her head, her back hunched with age. Her eyes went wide, then narrowed.
"Kalisa?" Kalynn couldn't hide her shock. Wizened and bent, this could not be—
"Sister," Kalisa's voice emerged from the woman, stiff and angry. She had to tilt her head to see them, and if possible, her eyes got harder. "Stalking Wolf."
"No more," Wolfe's tone was deceptively mild. "Just 'Wolfe' these days."
"Come in," Kalisa shuffled back. "Before you are seen."
"What happened to you?" Kalynn asked, unable to stop herself from asking as she crossed the threshold. Wolfe followed and closed the door behind them.
"You ask that?" Kalisa gave a harsh laugh. "You and the Chaosreaver, who tore the magic of the elements from the Heart of the Plains and the Kingdom of Xy?"
Wolfe put his hand on Kalynn's shoulder. "I don't regret rescuing my warprize."
"At what cost?" Kalisa snapped. "I lost everything. My love, my position, my flying—"
her voice hitched.
"Yes," Wolfe spoke cooly. "Interesting, what you have done with the place."
Kalynn shot him a warning glance, but finally took a moment to look around. "Is that cheese?"
The cave had once stored flying gear and saddles for the airion wing. Now there were rows and rows of wooden shelves, covered with wheels of cheese.
"Those of my blood, my warrior blood, mind you," Kalisa's words were brittle. "Those of my blood should have claimed the skies by now, riding airions, defending this land. Instead, they make and sell cheese." Her disdain was clear. "None of them dream of battle. None of them feel the call of the sky. Cheese." she looked at the shelves and her lip curled.
"The gift has not passed on?" Wolfe asked, frowning.
"And if it had?" Kalisa snapped. "There is no magic here, Chaosreaver, you saw to that. Airions need magic to survive, as so many things do. I preserved what I could, and used the last to sustain my life. The spell fades, after so long. I fade with it."
Wolfe extended his hand. "I could—"
"Don't touch me," Kalisa hissed.
Kalynn stepped back into Wolfe; the hate was palpable in her sister's eyes and her heart broke to see it. "Kalisa, please," she asked, extending her own hand.
Kalisa looked away. "Why have you come?"
Kalynn let her hand drop. "I have seen," she said. "The day comes, Guardian. Be ready."
"Nothing more helpful than that? No date, no time, no real idea, just a vague warning?" Kalisa snorted.
"Kalynn has seen," Wolfe snarled. "You have a duty, Guardian."
"I will do as I see fit," Kalisa snarled right back. "But do not think I do this for you. I do this for Xy, and for my people, and for my love that no one but I remembers. But do not expect forgiveness, Chaosreaver. Or you, sister, for that matter." Her swollen hands tightened into fists. "I thank you for your warning. Leave."
"Let Wolfe offer you some ease, at the very least," Kalynn took a step forward. "Please, Kalisa—"
"You say 'please'?" Kalisa shook her fist at them. "You, who created this nightmare? You, who deprived me of everything dear?" Her face was reddening, her eyes alight with madness. "If I had the power, I would smite you to the ground, and burn and burn both of you to ash." Her voice dropped into a dark, evil hiss. "You killed my Uppor, and I will never, never forgive. May the very air deny you breath. May the very—"
Wolfe's arm snaked around Kalynn's waist, and she was turned and through the glaring white of a portal in an instant.
They appeared in the tunnel, Wolfe muttering his own curses in her ear. "If you think I was going to let that bitch curse us out the door and up the mountain, think again."
Kalynn shook her head. Everything ached, her body, her heart, her soul. She felt as if all the strength had left her limbs.
"Bitter, withered, dried-up turd." Wolfe stepped to the saddle bags, and started pulling out their bedroll. "We will spend the night here, and leave in the morning."
"She might follow," Kalynn glanced back at the tunnel's edge.
"Without power? In her crippled condition?" Wolfe shook his head as he shook out their blankets. "No. Besides that path is bad enough no one is getting up here this night. Come and get warm."
"I'm not cold," Kalynn said.
"Then why are you shaking?" Wolfe asked as he knelt on the blankets. He opened his arms. "Come."
She went. Let him wrap her in a blanket, and sit beside her. With just a few gestures and words, he had a fire burning and a mug of hot kav in her hands. Then he joined her under the blanket, and wrapped his warmth around her.
"You're wasting your power," she muttered.
"No," he said quite strongly. "I am not."
Kalynn sighed and let her tears come. "She's like Charrin and Verice. They've locked their bitter hate in their hearts, and won't let it out."
"Only she's been at it for years in the making," Wolfe said. "Almost one hundred."
Kalynn choked out a smile. "Give or take," she reminded him as she took his hand.
"Give or take." Wolfe looked at their linked hands. "Here I sit, Stalking Wolf, Mage of the Plains, Chaosreaver, feared and hated and yet I cannot ease your pain."
Kalynn put her head on his shoulder. "No, Wolfe. You are my tent, my winter lodge, my shelter, my home."
"Then shelter in my love," Wolfe said. "Sleep."
Kalynn nodded, and closed her eyes, but sleep eluded her. Instead, her eyes drifted to the solid wall at the end of the tunnel. It seemed to her that shadows moved within, images...and her mind flooded with all the possibilities.
"Wolfe," Kalynn sat straight up.
"Eh?" he asked.
"They are tied to her, aren't they?" Kalynn asked. "She locked them away and—"
Wolfe was already staring at the wall. "Yes," he said distantly.
"I don't trust her," Kalynn said, hardening her heart to face the truth about her sister. "I think she would rather see them locked away forever. And with her health..." she let her voice trail off.
"If she were to die, the airions will be locked away forever." Wolfe shook off the blanket and rose. "If Xyson had only known," he said.
"Not even Seers have hindsight, Beloved." Kalynn rose to stand next to him. "Can you replace the spell?"
"No," Wolfe shook his head, his bushy white eyebrows beetled together. "That requires far more power than I dare use. No," He walked forward, and placed his hand on the wall. "But I can add to it. Bend it a bit."
He started to mutter under his breath, pressing his hand flat to the wall. Kalynn settled down, waiting quietly.
"There." Wolfe took a deep breath, and returned to her side. "I linked it to the crystal Sword and the Royal Signet Ring. Any with the ability to use magic, who wield the sword and the ring can issue the call." Wolfe shrugged at her questioning look. "I thought that any who would wield all three would have the best interests of Xy at heart." He took Kalynn's mug and drank. "Wouldn't old Xyson laugh at that."
"You have enough power left?"
Wolfe nodded. "We'll fly out at dawn."
Kalynn draped the blanket back over both of them. "I still grieve," she said. "She is old and crippled, and it will get worse for her from here." She pressed her hand to Wolfe's heart. "But no regrets."
Wolfe pressed his own warm hand on her cold fingers. "No regrets."
They sat in silence for a moment, then Wolfe turned his head slightly. "So," he said as he waggled his eyebrows. "Perhaps we should balance each other's elements this night?"
Kalynn laughed.
Chapter Sixty-Two
They gathered at sunset, on the First Night of the Festival of Light and Laughter.
Warna stood next to Verice as the staff, guests and guards clustered at the base of the stairs leading to the main doors of the keep. She breathed a nervous prayer to the Lord and Lady that all would go as planned.
She and Verice were dressed in simple white tunic and trous, as were about a dozen others. The others were all wearing mourning colors, somber, plain clothing. The crowd was thick, made up of people who had been present at the attack, or who had lost loved ones as a result.
Priest Dorne stood at the top of the steps, a small metal bowl in one hand, a wooden striker in the other. He stood, watching the sky as the crowd swelled, greeting each other and talking quietly.
Warna leaned in to Verice, letting her fingers entwine with his. He didn't look down, but squeezed her fingers tightly. She could feel the tension in his body, his back stiff and straight.
Finally, a guard on the far west wall lifted his hand and signaled that the sun was below the horizon.
Dorne lifted the bowl, and struck it once. The bowl rang with a pure sweet tone, calling all who heard it to silence. The tone hovered in the air, throbbing like a heartbeat, then faded away, slow and steady. Warna strained to listen, not sure when the sound stopped, leaving only silence in the courtyard.
"This night is the First Night of the Festival of Light and Laughter. With these seven nights and days we celebrate all the gifts that the Lord and Lady have given us."
Verice tightened his grip on Warna's hand.
"The first gift of the Lord was life, and the first gift of the Lady was death," Dorne said.
"And this night is sacred to the remembrance of all those that have gone from our midst." Dorne's voice rang out in the silence, echoing against the stones of the courtyard and walls. "Let us grieve for our loss, and honor their memories."
He struck the singing bowl again, but this time, the sound was joined by one mael's voice, catching the tune, and extended it into a song of loss.
Charrin stood off to the side, clad in white robes, embroidered with gold and green. His song floated above them, joined with soft sobs and whispered prayers from the crowd. Warna's tears welled, her throat closing, not only for their grief but for her own, for her own family.
The bowl went silent, and Charrin's final note faded in the air.
Verice released his hold on Warna's hand and stepped forward.
She felt his pain and ached for him. Ached for the sorrow etched in every line of his body. But her strong mael mounted the steps slowly as Dorne stepped to one side. He raised his hands and opened the main doors and stepped within the darkness and lit the mage lights to either side.
Warna and the white clad servants followed behind.
The crowd followed as well.
Verice was supposed to advance further into the hall, but he froze in the doorway, seemingly unable to move forward.
They all paused, the others looking at each other uncertainly. Warna understood. "Verice," she whispered as she touched his shoulder. "Wait here." She gestured to the others to follow her, and led them past Verice and into the wreckage beyond.
It hadn't changed. Nothing had been moved, or altered since the night of the attack.
The dying light outside was just enough to light the colored-glass windows, letting their hues spill onto the floor. Spring, Summer, Fall, and Winter stood silent guardians over the tables still set with dishes, some over-turned, with broken glass and pottery shattered on the floor. The high table, was cracked and the area before it covered in a large reddish-brown stain. Old dried blood.
Warna swallowed hard. One glance showed her that Ersal and Janella, as well as the other volunteers that stood with her were just as stricken. They'd thought they'd known how hard this would be, but the reality was so much harder.
They'd planned this in silence, with Charrin and Dorne outside, chanting a dirge. But suddenly that wasn't enough for the emptiness and the ache she felt within. Warna swallowed hard, and gave voice to her sorrow, one long mournful keen for her pain.
She reached out, picked up a soiled plate, and placed it in her basket.
Her keen was caught by Ersal and the others and amplified as they joined in, lifting their voices in wordless sorrow. Deeper voices joined in, as some of the men added their grief to the rising tide of sound.
Verice stood silent, in the doorway, as still as stone.
The sound of the keening seemed to free them. As they'd planned, the men began to remove the broken furniture and chairs, as the women gathered the shards of glass and pottery. Everything was taken away, the room cleared of everything, all of it carried outside with reverence.
When the men returned, they carried buckets of water, and clean white cloths.
Warna took the first bucket, and one of the cloths, even as she continued the song. She knelt on the floor, at the edge of the dried blood, and started to clean.
The outside light faded as they worked, night having truly fallen. Mage lights appeared around them, and Warna glanced at Verice, sure that he had lit them. But he still stood, unmoving and still. She wanted to go to him, but she knew it was best that this be done and finished as quickly as they could. Only then would she offer him whatever comfort he would accept.
The weeping grew as they worked, the keening broken with the harsh sobs of those that labored. Each took a turn, taking over from another when the pain grew to be too much. Warna eyes stung, and her voice grew hoarse, but she didn't stop. No one stopped, until the floor was clean.
Then the buckets and rags were taken up, and they all started out, weary, their clothing stained and damp. Warna lifted her hand to her hair, drained and exhausted.
A fluttering of wings caught her attention. Her gaze flew up to the huge circular window, as a small bird flew out. She gaped at its shattered opening. The window. Her stomach knotted in a flash of pain.
Lord and Lady above, how had they forgotten the window? She glanced at Ersal, who was staring up at the opening with the same stunned look. There was a sharp intake of breath from behind her, probably Janella. They'd focused on the clearing, and the cleaning. All their plans for the use of the Great Hall during the rest of the Festival—
A warmth at her side, and Verice was beside her. She feared the worst. His face was shuttered as he gazed up into the empty space.
He lifted a hand, and whispered under his breath. She followed his gaze to see the empty space fill with the golden light of a magical barrier.
Warna sighed with relief, and slipped her hand into his. Verice pressed his cheek to her head, and then led the way out and down the stairs.
Outside, Dorne took the lead, with Charrin singing, chanting a hymn to the Lord and Lady, asking for blessings upon the dead. He'd made no protest when Warna had asked him to sing the songs, even though they were of human crafting. His voice was lovely, and Warna was content as she walked at Verice's side and into the gardens between the walls.
A trench had been dug in the garden, and the wreckage of the hall piled within. The contents of the buckets were poured at the feet of the rantha bushes, and the buckets and cleaning cloths added to the pile.
Off to one side a small tent had been set up. Warna and the others went inside, to wash and change. Verice too, Warna insisted.
Once they were all reassembled, Dorne stepped forward, and struck his bowl again, letting the tone wash over them all, bringing them to silent attention.
Dorne handed the bowl to an acolyte, and took up a small pitcher. "With this oil, I ask the Lord of Light and the Lady of Laughter to bless this pyre." He poured the oil into the trough.
Warna watched in silence, standing close to Verice. She knew that the trough had been treated with oil, and given a base that would ensure that it burned through the night.
Dorne took up a torch offered to him by another acolyte. "Let this fire cleanse our hearts and bring us peace." He tossed the torch into the center of the trough. The flame flickered, and caught.
Charrin started to sing, an elven song this time, of loss and sorrow.
Verice stiffened suddenly. Warna glanced up, gasping at the rage and pain she saw in his eyes. She felt a tremor wrack through his body. His whispered words were in her ear. He was casting a—
The pyre flame roared up, blasting them all with the heat, towering over them.
Charrin faltered, his song lost in the clamor of the flames. Everyone stepped back, taken by surprise. Dorne cast a stern look at Verice, but his expression eased as he took in Verice's face.
The tower of fire raged, dancing in the night sky, consuming everything within. Verice's eyes were narrow, filled with malice and hatred.
Warna leaned in to him, not quite daring to break his concentration. Verice glanced over, frowning, and the flame sputtered and collapsed in on itself.
"Lord of Light, Lady of Laughter, we know that our loved ones are at peace." Dorne's voice cut through the crowd's murmurs of surprise. "We ask for the gift of your grace for our grief and pain. Give us strength to bear our sorrow, until the moment we are reunited in your light."
The fire eased down, the pyre already collapsing into coals.
"Let us go, to our homes and our hearths, and remember our dead this night," Dorne said, releasing them all.
The crowd started to disperse, moving off towards the garden door slowly. Dorne bowed to Verice and left with his acolytes. Charrin walked with him.
Verice didn't move, staring at the embers.
Warna waited beside him while the others left. They'd planned to attend the midnight services at the church, but that didn't feel right somehow. She felt so bone weary, so drained. And Verice...
She moved closer then, tucking herself under his arm, wrapping her arm around his waist. Verice put his arm around her shoulders, still staring at the pyre.
"Come," Warna said. She gave a tug, and he turned with her, allowing her to lead him away.
She wasn't certain why, but some instinct guided her to lead him back to the keep, back up those stairs and through the doors.
The Great Hall was silent now, the mage lights dimmed.
But at some point, Verice took control, guiding them to the point on the floor where the high table had been. He wrapped his arms around Warna, buried his face in her hair, and crushed her close.
Warna returned the embrace fiercely, allowing her tears to flow once more.
Verice's body shook. He was weeping, sobs of pure anguish. His knees gave out and he collapsed to the floor. She followed him down, supporting him until they knelt together, wrapped so tight that not even breath separated them
She sheltered her beloved as he finally allowed himself to grieve.
Chapter Sixty-Three
"Lord and Ladies, on this, the Third Night of the Festival, the Night of Music and Dance, I propose a toast," Lord Mayor Pernard held his cup high. "I propose a toast to our gracious Lord High Baron Verice and the Lady Warna!"
"Hear, hear," was the response from those seated in the Great Hall, raising their own glasses in response.
"My thanks," Verice said, glancing at Warna, seated next to him at the high table. "We thank you for your attendance, and offer you welcome. Enjoy the food and wine, my friends, to fortify ourselves for the dancing to come."
The servers piled into the Hall, carrying steaming platters, to noisy appreciation.
"It seems to be going well," Verice whispered to Warna.
"Until one of the servers dumps a platter of sliced beef on the floor," Warna whispered back. But her eyes were grateful as she turned to Charrin, seated at her side. "Bard Charrin, would you let me pick out some choice slices for you?"
Charrin's response was lost in the sounds of the hall, but his tone was snappish. He'd been remarkably pleasant when he'd arrived, agreeing to the details of the mourning ceremony, and to otherwise participate in Warna's plans. But his goodwill hadn't lasted long, and Verice could not blame him. For this night was the actual anniversary of the attack, and Summer's death.
It felt bizarre to be seated here once again, entertaining as if naught had happened. As much as his heart cried against it, the castle and keep were at the heart of Tassinic. Life had to go on, as painful as that was to think on. Warna and the entire staff had put every effort into easing back into the use of the Great Hall.
It still hurt.
Verice glanced at Narthing, seated at his side. His captain caught the look and returned it with a nod. They were both conscious of the hour.
So far, the Festival had been without incident. But if any were to plot against them, this would be the night. They'd taken every precaution, drilled all in attendance, servants, staff and warriors alike. All knew what they had to do.
Even Warna. Verice glanced at her waist, pleased to see that the dagger was still at her side. He'd given her one that he'd sharpened himself, and belted it around her when she'd hesitated. "I've no skill," she'd protested.
"Even so," Verice had said. "I'd have you armed."
She'd huffed at him, but she hadn't removed the blade as she returned to dressing her hair for the night's celebration.
Verice had made a pretense of sharpening his sword as he watched her.
She'd refused all but the plainest of clothes, but he had to admit that she looked lovely in her dress of brown and gold. She'd taken diamond hair pins from his jewel vault for this night, settling them in her hair in such a way that they had seemed to catch all the light in her golden tresses.
Verice drank his wine, and watched Warna, who was trying very hard not to help Charrin with his plate. Even now, those jewels sparkled in the mage light whenever she moved. She was a simple vision of beauty, and he ached to pull those pins from her hair, and let it fall over his naked skin.
Verice shifted in his seat with a sigh, raised his cup and took another sip.
He'd much to be grateful to Warna for. That first night, after he'd broken down, she'd stayed with him, protected him from any prying eyes. Somehow, she'd gotten him back to their bed with no one seeing them. He'd slept deeply, and in the morning, she'd handed him strong kav and urged him up before the dawn ceremonies had begun. Since that consisted of a choir of small, off-key, shrill children gathering in the courtyard to sing to him, he'd been more than thankful.
Warna and Ersal had planned this Festival with the anniversary in mind. They'd kept things subdued, allowing people to ease into the celebration. In years past, Verice could remember trying to plan events ever bigger and brighter, but this felt right. Maybe in the future—
But there was no future. Warna would leave when the Festival was over.
He stared into the depths of his cup. She'd never said a word about what had happened that First Night, never faulted him for breaking down. She'd wept with him, supported him during those dark moments, and then held him as he'd slept.
Verice started as Warna leaned over. "Best eat, m'lord. You'll need your strength for the dancing."
He raised an eyebrow. "You will be dancing as well," he pointed out.
"Only the rustic ones that I know," Warna said. "I'll not risk one of your quadrilles, with those fancy steps and hand gestures."
"They can be complicated," Charrin chimed in. "But you could learn with practice."
Verice glanced at his sightless, scarred eyes, but he could find no hint of sarcasm in the elven bard's tone or expression.
Warna simply laughed, taking the words for what they were worth. "A great deal of practice," she smiled. "Can I offer you more bread, Charrin? Or wine?"
"My appetite is not what it should be, m'lady," Charrin's voice was cool. "But some wine would not go amiss."
Warna poured for both of them. "As soon as the tables have been cleared, we can start. Songs and dances alternating, for so long as you wish to sing," Warna said. "Some of the players have asked to perform for us as well."
Verice stiffened, hiding his surprise.
"But at midnight?" Charrin's voice cracked.
"Priest Dorne will lead us in prayer," Warna said. "And we'll make an early evening of it here in the keep, but the celebration will continue in the rest of the castle."
"Aye," Charrin said, and he slumped in his chair.
Warna glanced at Verice, but he shook his head, and shrugged.
The dancing was marvelous.
Warna clapped with joy as she watched the intricate moves of the dancers. They filled the area before the high seat, interweaving a pattern with swirling skirts and flashing feet. They'd link arms one moment, and then barely touch fingers as they twirled away.
She'd finally convinced Verice to dance, and she enjoyed every move he made. He was dressed in his black leathers, his silver hair braided back, a circlet of gold on his head. He looked every inch the Lord High Baron he was. Part of her felt a bit overawed that a mael like him could desire her.
Part of her just wanted a chance to strip the leathers from his legs and spend a night worshiping the body beneath.
She shifted in her seat, and sighed.
"All's well?" Charrin asked. He'd sung on and off all evening. Warna was grateful that he'd chosen tunes that were appropriate, neither too sorrowful or too raucous.
"Oh, yes," she said. "It's just so lovely, that I don't really want it to—"
Alarm horns split the air.
The room froze, everyone stopping in mid-word, mid-step. The awareness flooded all of them at the same time that this could not be a drill. Then all at once, everyone moved, warriors pulling their weapons, others heading for their assigned places and or duties.
Verice cast Warna a look, but she was already standing, her heart racing but her feet knowing exactly what to do. He gave her an approving look, then ran for the main doors.
"What is happening?" Charrin asked, a note of panic in his voice.
Warna took his wrist. "Come with me."
She led him through one of the rear serving doors, and into a side hall. Charrin didn't resist her, but his voice was anxious. "Warna, please—"
"There's a disturbance," Warna said briefly, as she urged him toward the nearest cubby-hole. "Everyone knows their roles, Charrin. Ours is to hide." She pressed the wall, and glanced around as it slid open. "Kneel down, and crawl in," she covered his head, protecting it as he obeyed. She followed him in, careful to pull back her skirts as the wall slid shut.
"What will happen?" Charrin asked, his hand on her shoulder as if asking for reassurance.
"Verice will deal with anyone who's breached the peace of the Festival," Warna said as calmly as she could. Her heart felt like it would fly out of her chest, and she took a breath to try to slow its pace. "The 'all clear' will sound, and Verice will come to us. We aren't to leave until he opens the door." She laughed weakly. "Our job is to wait."
"Ah," Charrin's voice changed, its tone dark and determined. He wrapped one arm around her waist, tugging her into his lap awkwardly.
With the other, he pulled the dagger at her waist, and set the blade to her throat. Warna gasped, and grabbed his wrist trying to push the blade away, but Charrin had a strength greater than her own.
"Then we'll wait," Charrin murmured in her ear. "And when he comes, he will see you die at my hand."
Chapter Sixty-Four
The courtyard was eerily silent when Verice burst from the keep with Narthing at his side. It made Verice pause on the top of the steps, surveying the area.
The torches crackled in their braces, the light spilling all around. His warriors were spread around, their weapons gleaming in the torch light. The men on the walls were still on watch, flags flying in the night. Every doorway had a posted watch, but the windows were filled with Festival-goers, all staring down into the courtyard.
Scattered around were the various low wooden platforms that had been set up for dances and musicians. But Verice's eyes were drawn to the acting troupe's stage, which had been set between the main gates and the keep. His guards were standing over prone men, swords at the ready.
Ustov came forward. "Report," Verice snapped.
"Lord High Baron, the crowd was lively, drifting about a bit, watching the various dances," Ustov said. "We heard a scream, and saw a group of the actors dashing off the stage with drawn swords. The alarm sounded, and the closest warriors responded. There was a quick skirmish, but then the actors flung themselves down, crying mercy." Ustov glared at captives. "Seems they say it was part of the performance."
"Or not," Verice said softly.
"None of our people were hurt," Ustov continued. "But a few of the actors got sliced up." He straightened his shoulders.
"Let's see what there is to see." Verice kept his own blade out as he walked to the prone men.
Humans they all were, he noted as he prowled around them. Their weapons had been piled to one side, and most of them lay face down, spread eagle on the ground. A few were still on stage, clustered together, eyeing Verice warily.
Master Zester was seated cross-legged, off to one side, breathing like a man who had no experience with pain. He clutched at his arm, where red seeped through the cloth.
Verice sheathed his sword for the moment, accessing the man before him. Zester kept his head down, but he darted a glance up. His eyes had an odd, pleading look.
Verice stared at him, but Zester glanced around at the other captives and then hung his head as if waiting for sentence.
Something wasn't right.
Verice rose, mounted the platform, and pulled down the cloths that had been used to create a 'backstage'. He noted the barrels holding swords and spears, and frowned at a pile of shields and cloaks, more than the number of the company it seemed.
Finally, he moved off, gesturing Narthing to his side.
"The main gates are closed?" he asked softly.
"They would have shut the moment the horns sounded," Narthing said softly. He turned slightly, stretching his neck a bit. "The constable is there, so it's secure."
"I want the grounds searched," Verice murmured. "And a quick check on all the sentries on the inner and outer walls."
"Aye," Narthing said. "I'll see to it." He headed off toward the main gates at a trot.
Verice gestured to Ustov. "Come," he said as he returned to where Zester was seated.
"I thought I instructed you to announce a comedy, Master Zester." Verice knelt close to the man.
"M'lord Verice, I swear we were just having a bit of play-acting," Zester said loudly, but then he winced. "My arm," he pleaded.
"Quality work, there." Verice tilted his head at the pile of weapons. "I'd expected wooden swords, or more pot metal than steel."
"More realistic that way," Zester hissed through his pain. "The crowd likes it better with the ring of true steel."
"You're paying for it now," Verice said as he knelt next to the man. "Let me see that."
He peeled back the sleeve. Zester leaned closer in. "Help us," was his desperate whisper.
Verice didn't react.
Zester winced as Verice exposed the wound. "Prisoners. We've been prisoners in our own—"
"Arrest these men," Verice barked. "Arrest these men."
His warriors closed in. There were a few that resisted, but they were secured quickly.
"Tell me," Verice growled.
"They took us prisoner in our own theater," Zester said shakily. "There's more men, outside the walls, waiting for a signal."
"Do we have them all?" Verice asked. "All those within these walls?"
"Yes," Zester was starting to sag. "We thought maybe, if we did something, we could foil their scheme—"
"Almost cost you your life, Zester," Verice said. "Still, I owe you much for—"
"Bastards," Zester said. "Hiding behind our good name and reputation."
"Narthing," Verice called. "Zester, you need to help us sort them all out."
"They threatened to burn my theater," Zester said. "Lord, the men outside the walls may have fled to the town. They will—"
"No," Verice said. "The City Watch is also on alert. We'll get word to them."
Narthing returned to his side. "The sentries are being checked, and I've a squad to sweep the road to town."
"Let's not mar the Festival," Verice said. "Executions can wait. I want as much information from these prisoners as we can get."
"Aye to that,"
"I'll see to it," Narthing said. "We'll leave the castle gates closed and check any pass through."
"I'll just be a moment," Verice said. "I need to be certain Warna is safe."
Charrin tightened his grip around the human's waist as she shifted. "Be still, or I'll kill you now," he warned.
"I just—" he heard her breath catch, felt her slender fingers tighten on his arm. But she wasn't really struggling against him. He'd pulled her over, half-leaning, half-sitting on his lap. She'd braced herself with her free hand, but the other remained clasped on his wrist, wedged between his arm and her throat. He held the blade angled, just below her ear.
It was awkward and uncomfortable, but she wouldn't feel that way long.
Only until Verice opened the door to their hiding place.
The air warmed quickly, with the two of them in this small space. Charrin could see no detail, but he didn't really need to. He'd see enough to know when Verice was before him, and he'd hear the mael's pain. A pity he'd not see his face, but it was enough. It would suffice.
Time seemed to hang in the air, suspended as they waited.
"Why?" Warna broke the silence, her voice hoarse and pained.
Charrin ignored her, still straining to hear footsteps in the hall outside.
"You accepted his bread, his wine," she was trying to get her breathing under control, trying to calm him, distract him. "Where is the honor—"
"Where is his?" Charrin hissed. "He takes no vengeance, and King Barathiel will take no action." He licked his lips, and tightened his grip on her waist, drying his sweaty palm on the fabric of her dress. "He will watch you die, as my beloved Summer died. Let him know my pain."
Warna let out a pained sob, but she said nothing more. He felt her trying to ease herself into a more comfortable position. "Stay still," he snapped.
"You said you were trying to forgive," she whispered.
"You read more into my words than was there," Charrin gloated. "As I intended." He drew a breath, trying to tamp down on his nervousness. He'd planned to kill her at the high table, before all, stabbing deep within her heart and rejoicing as Verice - Verice \- tried to stem the tide of blood and pain.
But this was surer, better. He just had to be patient, to wait for the right moment. He could do this for his lady. For Summer.
A sob welled up in his chest for his lost lady. What right did love and beauty have to exist in a world she no longer graced? He missed her so, her touch, her laugh—
The human woman squirmed in his arms again, her hand moving on his arm. "Stay still," he growled. "I'm warning you—"
There were running footsteps in the hall, and the door slid open. Charrin could make out a body in front of the opening.
"Warna," Verice said, and then awareness flooded into his voice. "Warna."
Charrin laughed, and pulled the knife back, feeling her flesh part beneath the blade, and warm blood cover his hand. "Here," he pushed her body away, and laughed again as he relished Verice's cry of horror.
Chapter Sixty-Five
"Warna," Verice's voice was filled with horror.
"Now you know!" Charrin's joy grew as he saw the vague shape of Verice take the body of the woman into his arms. "Now you know what it felt like, Verice. My grief, my pain, my endless sorrow—"
Rough hands grabbed him as the guards pulled him from the hiding place. He let the dagger clatter to the floor. They forced him down face-first, binding his hands. Still Charrin laughed, his heart light for the first time since—
"Ow," said a woman's voice.
"What?" Charrin sputtered, straining his neck up to see. That sounded like—
"Hush, Warna," Verice's voice shook. "I need to put pressure on your palm, to stop the bleeding. The knife went deep—"
"Better my hand than my throat," Warna said.
The world crashed in on Charrin, and he started to howl horrible dry sobs, with eyes that no longer produced tears. He laid his head back down, the marble cold beneath his cheek. He'd failed, he'd failed, and the pain of that failure welled up within him.
Summer. His beautiful Summer.
Warna sat in the shelter of Verice's arms, and winced as he held her hand in both of his, putting pressure on her palm.
He cursed under his breath, his face as pale as she'd ever seen.
She'd not thought much other than to block the blade when she'd slid her hand up as Charrin had pulled the knife over her throat. She shivered, thinking of how close she'd come.
And now the bard lay on the floor, crying.
"Summon healers," Verice commanded. The cloth he'd wrapped around her hand was red with blood. Warna decided it might be best to avert her eyes. She buried her face in Verice's shoulder.
"Already called," said one of the guards. "What should we do with the bard, m'lord?"
"Kill him."
"Verice, no," Warna lifted her head from his shoulder.
Verice's face was cold; his eyes even colder.
"Look at him," she said softly.
"Look at this," Verice said, lifting her hand. "And this," his finger traced a line on her neck and she flinched at the sudden pain. "He almost—" Verice stopped.
"He didn't," Warna said. "Please, Verice. Don't—"
"Why?" Verice growled.
"Because he's helpless, and hurting. Because he's lost it all now. He's failed a king who doesn't forgive errors and betrayed you. He's nothing and no one, and less than naught." Warna shook her head. "Don't spoil the Festival."
There were footsteps behind her then, and she suddenly found herself at the mercies of the healers. Verice gave her up reluctantly, letting them take charge. She struggled to her feet with their support.
Verice stood, looking down at Charrin, implacable and stern.
"Verice," she said, holding her hand to her chest. She took a step in Charrin's direction. Verice frowned, and put his boot on the man's neck as she came closer.
"Listen to me, you treacherous bastard," Warna leaned over the bound mael. "You accepted the hospitality of this house, and you repaid it with perfidy."
The hallway was still, the guards and healers silent. Verice watched her with hooded eyes.
"I will sing of this, false one," Warna kept her voice low and hard. "And know this for a truth, while I may not live as long as you, my song will. Our people will sing of your betrayal for a thousand years, and then some."
She straightened, slowly, her strength starting to wane. "Vengeance is not the answer to your pain."
Warna stepped away then, sagging into the waiting arms of the healers. She paused to look at Verice, who gave her a simple nod.
Contented, she let them lead her where they would.
Charrin lay on the floor, awash in his failure, Warna's words echoing in his mind.
"Take him to a cell," Verice was speaking to one of the guards. "And keep him under guard."
"As you wish, m'lord."
There was a rustle of cloth, and then the vague shape of Verice knelt by Charrin's head. "My Lady Warna would have me spare your life," Verice spoke quietly, without rancor. "She is a merciful woman."
"I pity you," Charrin kept his voice down, but he didn't bother to block his hate. "To see you lose your heart to a human. Are you going to start a kennel, like you do for your dogs? Place another one in your life as soon as this one dies off?"
"Warna is kind," Verice continued calmly. "I am not. I will not spoil the Festival, Charrin, but—" Verice stopped.
"What?" Charrin demanded. "I do not expect to live beyond this last moment. I have failed. Execute me and—"
"No," Verice growled, but there was an odd-undertone to his voice. "I see now, that if not for Warna, I would be locked in the same hate as you."
Charrin snarled.
Verice arose. "Did King Baratheil know of this plan of yours?"
"No," Charrin spat.
"You will be confined. After the Festival, I will open a portal into Valltera, if they will have you." Charrin felt a warm hand on his shoulder, felt magical energies stir around him. Verice's voice was a like a shard of glass in his ear. "Perhaps you will see more clearly someday, old friend."
"I do not want your forgiveness," Charrin shouted, his rage and despair eating at him.
But Verice was already gone.
Verice cradled Warna as she slept, her bandaged hand supported by pillows. The healers weren't certain there'd be any permanent damage. He'd ask the Lady High Priestess to return and check with her gifts.
Ancestors, how had it happened? In that moment after opening the door, in the seconds between Charrin's hate, a spurt of blood, and Warna being pushed into his arms, he'd realized the truth.
From the moment he'd been able to understand, there had been the subtle message of the taint in his blood, brought on by an ancestor and his fit of passion for a human woman. He'd never understood it, and had offered that ancestor insult when it had been thrown in his face, or he'd been denied advancement as a result.
Now, he knew. He understood. His Ancestor's revenge, most likely.
Warna stirred in his arms, and Verice stroked her hair to soothe her back down into sleep. Now he knew, he understood, and he didn't know what to do. The darkness around them held no answers, just the soft sounds of her breathing.
She'd told him what she wanted, and he was obligated to fulfill her desires. It wasn't fair to her to insist she stay. She deserved a man, a human, to love and cherish her, to age with her through all the stages of a normal life.
She wanted to leave and he'd agreed, and he was a fool. For what was between them was more than physical on his part, more than just two bodies together in pleasure. The Ancestors were probably dancing in glee at forcing him to regret that thought.
The idea of wedding a human was foolish, of course. Warna had, at best perhaps fifty or seventy years left to her. Was it fair to him to have her stay and wither away before his eyes?
A jealous pain went through him at the idea that anyone else would share the moments she had left. Jealous that she might share her life, her joys, her sorrow with another.
He breathed in the scent of her hair.
There was time yet. To consider. To find a way to let her go.
But not this night.
"No permanent harm done," Lady High Priestess Evelyn said. "Although the knife went deep."
Warna smiled as Evie held her hand, making them tingle with the power of her healing. "Verice shouldn't have asked you to come," Warna said. "Right during the Festival."
"You forget," Evie laughed. "We have no such festivities in Edenrich. I was able to slip away with no one the wiser. You've disturbed nothing," she continued. "Although I do wish to speak to Lord Verice when he has a moment."
"He'll be here shortly," Warna sighed. "He won't be content unless he hears your report from you directly."
"I've heard of the Festival," Evie said as she worked. "But I've never seen it."
"It's amazing," Warna said. She described the seven nights and days. "This is the Last Night," she explained. "The Last Day and Night celebrate the gifts of magic. I wish you could stay," she added. "They say the displays of power are amazing."
"I wish I could," Evie said, as she gently pulled away from Warna's hand. "But my duties require me to be at the church this evening."
"Our loss, Lady High Priestess," Verice said as he came through the door.
"Lord High Baron." Evie rose, and bowed her head.
Verice settled next to Warna. "How does the Lady Warna?" he asked, taking up Warna's hand. Warna shivered at his touch. Verice glanced at her, a gleam in his eyes. But he turned back to Evie with all due attention.
"She's fine," Evie said, standing before them, suddenly looking serious. "There's no lasting damage, and the scarring will fade with time." Evie took a breath. "Lord High Baron, you have said that you are in my debt, and I wish to exercise that at this time."
"How so?" Verice's pose didn't change, but Warna could feel the sudden tension in his body. "What boon would you ask, Evelyn?"
"Only this, Lord High Baron," Evelyn licked her lips, clearly nervous. "I do not ask you to grant my request. I only ask that you hear me out in all the particulars and that you speak to no one of what I am about to tell you."
Verice frowned. "I do not understand."
"But you will listen?" Evelyn pressed. "And you will hold this secret, both of you?"
"Of course," Warna said. "Evie, sit and tell us."
"Say on, Lady High Priestess," Verice said. "Because I am certainly intrigued."
Evelyn remained standing, shaking her head at the offer of a seat. She drew in a deep breath, and let it out slowly. "It concerns a prophecy..."
Verice listened as he'd promised. Evelyn wove an incredible tale of a dagger-star birthmark, and a child born as the Chosen, who would claim the throne from the Usurper and return justice to Palins and its people.
"You've found such a child?" Verice asked.
"I have," Evelyn said with just enough hesitation that he knew there was more she wasn't saying. "I have her well hidden, but if you desire proof, I can bring—"
"I do not doubt your word, Lady High Priestess," Verice said.
"Just my sanity," Evelyn said with a faint smile.
"No." Verice shook his head. "Not even that." He paused, then spoke deliberately. "Evelyn, I've lived long enough to see prophecies both fulfilled and failed. Usually by the actions of the people caught up in them." Verice leaned forward. "Tell me, what have you besides a child and a birthmark?"
Chapter Sixty-Six
"What do you mean?" Evelyn frowned.
"It will take more than a birthmark to rend the Usurper from Palin's throne." Verice stood, starting to pace. "It will take men, money, support, arms, and a great deal of planning. You've none of that, have you?"
"No," Evelyn sank down into a chair, looking resigned.
"Verice," Warna said as she rose and stepped the Evelyn's side. "If there's any hope that we could—"
"It's just what he's doing to the people of Palins," Evelyn said. "What he does every day to innocent—"
"No," Verice said, folding his arms over his chest and shaking his head. He felt a pang for the sorrow in their eyes but on this he would not be budged. "I've just won a stalemate on my borders, and I must protect what is mine. My lands and my people. I cannot afford to support your cause, Lady High Priestess."
"I acknowledge the difficulties," Evelyn rose, her normal calm returning. "And if I should return, one day, with men, and money, and support?"
"Then I would pledge to listen and consider," Verice said.
"I will return." Evelyn lifted her chin, a spark of determination in her blue eyes.
"Of that, I have no doubt, Lady High Priestess."
On the Last Night of the Festival, they gathered on the keep balcony, bringing out chairs and pillows to watch the final magical displays in the night sky.
Warna had been rather surprised to find that Verice would not be displaying his skills. Yet his reasoning was not displeasing. "No, I won't spend my power that way," he'd leaned closer and whispered in her ear. "I'll save my energies for the magic we make between us."
She'd blushed, and shivered at his breath on her skin. Even now, the memory made her tingle.
The night sky was darkening, and the guests had all gathered. Priest Dorne gave her a nod as he chose a chair close to Narthing. No formal seating this night, the Last Night of the Festival.
They'd seen smaller magics all day. They'd strolled through the courtyard filled with people showing off their prowess. Tiny creatures that played with her fingers, butterflies of vibrant colors that settled in her hair, and one enterprising young faelle that had juggled balls of fire. Warna had especially liked the dancing teapot and cups. The young mage with that idea had tried too many cups, and they'd falter as he lost his concentration, but he'd laughed with the rest at his failure.
Now there were teams of mages working together to display their arts. Apparently, the Mage's Guild acted to coordinate all of it, otherwise it would have been chaos.
Warna relaxed in her chair, glad to know that it was in other hands. With the final feast done, she could relax and enjoy, without worrying about the details. The Festival had been a delight, but it had also been hard work. She glanced at Ersal, sitting with Janella, both looking just as relieved.
She settled back as a single bright red light soared into the sky, and exploded in a million sparks. Followed in quick succession by all the other colors of the rainbow. Warna flinched at the blasts, startled by the sounds. A glance at Verice showed there was nothing to fear.
Roses bloomed on intertwining vines, filled with buzzing bees and dragonflies that danced around the flowers. The roses faded, leaving the dragonflies to dance in the night, their jewel-colored wings glowing against the dark sky.
Warna clapped when one of the huge creatures floated down to hover over the balcony, then dissolved in a shower of gold and red sparks. She raised her hand to catch one. It faded even as it touched her skin.
The sky seemed to roll, and suddenly streams of horses galloped over wide plains of grass, their manes and tails flowing behind them. Warna caught her breath at the beauty of it all. Without thinking, she reached out her hand to Verice.
He took it in his, his hand warm under her fingers.
She looked at him, tears in her eyes. "Thank you," she whispered.
He tilted his head, raised one of those lovely arched eyebrows.
"For all this," she said, knowing he probably wouldn't understand what she really meant. "For the Festival. For everything."
A shadow crossed his face for just a moment, then he leaned over, still holding her hand. "You might not thank me when we have to start cleaning up after it all."
Warna's laughter bubbled out
Verice ignored the crowd around them as he claimed Warna's lips in a kiss that left them both breathless.
Warna blushed, settling back to watch the sky, still keeping his hand in hers.
She'd sounded so definite, thanking him, as if their time together had ended. Verice settled back as well, but he kept stealing glances at Warna. She was entranced by the display, and her face reflected her pure pleasure at the sights and sounds.
It was too soon. She should enjoy the results of all her efforts. Besides it would take weeks before the regular routines were restored, and the castle and keep set right after all this celebrating.
"What are those?" Warna breathed. "Dragons?"
The sky above was filled was filled with aerial combat, with airons diving and swooping down on their foes.
"No, those aren't dragons," Verice explained. "They're wyverns."
The scene flickered and changed, with tiny boats with white sails and a giant sea monster, tentacles flying and smashing into the sea, just barely missing the valiant boats.
The spectacle continued on, to the pleasure of the entire company, until at last the bells of the church began to peal midnight.
With that, the display once again erupted in explosions of light and magic, sending tiny shards of diamond bright lights floating down to the ground as the Festival counted down to its end.
Verice rose as the last of the colors faded, keeping a tight hold on Warna's hand. They bid farewell to their guests. Warna glanced at him, smiling a smile that was for him alone.
She knew well his intent.
He tried to remain the gracious host as he saw his company out. Courtesy was, of course, important. Still, he tried to make sure his guests kept moving.
The night was not yet over. He and Warna still had their own magic to make.
"Just how much cooking oil did the kitchens use?" Warna asked.
Ersal unrolled the accounting and placed it before her. "See for yourself, Lady."
"Ersal, I don't doubt your figures," Warna sighed. "But one would think the entire staff bathed in it, given those amounts." She pulled over the list of the supplies they were restocking. "Can the merchants provide so much to us?"
"We'll order extra each week," Ersal said. "Over time, we'll have enough."
"Well, next year, start ordering more earlier, before the Festival," Warna said. "It's not good to have our supplies so low, even if we can see to the daily needs."
"Yes, m'lady," Ersal said.
There was a knock at the door, and Ricard poked his head in. "Seneschal, there's a delivery of hams and the butcher is waving his cleaver at the carter. Will you come?"
"Lord and Lady, now what?" Ersal said, as he hurried off.
Warna chuckled, and turned to the next list of supplies. The festivities had been lovely, but they'd drained the castles supplies down to bare shelves in some cases. Of course, they hadn't had much on hand, but she wasn't pleased with the situation. She'd underestimated the food and drink necessary, that was certain. They'd not run out of anything, really, but larger reserves were needed. She'd leave notes for Ersal for next year—
Because she wouldn't be here.
Warna looked up with a sigh, not really seeing the room or the documents before her. The task of cleaning and restocking after all the celebrations was absorbing, and over-seeing the rebuilding of the window in the Great Hall, and the memorial in the gardens had taken a great deal of time.
They'd restored the practice of dining in the Great Hall every other night. Verice had seated her at the high table beside him. The staff certainly appreciated a return to the normal routine, and it was good to see the tables filled with laughter and talk, no matter how subdued.
The other nights, she and Verice dined privately. They'd talk of their day, the work being done, of the security at the borders, and the news of Edenrich and Valltera. And then—
Warna flushed.
She'd raised the issue of her departure, but Verice so far hadn't been inclined to discuss it. He'd ask how work was going with the restocking, or tell her a new bit of gossip he'd heard, or he'd lean over and kiss the breath from her body.
Warna frowned, thinking. How many days had it been since the Festival?
She added them up in her head, and her eyes widened. So long?
Warna closed her eyes in pain as she realized the truth.
Verice wouldn't do it.
For whatever reason, Verice was stalling. Delaying the inevitable. She huffed out a breath. Drat the mael. Putting off what had to be done, leaving it up to her to do it, no doubt. Typical.
Warna closed her eyes. She didn't want to be the one to do it, either. To say the words, to break the arrangement between them, as they had agreed to do.
To leave his bed.
Her sob caught her off guard, welling up in her chest. Verice deserved so much. As much love as she could give him for the rest of her days. But he also didn't deserve the pain she'd cause him, growing old, dying before his eyes.
She sank down into a chair, staring at the roses. Even freshly picked, one or two petals had fallen to the table.
She hadn't heard from her great-uncle yet, and that was a real reason to delay. Except that she could live in Octara, but she shied away from the thought. Of living in town, seeing him from a distance, just another face in the crowd, waving to her Lord High Baron.
Or worse, seeing him with a faella beside him, riding through the streets.
Warna clutched at the rose in her hand, and felt the thorn prick her fingers. No. That wasn't even to be thought of.
Unbidden, a verse of her song leaped to mind.
Life is bitter, life is grim
What need then to be with friends?
What need then to laugh with glee
when you smile so sweet at me?
What need to kiss, to touch, to take,
or my oath to ne'er foresake?
Warna closed her eyes against bitter tears.
It was time.
Chapter Sixty-Seven
Verice was seated at the high table, talking to Narthing, just starting to wonder why Warna was late when she appeared. She didn't smile, didn't head for her seat, just approached and stood before him.
In her eyes, he saw a look he both admired and feared. The determined, focused drink-the-entire-cup intention.
"Warna." Verice placed his hands on the table as the room went quiet.
"Lord High Baron." Warna wasn't really looking at him; her red-rimmed eyes were focused slightly above his head. "I wish to thank you for the shelter and protection you have extended to me. As painful as it is, as much as we might wish it otherwise, it is time to make public what we both have come to know."
'Ancestors,' Verice throat closed, his mouth as dry as the sun.
Warna's face was stark as she turned away, facing the confused and dismayed gathering. "Lord High Baron Verice and I, by mutual agreement, have decided to sunder our betrothal, for reasons that are our own." Warna's back was straight and stiff, her voice clear. "I will depart for Summerford as soon as I may, to join with my great-uncle and his family. I thank you all." Warna's voice wavered, but she kept on. "I thank you all for the care and kindness I have received at your hands."
With that, she walked out, the silence so deep Verice could hear her footsteps as she went through the main doors, heard her breaking into a run down the stairs and out into the courtyard.
"You're an idiot," Pernard said, not looking up from his plate.
The room was buzzing now, with angry glances being thrown his way.
Verice was aware of them as he stared out the doors, still stunned at Warna's action.
"That's a bit harsh," Narthing said calmly. "But accurate."
"In truth, the Lady Warna is a fine choice of a wife," Ersal didn't look up from his plate. "It strikes me that Lady Warna was a fine helpmate, skilled in running a household as large as this castle and keep."
"It's unlikely that you'd need to make a treaty or alliance marriage outside of Palins, given the current political situation," Pernard added. "And certainly not with the Elven Kingdom. You should feel no hesitation to marry as you would wish. Besides," and here the old mael cocked his head at Verice and gave him a sympathetic look. "There are few that would put up with your personality. Or be willing to overlook certain character flaws. Unless, of course, you've made her unhappy?"
Now his advisors were all glaring at him.
"No, that's not—" Verice shook his head. "She's—" he swallowed hard. "I'm—"
"I suspect that this is a misunderstanding. A private matter," Narthing said. "Something that needs to be discussed between the two of you." He raised an eyebrow as if waiting.
Constable Ricard leaned forward. "Go after her, you fool!"
Verice did just that. Striding from the Great Hall, down the stairs into the darkening courtyard. The dogs ran to greet him, milling around his feet.
The courtyard was empty. Verice looked to the walls, but there was no sign that the guards had noticed anything out of the ordinary. The castle gates were closed, so she was still—
The garden door was open.
"Hup, hup," he commanded. Brindle and the entire pack focused on him. "Warna," he commanded. "Find Warna."
Tails wagging, heads high, the dogs set off for the garden door, barking with joy at the game.
Verice followed.
Warna ran, picking up her skirts, blinded with tears, and found herself in the gardens.
She kept running, kept moving, afraid that her sorrow would catch up with her if she stopped. She hadn't wanted to do it, to say it, and Verice's face had been so shocked.
She ran until she couldn't breathe, and her face was a mess, and the path was narrowing because the gardeners hadn't come this far yet. She slowed, wiping her face with her hands, and finally gave up and used her skirts to wipe her eyes and blow her nose. It didn't matter, nothing mattered, not anymore.
And she kept walking, brushing aside leaves and branches, still crying, because she knew full well that she still had to face Verice, still had to talk to him, damn it, and it all hurt so very much.
A sound, the slightest stirring under a bush and she jumped away, her heart in her throat. It was the cat, walking up to her, rubbing against her skirts, its tail in the air. Warna stumbled slightly, trying not to step on the silly thing. She staggered to the side of the path.
Something caught at her skirt, and she turned quickly. Too quickly, for the rantha thorns caught the fabric and with her twist it wrapped itsself around her legs.
The cat ran off into the garden, its tail high, the tip flicking back and forth.
Warna cursed
Dogs barked in the distance. Warna jerked her head up, cursed again, and reached down to try to pull the thorns free.
Sand and Gray ran up, their tails wagging, barking at their joy of finding her. The rest of the pack wasn't far behind, and they all pushed into her hands, so pleased with themselves. "Careful," Warna said, trying to push them away from the vines, their lean bodies moving all around her. But the dogs were smarter than she was, seemingly able to avoid getting snagged.
"Warna."
Verice stood there, in the fading light. Her tears started fresh.
"I'm sorry," she said. "So very sorry, but it had to be done, Verice, and it was better that I do it, and you wouldn't—"
"Impetuous human," he said.
"It had to be done," Warna huffed at him. "And sometime in my lifetime."
He took a step forward, and she flinched back, the vine tightening around her. Her skirts started to tear and she froze at the sound.
"Warna, stand still." Verice knelt on one knee, shoving the dogs aside.
She obeyed, wiping at her tears again, without much success. She felt his hands on touching her skirts as he examined the tangle.
"The thorns are buried deep," he said softly. "I'm not sure I can free you. Not without tearing it. Hurting it." He looked up at her, his eyes so silver, so kind. "You're crying."
"Sorry," she said. "I can't seem to stop. I'm trying to be reasonable, and logical, and—"
"Marry me," Verice said.
Warna stared at him, in shock. "I just broke our engagement in front of your entire court."
"I know," Verice quirked his lips. "They are rather upset with me at the moment." He continued to look at her, his face calm and composed. "Marry me."
"No, no, you don't mean that," Warna sputtered. "Not for forever. Not for a lifetime. Verice, please. Just let me go."
"Is that a command?" Verice asked.
Warna snorted out a sob, trying to catch her breath. Her face was hot, and her nose stuffed up. "I can't, I won't—I'll hurt you."
"Hurt me?" Verice raised an eyebrow. "Warna, I am a Bearer of the Blood of Tethnar, a Lord High Baron of Palins, a skilled warrior—"
"And just as vulnerable as the rest of us," Warna said. She let her fingers ghost over his cheek, his skin warm under her cold fingers.
"Far too late to worry about that," Verice said. His hands moved in the fabric, trying to work the thorns free. "My heart is already pierced through, my rose."
Warna jerked back.
"Struggling against it won't help." Verice placed a firm hand on her hip.
"I'm so sorry," Warna whispered.
"I'm not," Verice stood, and wrapped his arms around her waist. "You are essential to my home, my hearth, and my heart. Whatever comes, for the rest of our lives and beyond, you are my love, Warna of Farentell."
Warna buried her face in his chest, wrapping her arms around him even as she felt the tug of the vines around her legs. Verice leaned in for a kiss, but she pushed back, wiping her face. "I'm a mess."
"You haven't answered my question," Verice said. "Marry me?"
Warna stilled then, shaking her head in disagreement. "Verice, the day will come when you will regret this choice."
"No," he said firmly. "Never. Every moment of our lives together will be worth any grief that might follow. We don't know what comes, do we? I could be the one to fall, to a sword or crossbow bolt."
Warna grasped his shoulders with a jolt of fear.
"I want 'us' for as long as we last," Verice said. "I want to have that with you. I want to build memories with you. I know there's pain to come but it would come regardless at this point, if I let you go, if I beg you to stay." Verice drew a deep breath, and backed up a step. "Please. Be my love and life and lady. Marry me."
Warna trembled, suddenly cold without his touch. "But what if tomorrow—"
"What if?" Verice sighed. "I don't know what tomorrow holds. Do you?"
"No," she admitted.
Verice held out his hand. Warna held her breath when she saw those long, elegant fingers shaking. "Please, Warna. Shall we find out? Together?"
For one breath out, she thought to deny him. But then she breathed in, and joy swelled within her heart. "Yes," she took a step, and then another. The thorns shredded her skirts as she threw herself into Verice's arms. "Lord and Lady, a thousand times, yes."
Verice wrapped his arms around her, and met her kiss with equal passion.
It was the cheering from the walls and the balcony above that broke them apart.
"Shall we go announce our betrothal?" Verice said into her ear.
"I'm not sure that's necessary," Warna smiled. "And only after I've changed my dress."
Verice laughed, and tugged her along, and they both raced back toward the keep, laughing, the dogs running along beside them barking all the way.
The End.
Epilogue
They were a quiet, still bit of peace in a world of utter madness.
Wolfe sheltered Kalynn in his cloak, holding her tight against him. They stood upon the walls of a besieged town, amidst fire and flame. The name of the place mattered not; what mattered was that war raged at the gates as waves of attackers rode forward, firing arrows and hurling deadly lances, only to ride away to circle round and come back again.
The defenders were outside the gates, trying to hold a precious bit of ground, striving in a hopeless cause.
Here on the walls, men struggled desperately to work the ballista under a rain of deadly arrows. "Bring up the naptha," one shouted. "We'll show these Firelanders!"
It would not save them, Wolfe knew full well. The town was lost; this was but the death throes. He tightened his grip on Kalynn's waist and concentrated on keeping them both cloaked, both wrapped in magical cushions of quiet and shelter.
The journey had been long and difficult, harder than he'd imagined. It hurt to see a beloved land stripped of magic, torn and sundered. Less than what it had been and worse; it had been by his hand.
Traveling without magic to aid them. He and Kalynn were worn to the bone.
But he'd enough reserves to do this task, what they had journeyed so far to accomplish.
Whether he had the will or not was another question.
Amid the frantic movements of the protectors, he waited for the right moment to move. The air was filled with grunts of pain and fear.
Wolfe moved then, urging Kalynn forward. He guided her through the frantic men and maels struggling to load sacks onto the throwing arm of the war machine. The air was filled with grunts of pain and fear. And over all the acrid smell of pitch.
He got Kalynn close to the wall, covering her with his body. He'd wanted desperately to spare her this, to leave her with the airons, but that wasn't possible. She trembled against him, but although there was fear in her eyes, there was also determination. He swallowed back tears at her pain. Best to be about this and done.
"Do you see him?" he whispered as the chaos raged around them.
She nodded, the hood of her cloak moving against his hair.
"Show me," he said, and the world tilted slightly as her vision became his.
The attackers had ridden forward now, and dismounted for the final battle before the gates. One man, small in build, but powerful, led his men over the ground, savagely striking down any that stood in his path. Fierce, and unstoppable.
"Him," Kalynn breathed.
"Light the sacks," came the call behind them, and Wolfe pulled up his reserves, readying himself. There was but one thing—
"Kalynn. Close your eyes."
She looked up at him, his precious love, with a frown. He pressed his fingers to her cheek. "You have seen," he whispered. "But you need not see this."
Behind them came the crackle of flames, and black, burning smoke. "Release!" came the command.
A man hit the pin with a mallet, and the ballista jumped, throwing its deadly load.
Kalynn closed her eyes, and pressed her face to Wolfe's shoulder.
For long moments, the naptha arced overhead, the small burning sacks spreading out, hovering over the battlefield. Wolfe followed one with his eyes, caught it with his power, and changed the arc of its path ever so slightly.
The man, his target, turned his head at the last moment. His ear was woven with a pattern of wire and beads that sparkled in the light.
Bonded. He'd destroy two lives, then. Not just one.
The naptha hit. The man exploded into fire, pain and burning flesh. He fell, sprawled out, screaming.
'I'd offer regrets,' Wolfe thought. 'But I do what must be done.' He leaned down, pressing his head to Kalynn's, taking in the gentle scent of her hair. "It's done," Wolfe whispered into her ear. "We can go."
She nodded silently as he started to wrap his power around them.
Below, from out of nowhere, a muscular, dark-haired warrior appeared, dropping two swords as he flung himself down beside the man on fire. His face torn in anguish, the warrior screamed out a name as he started to beat out the flames with his own hands. The sound came faintly to Wolfe's ears as the magic took them away.
"Marcus!"
About The Author
Elizabeth Vaughan is the USA Today Bestselling author of Warprize, the first volume of The Chronicles of the Warlands. She's always loved fantasy and science fiction, and has been a fantasy role-player since 1981. By day, Beth's secret identity is that of a lawyer, practicing in the area of bankruptcy, a role she has maintained since 1985. More information can be found at her website, WriteandRepeat.com.
Beth is owned by incredibly spoiled cats, and lives in the Northwest Territory, on the outskirts of the Black Swamp, along Mad Anthony's Trail on the banks of the Maumee River.
Acknowledgments
Every ending is a beginning and every beginning is an end.
This book brings to a close the Chronicles of the Warlands and the Epic of Palins. What an adventure it has been, both for my characters and myself as a writer. Friendships forged, lessons learned, and challenges overcome. The list of people who I have met, befriended, loved and lost during these years would fill another book.
I'm not sure how I can thank everyone involved in my journey. So I will take this moment to acknowledge every one of you, and that includes you, dear reader. Please know that you all have my gratitude and my thanks. You bring me joy.
Please also know that while this book ends the series, have no fear.
For I have more stories to tell.
Beth
Works by Elizabeth Vaughan
Warprize
Warsworn
Warlord
Dagger-Star
White Star
Destiny's Star
Warcry
Wardance
Warsong
Fate's Star
Copyright ©2019 by Elizabeth Vaughan
All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means without written permission of the author.
This is a work of fiction. Names, characters, places, and incidents either are the product of the author's imagination or are used fictitiously. Any resemblance to actual events or locales or persons, living or dead, is entirely coincidental.
No part of this book may be used or reproduced in any manner whatsoever without written permission, except in the case of brief quotations embodied in critical articles and reviews. For information address Elizabeth Vaughan at
beth@writeandrepeat.com.
Cover art by Craig White. Used by permission.
Cover design by Shawn King. Used by permission.
Visit Elizabeth Vaughan on the World Wide Web at:
www.writeandrepeat.com
Table of Contents
Chapter One
Chapter Two
Chapter Three
Chapter Four
Chapter Five
Chapter Six
Chapter Seven
Chapter Eight
Chapter Nine
Chapter Ten
Chapter Eleven
Chapter Twelve
Chapter Thirteen
Chapter Fourteen
Chapter Fifteen
Chapter Sixteen
Chapter Seventeen
Chapter Eighteen
Chapter Nineteen
Chapter Twenty
Chapter Twenty-One
Chapter Twenty-Two
Chapter Twenty-Three
Chapter Twenty-Four
Chapter Twenty-Five
Chapter Twenty-Six
Chapter Twenty-Seven
Chapter Twenty-Eight
Chapter Twenty-Nine
Chapter Thirty
Chapter Thirty-One
Chapter Thirty-Two
Chapter Thirty-Three
Chapter Thirty-Four
Chapter Thirty-Five
Chapter Thirty-Six
Chapter Thirty-Seven
Chapter Thirty-Eight
Chapter Thirty-Nine
Chapter Forty
Chapter Forty-One
Chapter Forty-Two
Chapter Forty-Three
Chapter Forty-Four
Chapter Forty-Five
Chapter Forty-Six
Chapter Forty-Seven
Chapter Forty-Eight
Chapter Forty-Nine
Chapter Fifty
Chapter Fifty-One
Chapter Fifty-Two
Chapter Fifty-Three
Chapter Fifty-Four
Chapter Fifty-Five
Chapter Fifty-Six
Chapter Fifty-Seven
Chapter Fifty-Eight
Chapter Fifty-Nine
Chapter Sixty
Chapter Sixty-One
Chapter Sixty-Two
Chapter Sixty-Three
Chapter Sixty-Four
Chapter Sixty-Five
Chapter Sixty-Six
Chapter Sixty-Seven
Epilogue
About The Author
Acknowledgments
Works by Elizabeth Vaughan
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.: Dominios Gratis Para tu WEB :.
Disclaimer:I take no responsibility for you or your actions from reading this. This is for educational purposes. This is illegal, so don't do it.
Among hacking and exploration I recently started playing a mmorpg game (World of Warcraft). The game uses virtual currency to allow players to buy new items. Chineese websites exist that sell the fake currency for USD.
how much virtual currency I was getting, my players name, etc. I changed the variable amount from 50.04 to 1.00 then put the url in firefox and continued the transaction on paypal. I changed the price from $50 to $1 and paypal accepted everything without a problem.
I then checked my player in the game and I had recieved what I was supposed to pay $50 for. I had altered the price and got away with it. After having proof this worked I contacted the owner of the website and repayed them $49.
From there I knew it worked. Wether the person at the cd store would print the invoice and ship it OR contact FBI is beyond me.
I have now shown a simple method to modifying prices on items that are sold with paypal. Please don't get arrested, I take no responsibility for your actions. Hope you enjoyed my first article. | {
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San Cristóbal – miasto w zachodniej Wenezueli, na południowo-zachodnim krańcu łańcucha górskiego Cordillera de Mérida, na wysokości około 825 metrów. Stolica stanu Táchira. Około 460 tys. mieszkańców (2001).
!
Miasta w stanie Táchira | {
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Putin using foreign news agency to wage WAR on U.S….Email Hacks just the beginning
30 Jul, 2016 by Warner Todd Huston
Looks like Russian strongman Vladimir Putin is at it again, this time using a faux "news agency" he set up in Scotland to run his propaganda.
Putin has launched a "news" website centered in Edinburgh, Scotland, to "counter western media" and one of the first things he did was claim that the murder of a UK politician who supported the "stay" half of the Brexit vote was committed to scare Britain into staying with the EU.
Putin has also been blamed for the hacks into the U.S. Democrat Party servers exposing embarrassing emails and memos that proved the Dems were working secretly to destroy Bernie Sanders and his followers.
According to The Daily Mail:
Paul Saunders, executive director of the Centre for National Interest told The Times, Putin is using the news agency to forward his agenda on the international stage.
He said: 'Following Russia's annexation of Crimea and support for separatists in eastern Ukraine, the EU and Russia have begun what appears to be a long-term confrontation.
'As the weaker party, Moscow is seeking whatever levers it can find to undermine its opponents.'
Following the Scottish referendum, the site questioned whether the vote was rigged an managed to convince 100,000 people to sign an online petition to call for a rerun.
The "news" outlet is also fond of publishing stories that are unfavorable to Hillary Clinton, the Mail reports.
Warner Todd Huston
Warner Todd Huston is a Chicago-based freelance writer, has been writing opinion editorials and social criticism since early 2001 and is featured on many websites such as Andrew Breitbart's BigGovernment.com, BigJournalsim.com and all Breitbart News' other sites, RightWingNews.com, CanadaFreePress.com, and many, many others. Additionally, he has been a frequent guest on talk-radio programs across the country to discuss his opinion editorials and current events as well as appearing on TV networks such as CNN, Fox News, Fox Business Network, and various Chicago-based news programs. He has also written for several history magazines and appears in the book "Americans on Politics, Policy and Pop Culture" which can be purchased on amazon.com. He is also the owner and operator of PubliusForum.com. Feel free to contact him with any comments or questions : EMAIL Warner Todd Huston and follow him on Twitter, on Google Plus , and Facebook.
More articles by Warner Todd Huston | {
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{"url":"http:\/\/mathematica.stackexchange.com\/tags\/numerical-integration\/hot?filter=all","text":"# Tag Info\n\n42\n\nControl the Precision and Accuracy of Numerical Results This is an excellent question. Of course everyone could claim highest accuracy for her product. To deal with this situation there exist benchmarks to test for accuracy. One such benchmark is from NIST. This specific benchmark deals with the accuracy of statistical software for instance. The NIST ...\n\n26\n\nThe only reason I am attempting to answer this is to perhaps get a Reversal badge. There you go... We will go slowly and this answer is the basis for what comes next. Let's start with two dimensions. You'll see why. We create a rectangular region: Needs[\"NDSolveFEM\"] mesh = ToElementMesh[FullRegion[2], {{0, 5}, {0, 1}}, \"MeshOrder\" -> 1, ...\n\n24\n\nSolving 1D and 2D complex Schroedinger wave equations with NDSolve I do not agree with you when you write: I know the NDSolve is not magic... My opinion is that NDSolve is one of the most complex functionality I've met so far in the Mathematica environment, with its millions of options and special function this is a real complex thing and it is hard ...\n\n23\n\nThere is an (undocumented?) feature of NDSolve which is handy for exactly this purpose: You can add more than just the start and end of the integration interval and enforce that these points will be met. The result is like you would run NDSolve on each of the corresponding intervals with the starting conditions given by the end point of the previous ...\n\n22\n\nTime-dependent case in the time-dependent case, $[H(t),H(t')]\\neq0$ in general and we need to time-order, ie, the operator taking a state from $t=0$ to $t=\\tau$ is $U(0,\\tau)=\\mathcal{T}\\exp(-i\\int_0^\\tau dt\\, H(t))$ with $\\mathcal{T}$ the time-ordering operator. In practice we just split the time interval into lots of small pieces (basically using the ...\n\n20\n\nEdit of July 10, 2014 As of V10, this equation can now be solved with a single, simple call to NDSolve: y = NDSolveValue[{ r D[y[r, z], z, z] + D[y[r, z], r] + r D[y[r, z], r, r] == r y[r, z], y[1, z] == 1, y[r, 1] == 1 }, y, {r, 0, 1}, {z, 0, 1}]; ContourPlot[y[r, z], {r, 0, 1}, {z, 0, 1}, ColorFunction -> \"TemperatureMap\", ...\n\n19\n\nLet me show how to roll your own numerical solution to a non-linear integral equation using a collocation method. It's fun! This will involve two approximations. First, we will approximate the function B[x] by its values at n particular points in the range {x, 0, 1}. The integral over x will be replaced by a weighted sum over n, i.e., a quadrature rule. ...\n\n17\n\nYou can always separate your inner integrals, convert them to functions and use in NIntegrate: i1[z_?NumericQ] := i1[z] = NIntegrate[-y, {y, 0, z}] i2[x_?NumericQ] := i2[x] = NIntegrate[Exp[i1[z]], {z, -\u221e, x}] NIntegrate[x i2[x], {x, -5., 5}] (* 30.0795 *)\n\n17\n\nYou can use the EventLocator method of NDSolve. Needs[\"DifferentialEquationsInterpolatingFunctionAnatomy\"]; eqns = {Derivative[1][a][t] == -a[t] - 0.2 a[t]^2 + 2.1 b[t], Derivative[1][b][t] == a[t] + 0.1 a[t]^2 - 1.1 b[t], a[0] == 0.5, b[0] == 0.5}; sol = First@ NDSolve[eqns, {a, b}, {t, 0, 1000}, Method -> {\"EventLocator\", ...\n\n17\n\nMy variant of Szabolcs code. It doesn't need an extra package: sol = First[ NDSolve[eqns, {a, b}, {t, 0, 1000}, Method -> {\"EventLocator\", \"Event\" -> Abs[a'[t]] +Abs[b'[t]] < 10^-5, \"EventAction\" :> Throw[end = t, \"StopIntegration\"]}]]; Plot[Evaluate[{a[t], b[t]} \/. sol], {t, 0, end}] As you can see it makes use of the ...\n\n17\n\nGenerally speaking, you can recognize a list because it'll have List as its Head. For example: Head[{1,2,3}] will return List. For your example conditional where you want to change what you do based on the Head of the resulting expression, you can use Switch, such as in: Switch[result, _List, what you want to do with a list, _, what you ...\n\n16\n\nYou can modify the global system variable $Assumptions, to get the effect you want:$Assumptions = aa[t] > 0 Then Integrate[D[yy[x, t], t]^2, {x, 0, 18}] 10.1601 Derivative[1][aa][t]^2 This may, however, be somewhat error-prone. Here is how I'd do this with local environments. This is a generator for a local environment: ...\n\n16\n\nAfter a lengthy study (I'm using version 8) I conclude that there is a bug in Mathematica in the Integrate function when applied to a Sqrt integrand. Ok. let's go (some patience is required because of the long text) Let us define the functions corresponding to your integrals. Remark: because of the relation $1 + cos(2x) = 2 cos^2(x)$ the two forms of ...\n\n15\n\nNIntegrate performs a certain symbolic processing of the integrand to detect discontinuities, singularities, to determine the method to choose and so on. If you know the integrand pretty well, the way to reduce the overhead is to set the method explicitly, set its SymbolicProcessing suboption to 0 (to allow to time spent on the preprocessing), and to add ...\n\n15\n\nThere is the function NFourierTransform[] (as well as NInverseFourierTransform[]) implemented in the package FourierSeries. The function, as with the related kernel functions, takes a FourierParameters option so you can adjust computations to your preferred normalization as needed. For your specific normalization, you apparently want the setting ...\n\n15\n\nSome frames from my version of the animation: Here's the code I used: orbit[posStart_?VectorQ, derStart_?VectorQ] := Block[{c = -Rationalize[6.672*^-11*7*^17], x, y, z, t}, {x, y, z} \/. First @ NDSolve[ Join[Thread[{x''[t], y''[t], z''[t]} == c {x[t], y[t], z[t]}\/Norm[{x[t], y[t], z[t]}]^3], ...\n\n15\n\nAccording to the Mathematica documentation on this page: Here is how to define a 5(4) pair of Dormand and Prince coefficients [DP80]. This is currently the method used by ode45 in MATLAB. DOPRIamat = { {1\/5}, {3\/40, 9\/40}, {44\/45, -56\/15, 32\/9}, {19372\/6561, -25360\/2187, 64448\/6561, -212\/729}, {9017\/3168, -355\/33, 46732\/5247, 49\/176, ...\n\n15\n\nI think it's worth pointing out that the problem can be solved \"straightforwardly\" (i.e., really using only NDSolve) once you know the options that Stefan used in ProcessEquations (which I upvoted because those options are the main ingredient): Below I show the original problem of a Gaussian wave packet with no initial momentum, and then a modified case ...\n\n15\n\nHere's my attempt. To get the matrix representing the Laplacian I use LaplacianFilter on an array of symbols and CoefficientArrays to extract the coefficients. n = 200; shape = ArrayPad[ConstantArray[0, {n\/2, n\/2}], {{0, n\/2}, {0, n\/2}}, 1]; shapeVector = Flatten @ Position[Flatten @ shape, 1]; symbolArray = Array[x, {n, n}]; symbolLaplacian = ...\n\n13\n\nI think you intended to use {li, 200, 800} instead of {li, 800, 200}. If you do so, then you could visualize the result : ListLinePlot@dnFpoints Moreover I would rather define daF in the following form : daF[l_]:= 500 * 0.28 Exp[-((l - 500)\/90)^2] c = 3 10^8; Edit Instead of using Table of dnFpoints I add an alternative method for calculation of ...\n\n13\n\nThis question is somewhat subjective, but here's my take on it: The reason the precise methods are mentioned in papers is to make results reproducible. One has to draw a line when it comes to describing methods. Will you mention what method you used to add or multiply numbers on a computer? What if the numbers are huge and you used FFT-accelerated ...\n\n13\n\nThis is fixed in version 9. This came up on MathGroup before. Since it hasn't been fixed for so long, I wasn't sure if it was really a bug, so I did some spelunking (and some speculation) today to find out what's happening. To jump to the end: I think it's a bug. First, let's see what arguments does LogLinearPlot really pass to the function: ...\n\n13\n\nAs it turns out, the designers of NDSolve[] have precisely anticipated this sort of use; this is where you can use the NDSolveStateData framework. To use acl's example: (* prepare PDE *) state = First[NDSolveProcessEquations[{D[u[t, x], t] == D[u[t, x], x, x], u[0, x] == 0, u[t, 0] == Sin[t], u[t, 5] == 0}, u, t, {x, 0, 5}]]; (* go up to t = 2 *) ...\n\n13\n\nNDSolve has a slew of options that allow you to control the method. You can find the standard reference here. There, we learn how to access Euler's method using NDSolve: Clear[x]; x = x \/. First[ NDSolve[{x'[t] == 0.5*x[t] - 0.04*(x[t])^2, x[0] == 1}, x, {t, 0, 10}, StartingStepSize -> 1, Method -> {\"FixedStep\", Method -> \"ExplicitEuler\"}] ]; ...\n\n13\n\nYou can get the curve in polynomial implicit form as below. poly = GroebnerBasis[{x^2 - ct, y^2 - st, ct^2 + st^2 - 1}, {x, y}, {ct, st}][[1]] (* Out[290]= -1 + x^4 + y^4 *) To get the area, integrate the characteristic function for the interior of the region. That that's where the polynomial is nonpositive (just notice that it is negative at the ...\n\n12\n\nIf you know the equation defining your ellipsoid you could use Boole[] to constrain the integration domain : myF[x_,y_]=Abs[x+y] NIntegrate[Boole[(x\/3)^2 + (y\/2)^2 <= 1] myF[x,y], {x, -5, 5}, {y, -5, 5}] Note that this will actually prevent myF[x, y] from being evaluated outside the domain specified by Boole. This feature of NIntegrate is described ...\n\n12\n\nThis approach finds equilibrium by checking that all derivatives up to the order of the differential equation are below a threshold. Following the template (defined below) suggested by the OP, here is an example for a damped harmonic oscillator: Needs[\"DifferentialEquationsInterpolatingFunctionAnatomy`\"]; eqns1 = {a''[t] == Pi^2\/2500 - (Pi^2*a[t])\/2500 - ...\n\nOnly top voted, non community-wiki answers of a minimum length are eligible","date":"2014-09-30 20:21:09","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.32373738288879395, \"perplexity\": 1839.5145534624794}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-41\/segments\/1412037663135.34\/warc\/CC-MAIN-20140930004103-00074-ip-10-234-18-248.ec2.internal.warc.gz\"}"} | null | null |
Carriera
Giocatore
Ha iniziato la carriera nel 1979-1980 in serie D nella Pro Tolmezzo, dove rimase per tre stagioni segnando 13 reti in 63 presenze.
Nel 1982-1983 giocò in Serie C2 nella Pro Gorizia, realizzando 6 reti in 32 presenze.
L'anno successivo venne acquistato dall', e dopo pochi mesi fu ceduto in Serie B alla Cavese, dove giocò 20 partite con 2 reti all'attivo. Con la squadra campana disputò anche le due stagioni successive in Serie C1, per un totale di 85 presenze e 16 reti.
Passò quindi al Cosenza, militante nel girone B di Serie C1, dove rimase per tre stagioni. Nella prima annata rossoblu giocò 31 partite, segnando 7 reti, tra le quali una contro la battuta per 1-0.
L'anno successivo, 1987-1988, il Cosenza ottenne una promozione in Serie B che mancava da 24 anni, con Urban che diede il suo contributo realizzando 3 reti in 30 presenze, fra cui quella contro la nell'ultima partita casalinga che i rossoblù di Gianni Di Marzio vinsero per 2-0.
Nella stagione seguente giocò tra i cadetti 36 partite, segnando 4 gol con la squadra allenata da Bruno Giorgi, la quale mancò il salto in Serie A per la classifica avulsa, terminando al quarto posto alla pari con e .
Lascerà il Cosenza per andare a giocare in Serie A, dopo aver totalizzato con i silani 97 presenze e 14 gol.
Passa quindi al di Franco Scoglio. L'esordio in serie A avvenne il 27 agosto 1989 in Genoa- (1-0). Con i grifoni rossoblù giocò 20 partite, segnando 2 reti, entrambe in una gara a Marassi contro l'Atalanta terminata 2-2. Sono gli unici gol realizzati da Urban in massima serie.
L'anno successivo (1990-1991) tornò in serie B vestendo la maglia della .
Chiuse con il calcio dopo aver vestito le maglie di (Serie B), (Serie C2 e Serie C1) e Cavese (Serie D).
Allenatore
Tra il 1996 e il 2001 ha allenato le giovanili del Cosenza.
Nella stagione 2002-2003 siede sulla panchina del , in Serie D, venendo esonerato alla 14ª giornata. Nel 2008, nella stessa categoria, è su quella della molisana Venafro, dove nel novembre dello stesso anno é esonerato.
Nell'aprile del 2008, a quattro giornate dal termine, é ingaggiato dalla Turris, in Serie D, sostituendo Merolla, ottenendo la salvezza.
Nel febbraio 2013 accetta la panchina del Vairano, in Promozione, con cui ottiene la promozione in Eccellenza.
Il 25 ottobre 2013 diventa nuovamente allenatore del Comprensorio Vairano sostituendo, come nella stagione precedente, l'allenatore Delle Vedove.
Nel campionato 2017-2018 allena il Venafro, in Eccellenza.
L'11 febbraio 2019 è tornato nuovamente sulla panchina del Comprensorio Vairano, in Promozione.
Il 9 gennaio 2023 viene nominato allenatore in seconda di Vincenzo Criscuolo al .
Dirigente
Il 19 luglio 2010 torna al Cosenza, chiamato da Renzo Castagnini, diventando Team Manager; a gennaio si dimette.
Il 2 agosto 2011, chiamato da Castagnini, è ufficialmente presentato come nuovo Team Manager del durante la presentazione della squadra. Il 2 dicembre lascia l'incarico.
Note
Bibliografia
Davide Rota, Dizionario illustrato dei giocatori genoani, De Ferrari, 2008.
Collegamenti esterni | {
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Tamil Nadu (Tamil: தமிழ்நாடு pronunciation (help·info) English: Land of the Tamils, IPA: [t̪ɐmɨɻ n̪aːɽɯ]) is a state at the southern tip of India. Tamil Nadu is bordered by Puducherry(Pondicherry), Kerala, Karnataka and Andhra Pradesh.
Colonised by the East India Company, Tamil Nadu was eventually incorporated into the Madras Presidency. After the independence of India, the state of Madras was created in 1956 based on linguistic boundaries. The name of the state was changed to Tamil Nadu in the year 1969.
Tamil Nadu politics has been dominated by the AIADMK and DMK parties. They are fore runner for few policies instated at national level such as reservation policies for dominant caste and sectors in the society. Both parties stemmed from the Dravidian movement, which demanded greater rights for the 'Dravidian' population of Tamil Nadu.
Lying on the southeastern coast of the Indian peninsula, Tamil Nadu is bounded by the Eastern Ghats in the north and Nilgiri, the Annamalai Hills, and Palakkad on the west. The state has large fertile areas along the Coromandel coast, the Palk strait, and the Gulf of Mannar. The fertile plains of Tamil Nadu are fed by rivers such as the Kaveri, Palar, and Vaigai, as well as the northeast monsoon. Traditionally a manufacturing state, Tamil Nadu is also a leading agricultural producer.
The sixth most populous state in India, Tamil Nadu has the largest national urban agglomeration. In recent times, population growth in the state has been amongst the lowest in the nation. Globalisation has brought increased export opportunities, making Tamil Nadu the third largest economy among the states of India. There has also been an increase in the number of educational institutions in Tamil Nadu, with the state containing the most vocational training institutions in India. Chennai, the state capital (known until 1996 as Madras), is the fourth largest city in India. Coimbatore, Madurai, Tiruchirapalli, Salem, Tirunelveli and Tirupur are other corporations of Tamil Nadu.
Tamil Nadu has been continuously inhabited by humans since prehistoric times, and its historical and cultural traditions are among the oldest in the world. The Tamil kingdoms of Chera, Chola, Pandya and Pallava were responsible for the production of some of the oldest surviving literature in India. Also, Carnatic Music, Bharatanatyam dance and Indian architecture evolved within the state. Indeed, several famous composers, such as Tyagaraja, lived and flourished in Tamil Nadu. | {
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Pepper Group has priced its second $1 billion non-conforming RMBS issue, Pepper Residential Securities Trust No 21 (PRS21). This transaction is Pepper's third securitisation for the year and comes just 4 months since its first ever billion dollar transaction.
Strong demand from both new and repeat investors saw the transaction upsized from its original size of $700m, with the issue being supported by 29 separate investors from the US, Australia, Europe and Asia.
Pricing was competitive in a widening market. Pepper structured the transaction in a manner that met the needs of its growing global investor base. The US dollar tranche once again enjoyed strong support.
Pepper Group was assisted in this transaction by National Australia Bank (Arranger) and nabSecurities LLC and Citigroup Global Markets Inc (Joint Lead Managers) and Commonwealth Bank of Australia and Westpac Banking Corporation (Co-Managers) on the US notes and Commonwealth Bank of Australia, National Australia Bank and Westpac Banking Corporation (Joint Lead Managers) on the AUD notes.
Since inception, Pepper has issued over AUD$13.2 billion of RMBS across 28 non-conforming and prime RMBS issues, making it one of the most experienced and regular issuers in the market.
The transaction settled today, 31 July 2018. | {
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The Best Time to Visit Oconomowoc, WI, US for Weather, Safety, & Tourism
The best times to visit Oconomowoc for ideal weather are
May 21st to September 30th
Oconomowoc Travel Guide
Other Oconomowoc Travel Info
Weather in Oconomowoc
Average temperatures in Oconomowoc vary drastically. Considering humidity, temperatures feel cold for about half of the year and otherwise nice with a very low chance of rain or snow throughout the year. The area is somewhat temperate — in the 58th percentile for pleasant weather — compared to tourist destinations worldwide. Weeks with ideal weather are listed above. If you're looking for the very warmest time to visit Oconomowoc, the hottest months are July, August, and then June. See average monthly temperatures below. The warmest time of year is generally mid July where highs are regularly around 81.1°F (27.3°C) with temperatures rarely dropping below 62.8°F (17.1°C) at night.
Oconomowoc Temperatures (Fahrenheit)
Oconomowoc Temperatures (Celsius)
Oconomowoc Perceived Temperature (F)
Oconomowoc Perceived Temperature (C)
Average Oconomowoc Temperatures by Month
Feb 27.2 20 13.5
Oct 59.1 50 42.3
Jan -2.9 -7.1 -10.7
Feb -2.7 -6.7 -10.3
Mar 6.1 0.9 -3.3
Apr 12.4 6.9 2.3
May 19.8 13.8 8.4
Oct 15.1 10 5.7
Nov 7.6 3.1 -0.8
Dec 0.1 -3.5 -6.9
If dry weather is what you're after, the months with the lowest chance of significant precipitation in Oconomowoc are January, July, and then August. Note that we define "significant precipitation" as .1 inches or more in this section. The lowest chance of rain or snow occurs around early January. For example, on the week of January 1st there are no days of precipitation on average. By contrast, it's most likely to rain or snow in late April with an average of 0 days of significant precipitation the week of April 23rd.
When can you find snow in Oconomowoc? Weather stations report no annual snow. Please note that a value of 0 for snow in the graph below may either mean there was no snow, or that snow is unreported.
The graph below shows the % chance of rainy and snowy days in Oconomowoc.
The graph below shows the average snow on the ground in Oconomowoc (in).
Jan 0% 0 0
Feb 2% 0 0.1
Mar 1% 0 0.1
Apr 3% 0 0.2
May 2% 0 0.3
Jun 2% 0 0.5
Jul 1% 0 0.2
Aug 1% 0 0.1
Sep 2% 0 0.2
Oct 2% 0 0.2
Nov 2% 0 0.1
Dec 2% 0 0.1
Jan 0 0 0
Feb 2 0 0.3
Mar 1 0 0.3
Apr 3 0 0.5
May 2 0 0.8
Jun 2 0 1.3
Jul 1 0 0.5
Aug 1 0 0.3
Sep 2 0 0.5
Oct 2 0 0.5
Nov 2 0 0.3
Dec 2 0 0.3
Oconomowoc has some very humid months, with other comfortably humid months. The least humid month is May (55% relative humidity), and the most humid month is December (74.2%).
Wind in Oconomowoc is usually calm. The windiest month is April, followed by January and February. April's average wind speed of around 8.3 knots (9.5 MPH or 15.3 KPH) is considered "a gentle breeze." Maximum sustained winds (the highest speed for the day lasting more than a few moments) are at their highest in early to mid April where average top sustained speeds reach 15.5 knots, which is considered a moderate breeze.
The graph below shows the average % humidity by month in Oconomowoc.
Jan 8.1 Gentle breeze 14.3 Significant breeze
Feb 7.8 Gentle breeze 13.8 Significant breeze
Mar 7.4 Gentle breeze 13.7 Significant breeze
Apr 8.3 Gentle breeze 15.1 Significant breeze
May 7 Gentle breeze 13.8 Significant breeze
Jun 5.8 Light breeze 12.6 Significant breeze
Jul 5.5 Light breeze 11.7 Significant breeze
Aug 4.9 Light breeze 11.1 Significant breeze
Sep 5.3 Light breeze 11.7 Significant breeze
Oct 6.7 Light breeze 13.2 Significant breeze
Nov 7.6 Gentle breeze 13.8 Significant breeze
Dec 7.4 Gentle breeze 13.5 Significant breeze
May 55%
Sep 66%
Is it Safe to Travel to Oconomowoc?
Our best data indicates this area is generally safe. As of Oct 07, 2019 there are no travel advisories or warnings for the United States; exercise normal security precautions. Check this page for any recent changes or regions to avoid: Travel Advice and Advisories. This advisory was last updated on Sep 23, 2019.
The busiest month for tourism in Oconomowoc, WI, US is July, followed by June and May. Prices for hotels and flights will be most expensive during these months, though you can save if you purchase well in advance. Tourists are unlikely to visit Oconomowoc in November. Those willing to visit at these times will likely find it the least expensive month.
Tourism graph is based on Google searches for services used by tourists relative to the rest of the year. Tourism data for this area is somewhat extrapolated based on nearby areas. Displayed data is calculated relative to the peak, so a score of 38.2 in November means 38.2% of the tourists vs. July.
Overall Oconomowoc Travel Experience by Season
Spring (March through May)
Humidity and temperatures combine to make this season feel moderately cold. Highs range from 73.1°F (22.8°C) and 29.7°F (-1.3°C) with far warmer temperatures in the later months. Rain is extremely rare with 0 to 1 days of significant precipitation per month. Spring is the second busiest for tourism, which makes it a good time for those looking for things to do.
Summer (June through August)
The middle-year months have very comfortable weather with high temperatures that are comfortable. These months see moderate precipitation with 0 to 1 days of precipitation per month. June – August is the busiest season for tourism in Oconomowoc, so lodging and other accommodations may cost more than usual.
Fall (September through November)
Fall daily highs range from 75°F (23.9°C) and 37.6°F (3.1°C), which will feel chilly given the humidity and wind. It rains or snows a barely noticeable amount: 0 to 1 days per month. Tourism is the slowest during these months due to the weather, so hotels may be affordably priced.
Winter (December through February)
Weather is far too cold this time of year in Oconomowoc to be enjoyable for warm weather travelers. The average high during this season is between 32.6°F (0.3°C) and 24.4°F (-4.2°C). On average, it rains or snows a insignificant amount: consistently 0 times per month. These times of year are fairly slow with tourists.
Best Times to Travel› the United States › Oconomowoc, WI, US
Southeast Wisconsin, the United States
Udaipur District, India | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,872 |
\section{introduction} The main theme of this note is an operation that we call lifting and use for spreading a special property of a monomial curve within a family of infinite examples. By a monomial curve $C_S$ in the affine space $K^n$ over a field $K$, we mean a curve whose points $(t^{m_{1}},\dots, t^{m_{n}})$ varies with the parameter $t\in K$. The curve has a strong relation with the semigroup $S$ generated minimally by the positive integers $m_1,\dots,m_n$. The smallest minimal generator of $S$ is called the \textit{multiplicity} of $C_S$. The monomials $t^{m_{1}},\dots, t^{m_{n}}$ generate the integral domain $K[S]$ of $K[t]$, which is known as the \textit{numerical semigroup ring} associated to $S$. The polynomial ring $R=K[x_1,\dots,x_n]$ is graded by the semigroup $S$, by setting $\deg _S (x_i)=m_i$, giving rise to a graded map $R \rightarrow K[S]$, which sends $x_i$ to $t^{m_i}$. Its kernel denoted $I_S$ is called the \textit{toric ideal} of $S$. When $K$ is algebraically closed, the vanishing ideal $I(C_S)$ of $C_S$ is $I_S$, and thus $K[S]$ is isomorphic to the coordinate ring $R/I_S$ of the curve $C_S$. The curve $C_S$ is singular at the origin if $S\neq {\mathbb N}$ in which case one wants to measure how nice the singularity is. An algebraic way to understand the quality of the singularity is to look at the coordinate ring $gr_{\mathfrak{m}}(K[S])$ of the \textit{tangent cone} which is isomorphic to the ring $R/I^*_{S}$, where ${\mathfrak m}=\langle t^{m_{1}},\dots, t^{m_{n}} \rangle$ is the maximal ideal of $K[S]$. Here $I^*_{S}$ is the ideal generated by the least degree homogeneous summands $f^{*}$ of $f$ in $I_S$. Many researchers investigated Cohen-Macaulayness of $gr_{\mathfrak{m}}(K[S])$ for this purpose, see e.g. \cite{arslan,CZ,huang,shen,shibuta}.
It is well known that the ideal $I_S$ is generated by finitely many binomials $x_1^{u_1}\cdots x_n^{u_n}-x_1^{v_1}\cdots x_n^{v_n}$ such that $u_iv_i=0$ and $\deg_S(x_1^{u_1}\cdots x_n^{u_n})=\deg_S(x_1^{v_1}\cdots x_n^{v_n})$. In general, the ideal $I_S$ has alternative minimal generating sets of the same cardinality. If a binomial $B$ or $-B$ appears in every minimal generating set it is called \textit{indispensable}. Hence, the ideal $I_S$ has a unique minimal generating set if and only if it is generated by indispensable binomials. Uniquely generated ideals are of interest in the emerging field of algebraic statistics, see \cite{goj,tak}. Recently, indispensable binomials are also used for characterizing monomial curves in $K^4$ with Cohen-Macaulay tangent cone, see \cite{AKN,pseudo}.
Our main aim in this note is to see how Cohen-Macaulayness spreads among liftings of a monomial curve. It is inspired by a recent paper by Herzog and Stamate (see \cite{HS}) on a similar additive operation on $S$ called shifting, which produces a semigroup generated by $m_1+k,\dots,m_n+k$ for every positive integer $k$. In that article, Herzog and Stamate show that tangent cones of shiftings are Cohen-Macaulay for all sufficiently large $k$, and that the Betti numbers of the tangent cones are eventually periodic in $k$. The second concern of this paper is to examine how lifting effects indispensability of binomials in $I_S$ and strong indispensability of a minimal free resolution of $K[S]$. Before stating our main results let us introduce more notations. Fix a numerical semigroup $S$ generated minimally by $m_1 ,m_2,\dots ,m_n$. By a $k$-lifting $S_{k}$ of $S$ we mean the numerical semigroup generated by $$m_1,km_{2},\dots,km_n,$$ where $k$ is a positive integer with $\gcd (k,m_1)=1$. The last condition is to avoid having isomorphic liftings. In the same vein, the monomial curve $C_{k}$ corresponding to $S_{k}$ is called a $k$-lifting of $C:=C_S$. When $C$ has multiplicity $m_1$, all of its liftings will have multiplicity $m_1$. There is a closely related operation called simple gluing that have been used in literature to produce more examples with an interesting structure from a single monomial curve. Let $T$ be a semigroup generated minimally by $m_{2},\dots,m_n$. If $m_1\in T$ and $\gcd(k,m_1)=1$, then $S_k$ is called a simple gluing of $T$ and ${\mathbb N}$. Notice that $S_k$ is a $k$-lifting of $S_1=S$ for any $k$. This technique has been used for the first time in \cite{watanabe} to prove that $S_k$ is symmetric if and only if $T$ is symmetric. It is used in \cite{morales} to produce monomial curves with Noetherian symbolic blow-ups and in \cite{thoma} to create monomial curves which are set theoretic complete intersections. In \cite{pf}, the authors proved that the tangent cone $gr_{\mathfrak{m}}(K[S_k])$ is Cohen-Macaulay when the same is true for the semigroup $T$ and $k\leq m_2+\cdots+m_n$. This is extended later in \cite{JZ}. Finally, it has very recently been used to study catenary degree (see \cite[Theorem 3.3]{Oneill}) which is an invariant of the semigroup measuring complexity of factorisations of elements. As $T$ is independent of $k$, all these results reveal common behavior of the liftings $S_k$, in the special case that $m_1\in T$.
We finish the introduction by describing the structure of the paper. In the next section, we establish a one to one correspondence between the binomials in both ideals $I_S$ and $I_{S_k}$ with monomials having no common divisor, associating minimal generators of $I_S$ to those of $I_{S_k}$, and preserving indispensability, see Proposition \ref{indispensables}. In Section $3$, we show that all but finitely many liftings of a monomial curve have Cohen-Macaulay tangent cones even if the tangent cone of the original curve is not Cohen-Macaulay. Moreover, all liftings have Cohen-Macaulay tangent cones when the original monomial curve has a Cohen-Macaulay tangent cone, see Theorem \ref{liftsofCM}. In the last section, we show that the minimal free resolution of $K[S]$ is strongly indispensable if and only if the minimal free resolution of $K[S_k]$ is strongly indispensable, see Proposition \ref{free}. Finally, we prove that the Betti sequence of the tangent cone is eventually constant under this operation and that all the Betti sequences are nothing but the Betti sequence of the original tangent cone if the latter is Cohen-Macaulay, see Theorem \ref{resTC}.
\section{Indispensability}
In this section we establish the correspondence between the indispensable binomials of a monomial curve and those of its liftings. Let us recall a graph encoding minimal generators of $I_S$. Let $V( d)$ be the set of monomials of $S$-degree $d$. Denote by $G(d)$ the graph with vertices the elements of $V( d)$ and edges $\{M,N\} \subset V( d)$ such that the binomial $M-N$ is generated by binomials in $I_S$ of $S$-degree strictly smaller than $d$ with respect to $<_S$, where $s_1<_S s_2$ if $s_2-s_1 \in S$. In particular, when $\gcd(M,N) \neq 1$, $\{M,N\}$ is an edge of $G( d)$ as $M-N=\gcd(M,N)\cdot [(M-N)/\gcd(M,N)]$ and the binomial $(M-N)/\gcd(M,N)$ in $I_S$ has strictly smaller $S$-degree. A binomial of $S$-degree $d$ is indispensable if and only if $G(d)$ has two connected components which are singletons, by \cite[Corollary 2.10]{CKT}. This means that $M-N$ is indispensable exactly when
$V( d)=\{M,N\}$ and $M-N$ is not generated by binomials in $I_S$ of $S$-degree strictly smaller than $d$.
Let $b \in S$. Every tuple $(v_1,\dots,v_n)\in {\mathbb N}^n$ satisfying $b=v_1 m_1+\cdots+v_n m_n$ is called a \textit{factorization} of $b$. Note that there is a one to one correspondence between factorizations $(v_1,\dots,v_n)$ of $b\in S$ and monomials $N=x_1^{v_1}\cdots x_n^{v_n}$ of $S$-degree $b$.
The following key fact will be used many times in the sequel.
\begin{lemma}\label{semigroups} There is a one to one correspondence between $S$ and $kS\subset S_k$ under which $m_1+S$ is mapped onto $k(m_1+S)$. Moreover, the factorization $(v_1,v_2,\dots,v_n)$ of $b\in S$ corresponds to the factorization $(kv_1,v_2,\dots,v_n)$ of $kb\in kS$.
\end{lemma}
\begin{proof} If $b \in S$, then $k b \in k S \subset S_k$. Conversely, if $k b \in S_k$, then we have $k b=v'_1 (m_1)+v_2 (k m_2)+\cdots+v_n (k m_n)$. So, $k$ divides $v'_{1}m_1$, which forces the existence of $v_{1}\in {\mathbb N}$ such that $v'_{1}=k v_{1}$, since $\gcd(k,m_1)=1$. Thus,
$b=v_1 m_1+\cdots+v_n m_n \in S$. So, the map sending $b\in S$ to $kb=kv_1 (m_1)+v_2 (km_2)+\cdots+v_n (km_n) \in S_k$ is one to one and onto. As $v_1\neq 0$ if and only if $kv_1\neq 0$, it follows that this map restricts to a one to one correspondence between $m_1+S$ and $k(m_1+S)$. Clearly, the factorization $(v_1,v_2,\dots,v_n)$ of $b$ corresponds to the factorization $(kv_1,v_2,\dots,v_n)$ of $kb$.
\end{proof}
It is time to describe the correspondence between the binomials in both ideals $I_S$ and $I_{S_k}$ with monomials having no common divisor. This has been noted for the first time by Morales (see \cite[Lemma 3.2]{morales}). We show that indispensable binomials are associated with indispensable ones under this correspondence. Let $B$ be a binomial in $I_S$ with monomials having no common divisor. Then, either $x_1$ divides no monomials in $B$ or it divides only one of them. In the former case, $B$ lies in $I_{S_k}$, so let $B_k:=B$. In the latter, $B=M-N$ with $M=x_2^{u_2}\cdots x_n^{u_n}$ and $N=x_1^{v_1}x_2^{v_2}\cdots x_n^{v_n}$, so we let $B_k:=M-N_k \in I_{S_k}$, where $N_k=x_1^{kv_1}x_2^{v_2}\cdots x_n^{v_n}$. In both cases, $\deg_{S_k}(B_k)=k\deg_S(B)\in kS$.
\begin{proposition} \label{indispensables} The map $\phi_k: I_S \rightarrow I_{S_k}$, given by $B \rightarrow B_k$, is a one to one correspondence between the binomials in both ideals with monomials having no common divisor, associating minimal generators of $I_S$ to those of $I_{S_k}$, and preserving indispensability.
\end{proposition}
\begin{proof} It is clear that the assignment is one to one. We prove that it is onto by using Lemma \ref{semigroups}. Now, assume that $M-N'$ is a binomial in $I_{S_k}$, where $M=x_2^{u_2}\cdots x_n^{u_n}$ and $N'$ is a monomial corresponding to the factorization $(v'_1,v_2,\dots,v_n)$ with $v'_1>0$. So, $\deg_{S_k}(N')=\deg_{S_k}(M)=kb$ lies in $k(m_1+S)$, where $b:=\deg_{S}(M)$. Lemma \ref{semigroups} implies that the factorization $(v'_1,v_2,\dots,v_n)$ of $kb$ corresponds to the factorization $(v_1,v_2,\dots,v_n)$ of $b$, for some $v_1>0$. Therefore, there is a monomial $N=x_1^{v_1}x_2^{v_2}\cdots x_n^{v_n}$ with $S$-degree $b$ such that $N'=N_k$. So, $\phi_k(M-N)=M-N'$.
Let $G(b)$ be the graph of an $S$-degree $b$ and $G_k(d)$ be the graph of an $S_k$-degree $d$. By Lemma \ref{semigroups}, there is a one to one correspondence between the monomials of $S$-degree $b$ and monomials of $S_k$-degree $kb$. So, there is a correspondence between the vertices of the graphs $G(b)$ and
$G_k(kb)$. By the first part, $M-N$ is generated by binomials in $I_{S}$ of $S$-degree smaller than $b$ if and only if $M-N_k$ is generated by binomials in $I_{S_k}$ of $S_k$-degree smaller than $kb$. This correspondence associates edges between $\{M\}$ and $\{N\}$ to edges between $\{M\}$ and $\{N_k\}$. As these graphs determine the minimal generators, this correspondence associates a minimal generating set of $I_S$ to a minimal generating set of $I_{S_k}$. Assuming that $B$ is an indispensable binomial of $S$-degree $b$, we get that $G(b)$ has two connected components $\{M\}$ and $\{N\}$ which are singletons by \cite[Corollary 2.10]{CKT}. Thus, $\{M\}$ and $\{N_k\}$ are the only connected components of $G_k(kb)$ and they are singletons. Hence, $B$ is indispensable if and only if $B_k$ is indispensable.
\end{proof}
\section{Cohen-Macaulayness of the tangent cone}
In this section, we study local properties of liftings of a monomial curve $C$ with multiplicity $m_1$. Recall that the $S$-degree and the usual degree of a monomial is
$$\deg_S (x_1^{u_1}\cdots x_n^{u_n})= u_1m_1+\cdots+u_n m_n; \quad \deg (x_1^{u_1}\cdots x_n^{u_n})= u_1+\cdots+u_n.$$
\begin{lemma}[\cite{herzog}] \label{Herzog} Let $C$ be the monomial curve corresponding to $S$. Then the tangent cone of $C$ is Cohen-Macaulay if and only if for every monomial $M=x_2^{u_2}\cdots x_n^{u_n}$ with $\deg_S(M) \in m_1+S$ there exists a monomial $N=x_1^{v_1}\cdots x_n^{v_n}$ with $v_1>0$ such that
$\deg_S M = \deg_S N$ and $ \deg M \leq \deg N. \hfill \Box$
\end{lemma}
\begin{remark} \label{remark1} It is sufficient to check the conditions in Lemma \ref{Herzog} for monomials $M$ with $u_i< m_1$, where $i=2,\dots,n$. This is because when $u_i \geq m_1$ we have $u_i=q_im_1+r_i$ and so $$\deg_S(M)=\sum_{j=2}^{n} u_jm_j=(q_im_i)m_1+r_im_i+\sum_{j\in\{2,\dots,n\}\setminus \{i\}} u_jm_j=\deg_S(N)$$
for $N=x_1^{q_im_i}\cdots x_i^{r_i} \cdots x_n^{u_n}$. Since $u_i=q_im_1+r_i<q_im_i+r_i$, it follows that $$\deg (M)=\sum_{j=2}^{n} u_j<(q_im_i)+r_i+\sum_{j\in\{2,\dots,n\}\setminus \{i\}} u_j=\deg(N).$$
\end{remark}
\begin{theorem}\label{liftsofCM} Let $C$ be a monomial curve and $C_k$ be its $k$-th lift. If $C$ has a Cohen-Macaulay tangent cone, then $C_k$ has a Cohen-Macaulay tangent cone for all $k>1$. If not, there is a positive integer $k_0$ such that $C_k$ has a Cohen-Macaulay tangent cone for all $k\geq k_0$.
\end{theorem}
\begin{proof} Take a monomial $M=x_2^{u_2}\cdots x_n^{u_n}$ whose $S_k$-degree $\deg_{S_k}(M)=k\deg_{S}(M)$ lies in $m_1+S_k$. It follows from Lemma \ref{semigroups} that $\deg_{S}(M)\in m_1+S$. This means that there is a monomial $N=x_1^{v_1}x_2^{v_2}\cdots x_n^{v_n}$ such that $v_1>0$ and $\deg_{S}(M)=\deg_{S}(N)$. Clearly, we also have $\deg_{S_k}(M)=\deg_{S_k}(N_k)$, for $N_k=x_1^{kv_1}x_2^{v_2}\cdots x_n^{v_n}$. So, under the correspondence in Proposition \ref{indispensables}, the binomial $M-N$ in $I_S$ maps to $M-N_k$ in $I_{S_k}$.
On the other hand, we have
\begin{eqnarray} \label{eqn3}
\deg(N_k)-\deg(M)&=&\deg(N_k)-\deg(N)+\deg(N)-\deg(M) \\
\nonumber &=&(k-1)v_1+\deg(N)-\deg(M).
\end{eqnarray}
Now, if $C$ has a Cohen-Macaulay tangent cone, it follows from Lemma \ref{Herzog} that there is at least one $N$ among all with
$\deg(N)-\deg(M)\geq 0$. Thus, we have $\deg(N_k)-\deg(M)\geq 0$ for the corresponding $N_k$ by Equation \ref{eqn3}. So, $C_k$ has a Cohen-Macaulay tangent cone by Lemma \ref{Herzog}.
If $C$ does not have a Cohen-Macaulay tangent cone, then again by Lemma \ref{Herzog} there is some monomial $M$ with $\deg_{S}(M)\in m_1+S$ such that for all $N$ with $\deg_{S}(M)=\deg_{S}(N)$ we have $\deg(N)-\deg(M)< 0$. Since $S$ is a numerical semigroup, there are only finitely many monomials $N$ with the $S$-degree $\deg_{S}(M)$ for a fixed monomial $M$. Let $N_0$ be the one with the biggest degree so that $\deg(N)-\deg(M)$ is the biggest possible negative number. Then, for large enough $k_0(M)$, we have $(k_0(M)-1)v_1+\deg(N)-\deg(M)\geq 0$. Hence, it follows that $\deg(N_k)-\deg(M)\geq 0$ by Equation \ref{eqn3}, for all $k\geq k_0(M)$. By Remark \ref{remark1} it is sufficient to check the condition of Lemma \ref{Herzog} for finitely many monomials $M$. So, if we choose $k_0$ to be the maximum of all $k_0(M)$ corresponding to these monomials, then Lemma \ref{Herzog} completes the proof.
\end{proof}
\section{Minimal free resolutions}
Let $S$ be a numerical semigroup and $S_k$ be its $k$-th lift as before. In this section we discuss the relation between their homological invariants. We start with the relation between minimal free resolutions of the semigroup rings $K[S]$ and $K[S_k]$. Recall that $R=K[x_1,\dots,x_n]$ is $S$- and $S_k$-graded, respectively, via
$$\deg_S(x_1)=\deg_{S_k}(x_1)=m_1 \quad \mbox{and} \quad \deg_{S_k}(x_i)=k\deg_S(x_i)=k m_i, \quad i>1.$$ As indicated in \cite{numata}, a minimal $S_k$-graded free resolution of $K[S_k]$ is obtained from a minimal $S$-graded free resolution of $K[S]$ via the faithfully flat extension $f:R \rightarrow R$, defined by sending $x_1 \rightarrow x_1^{k}$ and $x_i \rightarrow x_i$ for all $i>1$. These prove the following
\begin{proposition}\label{free} If $K[S]$ has a minimal $S$-graded free resolution given by
$$\displaystyle 0 {\longrightarrow} \bigoplus_{j=1}^{\beta_{n-1}} R[{-b_{n-1,j}}] {\longrightarrow} \cdots {\longrightarrow} \bigoplus_{j=1}^{\beta_1} R[{-b_{1,j}}] {\longrightarrow} R {\longrightarrow} K[S]{\longrightarrow}0,$$
then $K[S_k]$ has a minimal $S_k$-graded free resolution given by
$$\displaystyle 0 {\longrightarrow} \bigoplus_{j=1}^{\beta_{n-1}} R[{-k b_{n-1,j}}] {\longrightarrow} \cdots {\longrightarrow} \bigoplus_{j=1}^{\beta_1} R[{-k b_{1,j}}] {\longrightarrow} R {\longrightarrow} K[S]{\longrightarrow}0. $$ \hfill \mbox{ $\Box$}
\end{proposition}
It follows from Proposition \ref{indispensables} that $I_{S_k}$ has a unique minimal generating set or equivalently is generated minimally by indispensable binomials if and only if $I_S$ has the same property. This means that one of the first matrices in the resolutions of Proposition \ref{free} is unique if and only if the other is so. The corresponding notion introduced by Charalambous and Thoma (see \cite{haraJA}) for the full minimal free resolution is strong indispensability of the resolution. Recall that a resolution $({\bf F},\phi)$ is called strongly indispensable if for any graded minimal resolution $({\bf G},\theta)$, we have an injective complex map
$i\colon({\bf F},\phi)\longrightarrow({\bf G},\theta)$. As a consequence, we get the following result about indispensability of higher syzygies using Lemma \ref{semigroups}.
\begin{proposition} \label{strongly}$K[S_k]$ has a strongly indispensable minimal free resolution $\iff$ $K[S]$ has a strongly indispensable minimal free resolution.
\end{proposition}
\begin{proof} By \cite[Lemma 19]{bafrsa}, the algebra $K[S_k]$ has a strongly indispensable minimal free resolution $\iff$ $b-b' \notin S_k$, for all $b,b' \in {\mathcal B}_i(S_k)$. Proposition \ref{free} implies that ${\mathcal B}_i(S_k)=k {\mathcal B}_i(S)$ and thus $b \in {\mathcal B}_i(S_k) \iff b=k d$, for some $d \in {\mathcal B}_i(S)$. Thus, $b-b' \notin S_k$ for all $b,b' \in {\mathcal B}_i(S_k) \iff d-d' \notin S$ for all $d,d' \in {\mathcal B}_i(S)$, by Lemma \ref{semigroups}, which completes the proof by \cite[Lemma 19]{bafrsa} again.
\end{proof}
\begin{definition} For an ideal $I$, a finite subset $G \subset I$ is called a standard basis of $I$ if the least homogeneous summands of the elements of $G$ generate the $I^*$. In other words, $G \subset I$ is a standard basis of $I$, if $I^*$ is generated by $g^*$ for $g \in G $.
\end{definition}
We use the following crucial fact in order to relate Betti numbers of tangent cones of liftings.
\begin{lemma} (\cite[Lemma 1.2]{HS}) \label{HS} Let $I$ be an ideal of $R = K[x_1,\dots,x_n]$ with $I \subset \mathfrak{m} = (x_1,\dots,x_n)$. Suppose that $x_1$ is a non zero-divisor on $K[[x_1,\dots,x_n]]/IK[[x_1,\dots,x_n]]$. Let $\pi : R \rightarrow \bar{R}=K[x_2,\dots,x_n]$ be the $K$-algebra homomorphism with $\pi(x_1) = 0$ and $\pi(x_i) = x_i$ for $i > 1$, and set $\bar{I}=\pi(I)$. Let $g_1,\dots,g_r$ be a standard basis of $\bar{I}$ such that there exist polynomials $f_1,\dots,f_r \in I$ with $\pi(f_i) = g_i$ and $\deg (f^*_i) = \deg (g^*_i)$, for $i = 1,\dots,r$. Then,\\
(a) $f_1,\dots,f_r$ is a standard basis of $I$; \\
(b) $x_1$ is regular on $gr_{{\mathfrak m}}(R/I)$;\\
(c) there is an isomorphism
$$gr_{{\mathfrak m}}(R/I)/x_1 gr_{{\mathfrak m}}(R/I) = gr_{\bar{{{\mathfrak m}}}}(\bar{R}/\bar{I}),$$
of graded $K$-algebras, where $ \bar{{{\mathfrak m}}} = \pi({{\mathfrak m}}).\hfill \Box$
\end{lemma}
Before we state our final result, recall that the curve $C$ is of homogeneous type if $\beta_i (R/I_{S})=\beta_i (gr_{{\mathfrak m}}(R/I_{S}))$, for all $i$.
\begin{theorem} \label{resTC}Let $C_k$ be the $k$-th lifting of $C$. Then, there exists a positive integer $k_0$ such that for all $i=1,\dots,n-1$ and $k\geq k_0$,
$$\beta_i (gr_{{\mathfrak m}}(R/I_{S_k}))=\beta_i (gr_{{\mathfrak m}}(R/I_{S_{k_0}})).$$
Furthermore, when the tangent cone of $C$ is Cohen-Macaulay, $C$ is of homogeneous type if and only if $C_k$ is of homogeneous type for all $k>1$.
\end{theorem}
\begin{proof}
We first notice that $\bar{I}=\pi(I_{S_k})$ is independent of the value of $k$, as $\pi(B_k)=\pi(B)=B$ if $B$ does not involve $x_1$ and $\pi(B_k)=\pi(M-N_k)=M$ if $x_1$ divides $N_k$. Being the image of ideals with binomial generators, $\bar{I}$ have a standard basis consisting of binomials and monomials. These binomials are images of themselves under $\pi$ as they do not involve the variable $x_1$. So, we need to prove that for any monomial $M=x_2^{u_2}\cdots x_n^{u_n}$ in this standard basis, there is a binomial $B_k=M-N_k$ in $I_{S_k}$ with $\pi(B_k)=M$ and $\deg(B^*_k)=\deg(M)$. Since $M\in \bar{I}$, there is always a binomial $B_k=M-N_k$ in $I_{S_k}$ with $\pi(B_k)=M$ but the last condition is satisfied exactly when $\deg (M) \leq \deg (N_k)$. In the proof of Theorem \ref{liftsofCM}, we demonstrate that there is some positive integer $k_0$ such that for all $k\geq k_0$, $\deg (M) \leq \deg (N_k)$ is satisfied and thus the tangent cone $gr_{{\mathfrak m}}(R/I_{S_{k}})$ is Cohen-Macaulay for all $k\geq k_0$. Therefore, hypothesis of Lemma \ref{HS} holds as $x_1$ is always regular on $K[[S_k]]$. Thus, we have the following isomorphism
$$gr_{{\mathfrak m}}(R/I_{S_k})/x_1 gr_{{\mathfrak m}}(R/I_{S_k}) = gr_{\bar{{{\mathfrak m}}}}(\bar{R}/\bar{I}),$$
which implies that $$\beta_i (gr_{{\mathfrak m}}(R/I_{S_k})/x_1 gr_{{\mathfrak m}}(R/I_{S_k}))=\beta_i (gr_{\bar{{{\mathfrak m}}}}(\bar{R}/\bar{I})),\quad \mbox{for all}\quad i=1,\dots,n-1.$$
Since $x_1$ is not a zero-divisor on $gr_{{\mathfrak m}}(R/I_{S_k})$, it follows that
$$\beta_i (gr_{{\mathfrak m}}(R/I_{S_k})/x_1 gr_{{\mathfrak m}}(R/I_{S_k}))=\beta_i(gr_{{\mathfrak m}}(R/I_{S_k})),\quad \mbox{for all}\quad i=1,\dots,n-1.$$
Therefore, for all $k\geq k_0$ we have the following
$$\beta_i (gr_{{\mathfrak m}}(R/I_{S_k}))=\beta_i (gr_{\bar{{{\mathfrak m}}}}(\bar{R}/\bar{I}))=\beta_i (gr_{{\mathfrak m}}(R/I_{S_{k_0}})),\quad \mbox{for all}\quad i=1,\dots,n-1.$$
When the tangent cone $gr_{{\mathfrak m}}(R/I_{S})$ of $C$ is Cohen-Macaulay, we have $k_0=1$ by the proof of Theorem \ref{liftsofCM}. Thus, by the first part, we have $$\beta_i (gr_{{\mathfrak m}}(R/I_{S_k}))=\beta_i (gr_{{\mathfrak m}}(R/I_{S})),\quad \mbox{for all}\quad i=1,\dots,n-1$$
and by Proposition \ref{free}, we have $\beta_i (R/I_{S_k})=\beta_i (R/I_{S})$, for all $ i=1,\dots,n-1$. Therefore, $C$ is of homogeneous type if and only if $C_k$ is of homogeneous type.
\end{proof}
\section*{Acknowledgements}
The author thanks the anonymous referee for comments improving the presentation of the paper.
\bibliographystyle{amsplain}
| {
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} | 6,247 |
Melbourne is a city and county seat of Izard County, Arkansas, United States. The population was 1,848 at the 2010 census. It is home to the main campus of Ozarka College.
Geography
Melbourne is located at .
According to the United States Census Bureau, the city has a total area of , all land.
List of highways
Arkansas Highway 9
Arkansas Highway 69
Demographics
2020 census
As of the 2020 United States census, there were 1,830 people, 836 households, and 422 families residing in the city.
2010 census
At the 2010 census there were 1,848 people in 787 households, including 476 families, in the city. The population density was . There were 838 housing units at an average density of . The racial makeup of the city was 97.55% White, 0.36% Native American, 0.18% Asian, 0.42% from other races, and 1.49% from two or more races. Hispanic or Latino of any race were 0.60%.
Of the 736 households 25.8% had children under the age of 18 living with them, 45.1% were married couples living together, 13.3% had a female householder with no husband present, and 39.0% were non-families. 35.3% of households were one person and 17.4% were one person aged 65 or older. The average household size was 2.15 and the average family size was 2.78.
The age distribution was 21.9% under the age of 18, 9.9% from 18 to 24, 24.4% from 25 to 44, 22.7% from 45 to 64, and 21.2% 65 or older. The median age was 40 years. For every 100 females, there were 83.2 males. For every 100 females age 18 and over, there were 76.5 males.
The median household income was $22,757 and the median family income was $31,900. Males had a median income of $23,529 versus $18,264 for females. The per capita income for the city was $13,110. About 14.5% of families and 18.4% of the population were below the poverty line, including 25.9% of those under age 18 and 21.9% of those age 65 or over.
Education
Public education for elementary and secondary school students is available from Melbourne School District, which leads students to graduate from Melbourne High School. The school's athletic emblem and mascot is the Bearkatz.
Notable people
Michelle Gray - Republican member of the Arkansas House of Representatives for District 62; resident with her husband, Dr. Adam Gray, of Melbourne
Glen D. Johnson - Member of the United States House of Representatives for Oklahoma's 4th congressional district; born in Melbourne, died 1983
Gallery
References
Cities in Izard County, Arkansas
Cities in Arkansas
County seats in Arkansas | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,034 |
From the creator of The Honest Toddler comes a fiction debut sure to be a must-read for moms everywhere
There are good moms and bad moms—and then there are hot-mess moms. Introducing Ashley Keller, career girl turned stay-at-home mom who's trying to navigate the world of Pinterest-perfect, Facebook-fantastic and Instagram-impressive mommies but failing miserably.
When Ashley gets the opportunity to participate in the Motherhood Better boot camp run by the mommy-blog-empire maven she idolizes, she jumps at the chance to become the perfect mom she's always wanted to be. But will she fly high or flop?
With her razor-sharp wit and knack for finding the funny in everything, Bunmi Laditan creates a character as flawed and lovable as Bridget Jones or Becky Bloomwood while hilariously lambasting the societal pressures placed upon every new mother. At its heart, Ashley's story reminds moms that there's no way to be perfect, but many ways to be great.
Bunmi Laditan
Confessions of a Domestic Failure
To my hearts: M, T and F.
Contents
Monday, January 21, 5 A.M.
Tuesday, January 22, 5 A.M.
Wednesday, January 23, 10 A.M.
Thursday, January 24, 9 A.M.
Friday, January 25, 10 A.M.
Saturday, January 26, 10 A.M.
Sunday, January 27, 4:30 P.M.
Monday, January 28, NOON
Tuesday, January 29, 12:30 P.M.
Wednesday, January 30, 2 P.M.
Thursday, January 31, 9:30 A.M.
Friday, February 1, 11 A.M.
Saturday, February 2, 11 A.M.
Sunday, February 3, 9 A.M.
Monday, February 4, 11 A.M.
Tuesday, February 5, 11:30 A.M.
Wednesday, February 6, 3 P.M.
Thursday, February 7, 9 A.M.
Friday, February 8, 11 A.M.
Saturday, February 9, 9 A.M.
Sunday, February 10, 9:20 A.M.
Monday, February 11, 11 A.M.
Tuesday, February 12, 8 A.M.
Wednesday, February 13, 11 A.M.
Thursday, February 14, 2 P.M.
Friday, February 15, 6:30 A.M.
Saturday, February 16, 11 A.M.
Sunday, February 17, 1 P.M.
Monday, February 18, 10 A.M.
Tuesday, February 19, 9 A.M.
Thursday, February 21, 1 P.M.
Friday, February 22, 1:30 P.M.
Sunday, February 24, 3 P.M.
Monday, February 25, 10:30 A.M.
Tuesday, February 26, 10:30 A.M.
Wednesday, February 27, Middle of the Night Sometime/Too Tired to Care
Thursday, February 28, 5 A.M.
Friday, March 1, 4:45 P.M.
Saturday, March 2, 8:30 A.M.
Sunday, March 3, 9:30 A.M.
Monday, March 4, 10:30 A.M.
Wednesday, March 6, 6 A.M.
Thursday, March 7, 5:45 A.M.
Friday, March 8, 6 A.M.
Acknowledgments
Monday, January 21, 5 A.M.
Aubrey's ear-piercing cry rattled over the baby monitor, yanking me out of a deep sleep.
My eyes fluttered open. I looked at my phone's clock. No, no, no, no, no.
I'd dreamt I had a full staff: a nanny, butler, housekeeper and full-time masseuse. The laundry mountain of shame that lives permanently on my living room couch had vanished, and in its place, eighty-one bottles of delicious exercise wine. What's exercise wine? It's a wine that, when consumed, stimulates your muscles, resulting in rock-hard abs. While my nanny, who wasn't hot enough to be a threat, played with Aubrey on the floor, I enjoyed sip after mouthwatering sip and watched my kangaroo-pouch stomach tighten into a washboard.
Another scream over the monitor.
I don't know whose grandmother I dropkicked into a well in a previous life to have an eight-month-old who regularly wakes up before the sun, but I wanted to apologize. I glanced at my darling husband, David, who was sleeping soundly. I watched him breathe deeply and suppressed the urge to smother him with a pillow. How was it that he could hear me adjusting the thermostat from two rooms away but could sleep through the ear-stabbing howls of our eight-month-old every morning?
"I know you're faking," I whispered, trying to call his bluff. No movement.
I threw my legs over the side of the bed and bent down to find my trusty black stretch pants. They're the same ones I'd been wearing for the past two, three, maybe six days. They didn't smell bad, they smelled...rich with character.
After making my way to the bathroom, I splashed a bit of water on my face, hoping the H20 would magically fade the dark circles around my eyes. I glanced into the mirror and was surprised to see Medusa staring back at me, but instead of snakes coming out of my head, there was just a ratty ponytail. I ran my fingers through the mess and cringed. If my hair got any greasier, I'd be able to stand outside on a hot day and cook breakfast on it.
I was exhausted. My back hurt. My head hurt. My eyelashes hurt.
I tried to remember when my last good night's sleep was. It had to be when I was six months pregnant. That's when the heartburn kicked in. Did I say heartburn? I meant boiling hot lava. Flaming acid rain. Whatever it was, it meant I had to sleep sitting up in bed while Aubrey Riverdanced on my bladder. If there was any justice on Earth, women would take the first twenty-week shift of pregnancy and men would take over for the last four-and-a-half months. But based on how a common head cold transformed my husband from a thirty-five-year-old man to a ninety-six-year-old granny with malaria, I wasn't sure he'd make it through one day with child.
Another angry scream shot through the baby monitor.
"I'm coming. I'm coming," I whispered, dabbing at my face with a towel. I stared at my tired reflection in the mirror.
When Aubrey was finally born, every ounce of throat-searing bile was (mostly) forgotten as I looked into her adorable little face covered in that weird, white marsh scum* infants are born with. I wish someone had warned me about the vernix situation. Maybe then I wouldn't have screamed, "IS SHE A LEPER?" in front of two nurses, the doctor and a team of horrified interns. David teased me for weeks. Every time I'd hand her to him, he'd make a cross with his fingers and yell, "Unclean!"
She really was a beautiful baby. Or I thought she was. Everyone thinks their newborn is a looker when the truth is, 99.99 percent of them look like Groucho Marx.
* When you think about it, my uterus was kind of like a marsh: it was wet, dark, warm. All that was missing were the alligators.
* * *
I looked down and noticed that the pants I had slipped on in the dark featured a large hole in the crotch. A custom air vent, I rationalized.
It was almost impossible to believe that two years ago my mornings started with a ridiculously long shower as I got ready for work at Weber & Associates. I was a rising superstar in the marketing world. Back then, my mornings revolved around my intricately detailed makeup routine, dressing in trendy but professional skirt suits, and the vanilla latte and egg, cheese and ham croissant that I'd devour on my commute. Now breakfast consisted of whatever finger-food scraps Aubrey doesn't eat and peanut butter on a spoon while standing up with my face in the pantry. This wasn't how I pictured motherhood at all.
In my motherhood fantasy, I'd wake up at 7 a.m. and float into my still-sleeping baby's designer periwinkle-and-slate nursery (with a plum accent wall—like in Real Simple's Fall issue). Everything in the spotless, clutter-free baby sanctuary would be made by obscure Etsy artists living in the woods in Oregon, Italian designers or handmade by yours truly. You'd be able to feel the oak knots in the crib. They'd tell a story.
While my baby slept, I'd sit in her custom-made organic bamboo-and-pine rocking chair and write her a poem every day. She'd treasure these poems for her entire life and eventually turn them into songs. She'd win armfuls of Grammy Awards while I, an old but hot grandma, cheered her on from the star-studded audience. I can already see the award show camera go from her, in a beautiful gown on stage giving her acceptance speech, to me, tearfully clapping for my baby girl. She'd blow me a kiss, I'd catch it, and people around the world would be inspired by our mother-daughter connection. "How did she raise such an amazing young woman?" they'd ask themselves.
I'd wear stylish but casual clothing: white sundresses and practical but fabulous strappy Bohemian wedges. I'd save the skinny jeans for playdates.
Speaking of playdates, I'd be invited to so many of them that I'd be turning them down. "Sarah, I'd love to pop by, but I'm making organic applesauce and canning tomatoes from my garden today, sorry!"
I'd have one of those cute planners to keep all of my events straight—a pink leather-bound agenda with a matching pen that I'd keep in my fantastic diaper bag. The fantastic diaper bag that I'd never forget at home.
Aubrey would wear nothing but 100 percent organic cotton matching separates, lots of delicate vintage lace and those $60-a-pop suede booties in every color. I'd visit the farmers' market daily and sniff loads of fresh fruit, vegetables and local honey before selecting the items that would become the rustic, delicious dinners that I would Instagram to the delight of my hundreds of thousands of followers.
My meals would be beautiful and epic. People on Facebook would stare in admiration at the photos of my homemade Bolognese with handmade pasta. I'd definitely have one of those countertop pasta-drying things that look like they're for hanging miniature laundry.
Obviously, I'd cook while wearing seasonally themed aprons with Aubrey warm and cozy in the baby wrap I got at my shower a year ago and that I have yet to learn how to put on. David would brag to all his friends about how naturally I took to motherhood and how he always knew I'd be a great mom.
My reality? Aubrey screams me awake at 5 a.m. every morning and I'm about six months behind on the laundry that's taking over my living room like some kind of poisonous mold.
Forget about all of the cute outfits I thought I'd be putting my firstborn in. Every day my daughter wears one of four pairs of footie pajamas. She can't even walk and the feet are getting worn out from use. Two of them are stained: one from a diaper blowout (since when does infant poop stain?) and another from red wine (don't judge me). I wear the same three pairs of black yoga pants and a rotating army of stretched-out tank tops that can barely contain my jiggly muffin top.
Two weeks ago in the grocery store, an elderly woman looked us up and down, shook her head and handed me $20. I wanted to yell, "We're not homeless. I'm just too tired to care!" but she'd already turned down the baked goods aisle.
My thoughts were interrupted by another howl over the baby monitor as I hurried to pee. I finished up and washed my hands more slowly than I should have, savoring the last few moments of my day alone.
Before having Aubrey, I thought I'd be an amazing mom. I thought I'd be Emily Walker. Yes, THAT Emily Walker, the mom everyone wants to be; the famous mom blogger turned media darling who went from sharing her perfect family (including five children) and their perfect life with an audience of millions of mediocre moms to getting her own morning television show where she tells moms everywhere how to knit, craft and bake their way to a better life, all while getting to yoga class on time.
Not that I go to a yoga class. And let's not even talk about my body. I refuse to let David see me naked. The few—and I mean few—times we've found ourselves in a compromising position since Aubrey was born, I insisted that the lights remained off and as much of me stayed under the covers as possible. Yeah, I'm a regular vixen.
But Emily Walker has five kids and looks incredible naked. I know because on her blog are gorgeous photos from her vacation in the Bahamas (sponsored by a sunscreen company, of course). In one of them, she's lying on a huge yacht in a bikini that looks like a piece of dental floss. She doesn't have a single stretchmark on her toned, tight abdomen. Not one. I only have one kid and not only can I tuck my stomach into my pants, but it also looks like a bear clawed its way down my doughy center. But who's keeping score? Okay, I am.
Motherhood has done a number on my body. My hair has somehow become an oil slick and bone-dry at the same time. My skin is always broken out from the hormonal roller coaster I can't seem to get off of. Last week I cried during a commercial for yeast infection cream. David looked at me like I was insane. In my defense, the mother and daughter bonding over their shared vaginal fungus really touched me.
I thought being a stay-at-home mom would be easier. But the house is a disaster. David doesn't say anything, but I can tell by the judge-y way he looks around when he gets home that he's noticed we currently live in an upscale rattlesnake's nest.
I'm not exactly the best home chef, either. My idea of cooking is flipping through takeout menus with a spoonful of Nutella in my mouth or throwing something together at the last minute as if I'm on one of those "race against time" cooking shows. The result is usually spaghetti or quesadillas—you know, the kind of food fourth graders eat for lunch. Basically, I'm failing.
Don't get me wrong, I have no regrets. I love Aubrey. I just didn't think I'd get pregnant so fast after David and I got married. I know how babies are made, but getting knocked up on the first try was a surprise. I was equally surprised to get laid off while on maternity leave. I guess that's what happens when a company has to tighten its belt after the CEO is caught embezzling money. I never even got to ride on his yacht. Pity. So, here I am, an accidental stay-at-home mom.
In two short years I went from being a professional thirty-two-year-old semifashionable woman who ordered cranberry martinis during happy hour and spent Friday nights hopping from fusion restaurants to invite-only "what's the password" bars, to a thirty-four-year-old lumpy, bone-tired, hormonal mom who lives in semiclean activewear and spends Friday nights passing out at 7:48 p.m.—three minutes after I get Aubrey to sleep.
Just when I was really starting to feel sorry for myself, another impatient yelp boomed through the baby monitor. I peeked out of the bathroom into the bedroom where David had turned onto his side.
"Still pretending to be asleep, huh?" I spoke directly at him. Still nothing.
I shook my head but let him off the hook. In an hour he'd be off to work, fighting to make a name for the advertising agency he'd left his job to start four months before I decided not to find another job. I knew he was under a lot of pressure to make his company successful. If his sales skills were half as good as his early-morning acting skills, he'd have no problem at all. But in all seriousness, I was proud of him for fighting for his dream. I just wished he'd get up with the baby once in a while.
"I'm coming. I'm coming," I said, as I walked toward my daughter's bedroom. She was standing up, full of more energy than anyone should have before dawn. Her smile was contagious and I found myself cracking a slight one as I scooped her into my arms. If there was anything more delicious than a baby in footed pajamas I didn't know what it was. I mean, ham and cheese croissants came close, but she was still cuter. Before having Aubrey I thought it was horrifying when people talked about wanting to eat up their babies, but now I totally got it.
She babbled enthusiastically as I nuzzled her cheek. My heart dissolved into warm fuzzies as she pawed at my shirt. I looked down at her sweet face and tried to memorize every curve and dimple. I may not be the world's best mom, but gosh, how I love this little girl.
"Just so you know, when you're ready to talk, it's perfectly fine to call for Daddy in the morning," I said, as we made our way downstairs and into the kitchen. I flipped the switch and blinked as the light burned my eyes. It was too early.
Coffee. Must ingest caffeine. Before becoming a mom, I loved coffee, but now I needed it to function. My body went on autopilot as I fumbled with the coffeemaker with one hand. Aubrey cooed to herself on my hip. I pressed the Start button and the machine began to gurgle.
In a few hours, my ex-coworkers would be in the main conference room brainstorming PR campaigns for a new sugar-free energy drink or sparkly nail polish over a catered breakfast, while I was still sitting in my living room trying to stay awake.
I grabbed my coffee and walked with Aubrey, still happily on my hip, into the living room. I plopped her down on the enormous play mat that dominated the room and she quickly got to work finding her favorite toys. I flipped on the television and found a comfortable spot on the couch, cradling my coffee mug in my hands. Sensing my comfort, Aubrey began to squawk angrily. I picked her up and sat her on my lap for snuggles. She immediately dove for the hot coffee in my hand. I managed to take a few urgent sips before placing it on the end table and out of her sight. I looked longingly at my warm cup of daily motivation. I'd finish it when Aubrey napped. Of course, it'd be stone-cold by then, but that's what microwaves are for.
I heard a familiar voice on the television.
It was Emily Walker, mom blogger turned media superstar, on her highly acclaimed morning show, aptly titled The Emily Walker Show, doing a cooking segment with her latest celebrity guest.
Emily, impeccably dressed in a canary yellow ensemble, stood next to the redheaded bombshell and looked into the camera.
"Your kids are absolutely going to LOVE these butternut squash date scones!" Emily said, waving her hands enthusiastically.
"Which kids would love those? Human ones?" I said to Aubrey, as if she could understand anything I said. She blinked.
Emily held up a book. "Don't forget to pick up Alicia Winter's new wheat-free, sugar-free, dairy-free, fat-free dessert cookbook! It's in stores now!"
"I'll get right on that," I said sarcastically to Aubrey, who was now happily chewing on a runaway strand of my hair. I really needed to get some friends. Surely they'd appreciate my witty commentary more than an eight-month-old could.
Truth be told, I'd love to be the kind of mom who showed up to playdates with a tray of delicious, homemade treats: baby carrots cut up to look like snakes, baskets of muffins made with beet puree, and hand-churned yogurt in mini glass mason jars topped with fruit I preserved myself. The other moms would watch in astonishment as their children devoured my domestic creations. But so far I've been invited to exactly zero playdates. Even if I were asked, I'd probably bring a few bags of drive-through fries. Fries are a vegetable, right? They're also vegan.
I stole another sip of my coffee and turned up the volume.
Emily was now sitting on her trademark pink EW-logoed interviewer couch, having what she called a Mama Heart to Mama Heart. It's how she ended every episode of her show—with a few words of her own brand of wisdom.
"My mission for The Emily Walker Show has always been to inspire mothers." The camera zoomed in tight. "I see you there, mama. You're tired, frumpy, exhausted..."
I looked down at my stained purple sweatshirt and holey pants and glanced around the room. Were there cameras in here?
Emily narrowed her eyes dramatically. "Every day I get hundreds of emails and letters asking me how I raise my five beautiful children while running my empire, and I'm thrilled to announce that my book, Motherhood Better, comes out today. In it you will find the keys to my success and your own. Are you ready to be the mom you've always known you can be? Are you ready to truly enjoy motherhood?"
I found myself staring at the camera, hypnotized. She was saying all of the right things. It's true. I had always wondered how Emily's social media accounts were constantly full of gorgeous meals and perfectly groomed children, and boasted of her latest ventures, when the only thing I'd accomplished last week was moving my laundry pile from the bedroom floor to the recliner. I'd also figured out that a spoon half full of Nutella and half full of peanut butter dipped in powdered sugar tastes like a Reese's cup.
"My new book, Motherhood Better, will take you from frumpy to fabulous, struggling to spectacular. It's time to become the mother you've always known you could be."
This was exactly what I needed. With that realization, I practically flew off the couch, startling Aubrey, and grabbed my computer from the dining room table. Within minutes I'd purchased the book from BookSpot, a local store downtown and opted for same day pickup. This was an emergency, after all.
I was almost shaking with excitement. This was my moment. This is exactly what I'd been waiting for. That, and I was running out of places to hide laundry.
I opened my email and was excited to see a confirmation message waiting for me.
You purchased Motherhood Better by Emily Walker.
I looked at my phone. Only four hours until the store opened. Today I will become a mother, better. A better mother? Anyway—I'll get the book today is what I'm saying.
2 P.M.
I'd finally gotten Aubrey down for a nap and was lounging on my bed, trying not to let the two sinks full of dishes distract me from my well-deserved break. The day had been one for the record books. Everything that could have gone wrong had, and I learned some important lessons.
Lesson #1: If you forget the diaper bag at home and your baby needs changing at a bookstore, remember that you CANNOT, in fact, craft a diaper out of an old ziplock freezer bag that you found in the trunk of your car and a pair of emergency period panties from your glove compartment.
Lesson #2: When you arrive at home and see that your mother-in-law, Gloria, has popped in for a surprise visit with one of her classic six-cheese casseroles because she thinks (knows) you can't cook and doesn't want her David "starving to death," don't forget about your ziplock bag/period-panty diaper monstrosity and hand the baby to her.
Lesson #3: When your mother-in-law gasps and recoils in horror upon changing the baby and seeing your ziplock bag/period-panty diaper debacle (complete with a stained merlot mosaic of periods past), think of something clever and blasé to say rather than just standing there with your mouth open. Don't manically yell "Yolo!" She'll just ask what "yolo" means and you'll sound like an idiot explaining it. Also, don't try to cover your tracks and say that yolo is an ancient Tibetan prayer, because even though your mother-in-law doesn't know how to call before she visits, she does know how to Google.
Lesson #4: Be more prepared. Keep the diaper bag by the door. You should be better at this by now.
What kind of people "just pop by" anyway? Perhaps my dear husband casually let his mom in on the not-so-secret secret that I'm not taking to motherhood as naturally as I thought I would. In my defense, Aubrey is only eight months old. Eight months into any job isn't really enough time to become an expert.*
* Not that I'm calling motherhood a job. It's a blessing. Really, it is. Such a blessing. I'm blessed. Truly. #soblessed
Despite my sweet mother-in-law going on and on about how motherhood is an instinct, I can't be the only newish mom having a bit of a time finding her groove.
To be fair, I had very little preparation for this whole motherhood thing. Before Aubrey, the only newborns I'd ever held were my sister Joy's kids, the last of whom, my niece, was born just a month before I joined #TeamMom. That's a day I'll never forget, and not just because my niece was so adorable. Joy had just dropped the enormous bomb that she was giving her baby girl the name we'd both loved, I mean LOVED, as in we'd named every doll and teddy bear Ella since we were four and seven. When we found out that we were both pregnant, we even met at a coffee shop and decided that neither of us would take the name. So when the nurse said, "Isn't Ella darling?" I almost hit the ground.
"Don't be childish, Ashley," was Joy's response as she lay looking like a freaking goddess in her hospital bed. She was probably the first woman there to give birth in a $200 custom nursing gown. It was gorgeous. Pink apple print with cute little yellow blossoms.
It wasn't just the gown. Joy always looked fantastic. Her hair was even prettily tousled like she'd been boating all day rather than pushing six pounds and seven ounces of person out of her vagina.
When I told her I wasn't being childish and brought up the conversation in the café, Mom chimed in to defend her like she always does.
"Stop it, Ashley. Your sister just had a baby, for goodness sake. And she really does look like an Ella."
I had Aubrey one month later.
I love Ella and, of course, her brother, my three-year-old nephew, George, but I'd be lying if I said it didn't sting a little every time I hear her name.
"Aubrey is a gorgeous name," Joy gushed when she came to visit me in the birthing center. Joy and Mom were dead against my giving birth to my first outside of a hospital. In our typical Easton style, they never actually told me this. They just sent me every birthing center/natural-birth-gone-wrong horror story ever published while I was pregnant.
So maybe I did feel a little smug when Aubrey was born all warm and perfect in my hippie den aka birthing center. That is, until Joy spoke.
"You really are brave, Ashley. I never could have rolled the dice with my baby."
Once again, Mom backed her up. "Yes, Ashley, you're very lucky."
Lucky? They acted like I'd run blindfolded across six lanes of traffic while balancing my baby on my head rather than just given birth in the #1 birthing center in the nation, directly across the street from a top-rated, fully equipped hospital.
Before Aubrey was born I'd decided that I'd be one of those all-natural moms who made their own peanut butter, wore their baby 24/7 in one of those slings and breast-fed well into toddlerhood. Giving birth to Aubrey in a birthing center was just what I needed to catapult me into my new, organic lifestyle.
But my earth-mother adrenaline rush lasted until about four days after Aubrey was born, when my milk didn't come in. After Aubrey lost two pounds, even my "fight the man" midwife had to admit that something was very wrong.
"You might just be one of those women," she said to me in a hushed whisper, as if we were undercover spies trading government secrets. "One of those women who don't make milk."
"BUT YOU SAID THEY WERE ONE IN FIVE MILLION!" I cried, pushing my raw nipple into Aubrey's screaming mouth. "I HAD A NATURAL BIRTH!"
Two lactation consultants, bloodwork, a dozen delicious but ineffective lactation cookies, two boxes of lactation tea and a rented breast pump later, I gave in and bought my first tin of failure powder. That's what a mom from my online breastfeeding forum calls formula. Failure powder. For failures like me. Did I mention that Emily Walker made so much breast milk for her last baby, Sage, that she donated gallons to her local milk bank?
Joy was as helpful as she always is. "I'd totally pump for Aubrey, but I'm making just enough for Ella as it is. Sorry." I could tell she really was sorry, but it didn't help with the feeling of crushing disappointment. The studies that go around Facebook every fifteen minutes about how babies who aren't breast-fed grow up with dragon scales covering their entire bodies didn't help.
Eight months later I still hate myself just a little every time I scoop that white powder into the bottle. Formula. I'm a formula mom. This wasn't how I saw it all happening. It's not that I think formula is evil; I just always pictured myself breastfeeding under a willow at the park, its leaves gently swaying in the warm breeze, onlookers stealing admiring glances at me. Ask me how many admiring glances I get whipping out a nine-ounce bottle at Starbucks. ZERO. One mom even asked—with tears in her eyes, no less—if she could breastfeed my baby for me. As if Aubrey is some malnourished third-world baby on television with flies buzzing around her emaciated body. I may have lied and said that she's allergic to human milk.
Oh, and we stopped using the million-dollar-a-can organic formula blend when Aubrey was three months old. Now she's on the cheap brand stuff. She's the only eight-month-old I know with zero teeth—probably from all of the trace minerals she's missing from my malfunctioning mammary glands. Formula. When she drops out of community college, we'll all know why.
Yesterday, Emily Walker posted a photo of herself breastfeeding her eighteen-month-old in front of the Eiffel Tower. She's doing her show live from Paris for her Motherhood Better book tour, and I'm sitting in funky pajamas trying to remember the last time I shaved my armpits.
Back to the lessons I learned today. So in all of the "confusion" (shorthand for poopy-diaper-ziplock-bag-period-panty-replacement among us moms) I left my copy of Motherhood Better in the bookstore bathroom. I called and they said my copy had been thrown away (an employee complained that its proximity to the baby changing area was unhygienic) but they're giving me another one free of charge. David is picking it up on his way home from work. I asked him to pick up dinner, too. I'm exhausted from a day thinking about all the ways I'm screwing up his child, and the fridge is practically empty other than chardonnay, string cheese and almost-rotten produce.
It's not that I don't want to run to the store for groceries when Aubrey wakes up, it's just that leaving the house feels like more trouble than it's worth.
If I could ask the entire world one question, it would be: Why does it seem like people hate moms so much? Before anyone could accuse me of overreacting, I'd point out my first piece of evidence: the size of parking spots. Last time I was at the grocery store, as I squeezed my eight-months-postpartum body between millimeters of steel like a human panini, I had to wonder whether whoever paints those lines either...
Has never seen a human family before.
—or—
Despises mothers with the heat of a thousand diaper rashes.
How hard would it be to paint the white lines two inches farther apart? Would these mom-hater paint despots rather we go around scraping their BMW two-seaters with our minivan doors?
Is it deliberate fat shaming? Yes, I've only lost seven pounds of baby weight (which is weird, because the baby weighed eight pounds, two ounces), but we can't all be celebrity moms who go straight from hospital gowns to string bikinis.
And unlike those magical Hollywood moms, I didn't have a personal chef on call to make me macrobiotic, paleo, organic, fat-free, sugar-free, carb-free (taste-free?) meals every day.
It probably doesn't help that the closest thing I get to doing sit-ups is lying on the living room floor lifting my head for sips of Shiraz, but a girl's gotta live a little. And there's no way I could quit gluten. Do they know how many carbs it takes to stay awake when you have a baby who sleeps about fourteen minutes a night? A lot. Cutting carbs would make me a bad mother and I have to put my child first.
I got up and made my way into the kitchen, savoring the silence of nap time. I browsed the pantry for a few seconds before grabbing a jar of chunky peanut butter. After selecting a spoon from the dishwasher, I helped myself to a heaping mountain of peanut-buttery delight.
"I really should exercise," I said to no one in particular, my mouth full of sticky goodness.
Last week Emily had a celebrity trainer on her show. She showed the audience how to lie on their backs and bench press their babies while wearing a hot pink sports bra and matching designer leggings. I was tempted to get on my living room carpet and give it a shot, but I had a premonition of Aubrey puking partially digested milk into my hair. I smelled bad enough without being doused in baby vinaigrette.
I took another spoonful of peanut butter. Peanuts have protein, right? Protein is important.
Back to the ridiculous parking spaces. Every time I parked and had to squeeze my jiggly post-baby stomach between vehicles it was just another reminder that I'm not where I should be, body-wise. It's hard enough getting out of the house with an eight-month-old who only poops when we're in stores.
Which led me to...
Piece of Evidence That The World Hates Moms #2: Public Changing Tables.
Nobody's asking for a Four Seasons-inspired changing room with baby bidets and Egyptian cotton, rosewater-scented wipes individually handed to me by a gloved bathroom attendant, but three days ago I almost gagged changing Aubrey on a sticky, crusty monstrosity with broken straps, soiled with what I HOPED was dried prune baby food. I did my best to clean the biohazard with wipes and hand sanitizer, but really?
Sometimes it feels like moms are supposed to be invisible in society. Seen but not heard. We're supposed to quietly and quickly go about our task of raising perfectly mannered, groomed Gap babies who speak four languages before they're six without distracting the rest of the world from their important work.
I took one more heaping spoonful of peanut butter before replacing the lid and closing the pantry door. How nice would it be to live in a world that actually considers mothers? In Sweden, everyone takes care of everyone else's babies. Seriously. I read somewhere that when parents go to cafés or restaurants, they just leave their strollers outside by the door on the sidewalk, knowing that if the baby cries or needs help, passersby will jump right in and breastfeed or whatever. That sure beats feeling like every peep your baby makes in public is a capital crime.
I've watched way too many episodes of Law & Justice to put my faith in a stranger on the street, but it kind of sounds like paradise. The last (and only) time we took Aubrey out to eat, I ended up standing outside the restaurant bouncing her around while she screamed and tried to buck out of my arms like a wild pony. I ended up eating my cold eggplant parm out of a Styrofoam box in the kitchen at midnight. Good times.
My train of thought was interrupted by a baby yell. Was that Aubrey? I listened again. Nothing. Lately, I'd been experiencing phantom cries—thinking I heard Aubrey make noise when she hadn't. David thinks I'm losing it. He's not wrong.
Oh, wait, there was that sound again. Definitely Aubrey. I guess the dishes will have to wait.
9:30 P.M.
I was lying in bed next to David, who was sleeping soundly. Instead of joining him in dreamland, I had Emily's book propped open with one hand, and my phone's flashlight in the other, illuminating the page.
So far, the book was everything I expected. It only took half a chapter to make me feel like crap. Inspired crap, but crap.
Motherhood can be a joyful experience if you allow it to be. Too many moms spend their days in tense anger or regret, which is then energetically transmitted to their children.
Good to know. I've been frying Aubrey's heart via my toxic gamma rays.
As a mother, you are the gatekeeper of your child's health. It's up to you whether their bodies are filled with preservatives and chemicals, or nourished with homemade broths and fresh-from-the-oven grain-free breads.
I ran downstairs, flipped on the light and grabbed the Funny O's that Aubrey gobbles up from her high chair every morning. I turned the box around to read the label.
Whole grain oats. That's good. Oats grow in fields under sunlight and in the fresh air.
Modified corn starch. Okay, well corn is a vegetable. Modified. I tried not to picture Aubrey growing an extra hand out of her forehead.
Sugar. Salt.
Are babies supposed to eat this? I vowed to myself to spend the extra dollar on the organic ones next time. I guess the book was working. Sitting down on the couch I continued reading.
Motherhood and meal preparation go together like peanut butter and jelly.
Note to self, I thought. Learn to love cooking.
If June Cleaver were to enter my kitchen right now, she'd wonder two things...
How does someone with such poor culinary skills make such a terrible mess?
—and—
Where is that smell coming from?
To address the first query, people who have well-below-average cooking skills make bigger messes because, much like intoxicated folks, they are confused and disoriented. For example, last month I felt ambitious after watching a FoodTV episode about Eastern cooking and tried to make curry. I remember hearing that in India, they always stir-fry the spices to bring out the flavors. My interpretation of this step involved burning the spices in oil until they were a greasy, black, charred mess that not even cubed chicken, chickpeas and coconut basmati rice could save.
It was a very sad, very bitter stew.
David did his classic, head-cocked-to-one-side smile-frown before saying, "No, no, it's good, just...strong." He choked down another bite before gulping his entire glass of water in eight seconds. I think he was starting to sense how close to the edge I was, and was afraid to hurt my feelings lest I dissolve into a puddle of tears. Good. He'd always been good about picking up on my feelings. Needless to say, he didn't pack the leftovers for lunch the next day.
* * *
Three hours after my disastrous curry dinner, the kitchen still looked like a culinary crime scene. Almost every pot, mixing bowl and wooden spoon was out, vegetable trimmings were still on the counters and the sink was overflowing with dishes.
It's tragic that such chaos birthed such bland food, and it's a downright crime and shame that cooking must always be followed by cleaning.
Now, to answer the second question. What's that smell?
The odor June would have taken exception to is coming from under the counter. Six weeks ago, when I was feeling particularly roosty and productive, I joined a Facebook group of homesteaders. These are people who don't believe in grocery stores and try to live off the land as much as possible, in case civilization collapses. I just wanted to learn how to make bread.
One of the members told me about how she grows potatoes in her crawlspace. Despite the fact that I am barely able to nurture a human child, I decided to try this form of indoor gardening in the darkness of a floor-level kitchen cabinet.
The result was a gallon of rotten potato goo. My "starter spuds" melted into slop and seeped into the wood. I've tried bleach and vinegar, and I aired out the cabinet for weeks but the putrid smell still lingers. Would it have killed the potatoes to at least turn into vodka?
Earlier this afternoon, I made the mistake of hopping onto Emily Walker's Instagram to get a bit of dinner inspiration. Do you know what she made for her family tonight? Roasted rosemary organic chicken on a bed of garlic mashed potatoes with a side of sautéed baby spinach and crushed cashews. The photo looked like it was pulled right out of a gourmet cooking magazine. Even her tablecloth was fancy. My heart sank a little. There was no way I could do that with Aubrey crying on my hip, clawing at my neck like a gremlin. How did Emily do it? I consider grilled cheese with sliced red bell peppers a gourmet meal.
I let out a sigh and looked around the dark living room, as if help was in one of the corners cluttered with Aubrey's toys. Sensing no woodland fairy was going to pop out of nowhere and fix my life, I sat down on the couch and my hand settled on something hard. My laptop. I went onto Emily Walker's website, hoping to find an easier recipe for tomorrow, but instead saw a teaser link to a "special announcement" on the homepage.
Are you ready, mommies? the teaser read. I clicked the link.
To celebrate her book, she was launching a program called the Motherhood Better Bootcamp. Twelve moms would be chosen to be personally mentored by Emily herself, and—get this—at the end of the five-week transformation period the whole group would get flown out to Emily's home in Napa Valley, California, for three days of wine, rest and relaxation.
I continued to read. There was more.
The mom who had the biggest transformation would win $100,000.
One hundred thousand dollars.
One thousand dollars, one hundred times.
I was totally doing it. Not just for me, but for Aubrey. She deserved a great mom. A happy mom. A capable mom. She was too young to care that I had no idea what I was doing now, but what about when she was six or seven? By then she'd be old enough to compare me to the squash-scone-making moms of all her friends. I needed to change before that happened.
Fingers and toes crossed.
I clicked through to the Motherhood Better Bootcamp application. I filled in the basic information and then began tackling the harder questions.
"Why do you want to be accepted?" I resisted the urge to write, "Because I suck at being a mom," and wrote "To become the mom I know I can be in my heart." That sounded like something Emily would say.
It was almost midnight when I finally finished. My hand trembled a little as I pressed the green Submit button.
A message screen opened.
Thank you for applying to the Motherhood Better Bootcamp. The chosen participants will be announced next week. Have a beautiful day and don't forget to sparkle.
I looked at my phone. It was 12:14 a.m. Yeah, I'll sparkle tomorrow. Like a zombie dipped in glitter.
Tuesday, January 22, 5 A.M.
Aubrey woke up extra early this morning. #SoBlessed. I'd planned on doing a few leg lifts but of course I had to check Facebook and fell right down the rabbit hole.
What's Facebook? It's where moms like me post about how much we love the husbands who annoy the living bejesus out of us, and share expertly edited photos of our kids* and generally talk about our lives like we're living in an enchanted fairy tale blessed by rainbow angel unicorns. In short, it's for lying. But I'm addicted.
* Joy will never admit to this, but I know for a fact that she thickens her kids' eyelashes in Photoshop—I caught her in the act once.
Joy (Easton) Thompson
Status: Ella is LOVING her new BabyBGo Stroller!
Below the status update was a photo of my dear sister in fitted black yoga gear—the expensive kind, not the cheapies I wear—pushing my adorable niece in a brand-new stroller that cost as much as my laptop. Her cleavage was perfect (nursing). "How is she so tiny?" I wondered, trying to blow up the photo. Maybe I should have tried those post-baby waist cincher things she swears by, but forcing myself into a corset while I was still bleeding post birth felt like a little much. Anyway, what is this, the Renaissance? She looked great, though. I hated her.
Uncle Grover (yes, her husband, my brother-in-law, was named after a Muppet) must be doing really well. He's an actuary. I have no idea what that means, and when he talks about his work during family functions I usually picture him dancing on Sesame Street hand in hand with Elmo.
Note to self: Look up how much actuaries make. I'm super proud that my David is finally pursuing his dream and starting his own advertising agency and all, but it'd be nice to have some extra money for sexy yoga clothes and fancy strollers.
But my sweet niece, Ella, really is beautiful. She looks just like her mom: dimpled cheeks, almond eyes, jet-black hair and a toothy smile. (Aubrey has yet to pop even one tooth.) Aubrey looks so much like David that I get asked constantly if I'm the babysitter. If I were the babysitter, wouldn't I be better dressed and have time to put on some makeup?
This is exactly why I hate Facebook. I know it's just a website, but I truly believe from the bottom of my sleep-deprived heart that it has created absolute monsters out of the lot of us. If we're not bragging and showing people (people we barely care about) our Pinterest projects (I'll tackle this cold sore of a website later), we're comparing our lives with everyone else's. I hate it. I hate it for making me jealous of Suzy Wexler, someone I haven't seen since high school graduation sixteen years ago, but somehow know way too much about—including, but not limited to, the fact that her husband buys her flowers every single Friday.
Every Friday.
Did I mention that she lives in a gorgeous waterfront home in Malibu and is now a television executive? She and her husband, who looks like a silver-haired former Abercrombie model, have three kids plus two dogs that resemble tampons on legs. Somehow Suzy still looks like she could grace the cover of Self. As if I needed another reason to think I suck at life, Suzy's three-kid body looks about five hundred times better than my slashed-with-stretch-marks-like-I've-been-in-a-naked-knife-fight, pizza-dough-belly, one-kid body. David tells me I'm beautiful, but it's while he's pawing me in the dark, obviously trying to butter me up for some action.
In short, I did NOT need to wake up to a photo of Suzy Wexler's thin, beautiful form lying on a beach chair in front of her backyard pool. Not when I'm still wearing maternity tops.
Of course, I accidentally clicked Like on said photo, which prompted an almost immediate, Thanks Ashley! How are you? from my ever-polite old high school friend.
It should be illegal to be gorgeous and sweet. It's not fair. Just pick one. You cannot be a good person and hot. Hot and evil, yes. Homely and sweet, that's okay, too. Pick a lane.
I told her how much I'm loving motherhood, not being able to lose my baby weight and feeling like I'm losing my mind. Okay, maybe I left out the last couple of things.
It ended with Suzy saying, We have to catch up sometime!
Of course, Suzy. I'll just jump on a plane to Malibu with Aubrey and put on my ratty pregnancy swimsuit with the full skirt to hide my grizzly-bear bikini line while we chat and drink mimosas. You can tell me what it's like to be successful and meet celebrities every day, and I can tell you about the Target bill that I'm currently hiding on top of the microwave until I can explain to my better half how I spent $2,000 on miscellaneous goods.
I hate having to explain my purchases to him, like I'm a child, just because he's the breadwinner.
Note: I'm doing my best to get my spending under control but it's hard when (1) Target is life and (2) spending money is my love language.
I'm planning on deactivating my Facebook account just as soon as I upload some photos of Aubrey in a dandelion field from last weekend.
11 P.M.
Motherhood is a gift that keeps on giving. When your child whines, they're telling you they love you. Learn to hear their nighttime cries as a heavenly song composed by your little angel.
—Emily Walker, Motherhood Better
Aubrey just woke up. Her new thing is to go directly from REM to a level-ten scream. It's awful, and I'm considering calling for an old priest and a young priest. I settled her down, but now I'm wide awake and exhausted at the same time.
David always says, "Just lie down, you'll fall asleep eventually." Yeah, after my mind picks apart every mistake I've ever made since I was three, every possible bad thing that could ever happen to Aubrey in her entire life and then tosses around the "What am I going to make for dinner tomorrow?" query. It's so easy for men to fall asleep. Scientists should study whatever enzyme it is that they produce that helps them turn off their brains at night and drift into that deep, annoying I-can't-hear-the-baby-crying slumber. They could turn it into a sleeping pill that women can take.
But good for him for being able to snore it up while I can't even remember what it feels like to sleep through an entire night. Great for him. I'm happy. He needs the sleep. He works outside of the home, right? He has to fight traffic. All I have to fight is the 1 p.m. urge to inhale my weight in cheesy puffs. But, I mean, isn't raising a child a job, too? Yeah, I do it at home, but it isn't exactly a cakewalk. It's not like I lounge on the couch painting my nails, eating bonbons all day.
I'd give blood plasma for a night nanny. It's not fair that only celebrities who are already rich, famous and beautiful also get to be rested while I'm lying here in stretch pants covered in mysterious stains trying to remember the last time I took a shower. The other day I thought I smelled curdled milk. It was me. I smell like a yogurt factory.
I guessed I should try to sleep again, even though I knew the moment I lay down she'd start crying.
Help.
Wednesday, January 23, 10 A.M.
Coffee is a crutch for stressed-out, joyless moms. To stay energized, I start each morning with positive affirmations and loose-leaf hibiscus-beet tea sweetened with honey from my family's own hive.
—Emily Walker, Motherhood Better
Impossible Goal of the Day: Stay awake.
It was not even noon and I was a complete zombie. I didn't end up falling asleep until 4 a.m. and Aubrey was up by 5. When David kissed me on the cheek and jetted out of the house, I would've held on to the hem of his jacket and panic-whispered, "Take me with you!" if I didn't think I'd look like a complete lunatic. Instead, I gave him a very quick peck and felt guilty for an hour afterward. It wasn't his fault I was struggling with this whole motherhood thing. Note to self: Be a sweeter wife and ask how business is going.
I was on my fourth cup of coffee, so while my body felt dead, my mind was racing. I felt like a coked-out sloth. Can sloths do cocaine? It's made from a jungle plant, right? What if sloths figured out the recipe and started making it? We'd have an epidemic of drug-addicted sloths. We'd have to change their name from sloths to fasts. We'd also have to invent sloth rehabilitation centers complete with beautiful waterfalls and sloth sharing circles of trust.
I pulled out my phone. How was it only 10 a.m.? It was as if time was moving slowly to punish me for staying up too late. It was then I remembered. The Motherhood Better application. Emily was probably reading it right now in her massive Los Angeles kitchen, sitting at the counter with her five perfectly dressed children. She was most likely wearing a bone-white cardigan over a pink, lace-trimmed sundress and strappy flats. I bet she drinks her organic teas out of real china. I looked down at the plastic, lidless sippy cup I was slurping my vanilla-flavored coffee in.
I needed to win this.
Aubrey brought me back to earth by throwing a handful of Funny O's at me. One landed in my coffee.
We had to get out of the house or I was going to fall asleep right then and there. Wait—would that be bad? Yes, time to go.
3 P.M.
I tiptoed out of Aubrey's dark room toward the door. Turning back, I took a moment to admire her little body, splayed out on her back in the green-and-yellow pajamas she lived in these days. I closed the door slowly, stopping before it was completely shut. I'd learned the hard way that the smallest click of the door closing woke Aubrey up. Nobody tells you that babies hear like dogs.
Today turned out to be better than I'd ever imagined it could be on so little sleep. I'd made a friend! This was huge, because I was just reading about how Emily Walker believes creating your mama village is an essential part of happy motherhood. Of course, the mom friends who show up on her blog all look like freelance models, but who cares? We were all the same on the inside. Of course, their insides probably had no cellulite but that's neither here nor there, either.
Here's how it happened. I was sleep-shopping at BabyOutlet (spending money helps me stay awake) and the sweetest-looking mom with her four-year-old son in tow approached me out of nowhere and asked how old Aubrey was. Everyone knows that inquiring about the age of a baby is how moms break the ice. I must have been letting off some seriously positive vibes because we talked right there in the six-to-twelve-months girls' section for fifteen minutes and exchanged phone numbers! She raved over Aubrey and said that her cousin's best friend's stepsister's daughter didn't get her first baby tooth until ten months and that it's totally normal. Her name was Isabel and I loved her.
Get this. She's already texted me and invited me to a playdate for the following day. I was practically giddy and would have done a cartwheel if I'd had the energy. I was only two chapters into Motherhood Better and was already about to meet my group of probably lifelong mom friends. My own mama village—as Emily called it.
I could already imagine how we'd spend afternoons together drinking tea (wine), laughing, baking bread, making double casseroles so we could trade, gardening, telling secrets...and then when our kids grew up and married each other we'd all go on epic road trips in between meet-ups with our grandchildren who were practically all related. Okay, maybe that last part was a little creepy, but I was excited.
As I was walking down the stairs, being careful to avoid the two that creak, my phone buzzed in my pocket.
It was Isabel.
Just wanted to let you know you can bring friends tomorrow!
How sweet! If I'd had any other friends, I certainly would have. I texted back that I'd ask around, which I did. I asked around the living room. There was no need to tip her off that I was a loner.
I curled up on the couch and flipped on the TV. Soaps. Soaps. And more soaps.
It didn't matter, though. Within thirty seconds I was asleep.
9 P.M.
David was brushing his teeth in the bathroom when Isabel texted me to let me know that there would be gifts at the party tomorrow.
My shoulders did a little dance as I sat in bed. Gifts? Maybe this was her circle's way of welcoming me into the fold. I was going to bring my famous Lemon Poppyseed Cake. Technically, it was Joy's famous Lemon Poppyseed Cake, but nobody needed to know that I stole the recipe off my sister's computer after she stole my baby name.
David stepped out of the bathroom in his blue-and-white striped pajama pants and white tee and saw me grinning.
"You met this woman where, again?" he asked, sliding into bed next to me.
I frowned. "David. This is how moms meet," I said, trying to sound like I'd done this before. "If I get any weird vibes or if she sacrifices a lamb on the front lawn, I'll get right out of there. I'll go back for Aubrey the next day," I teased.
David smiled and slithered his way up the bed toward me like a crocodile. He was in a great mood today after winning a bid to handle the PR for LuxSpecs, a high-end line of sunglasses.
He reached for me and wrapped his arms around me, massaging my back.
My danger alarm went off, and I gave him a quick shoulder squeeze.
"Watcha doing there, buddy?" I asked.
He purred in my neck. I knew exactly what he was doing, but seeing as how I'd just gotten Aubrey to bed fifteen minutes ago and hadn't had a chance to shower since...she was born, not to mention spending a day being drooled and spit up on, I felt about as sexy as an ingrown toenail. We really should have sex soon, it had been too long. Just not tonight.
"David, David," I said, backing away from his neck nuzzles. "I haven't showered in forever. I feel like a moldy dishcloth. Rain check?" I felt terrible. Minus-twenty wife points.
"Awwww," he said, and kissed me tenderly. His lips were so soft. Those lips. I loved them the minute I first kissed him, all those years ago in the rain outside of our office building. We'd been friends for three years and neither of us knew that the other had been harboring feelings until that kiss.
I kissed him back and sighed, remembering the simpler days when my hair was clean and we could spend an entire Saturday morning snuggling in bed.
He pulled me into a spooning position and began exploring my body with his hands. I yelped self-consciously when they grazed my stomach. I still couldn't bear him feeling the loose kangaroo pouch Aubrey had left me with. Hot shame shot down my spine and I covered my abdomen with my hands, protecting it from his.
He sensed my discomfort and placed his hands over mine. "Hey," he said, in the most gentle voice I've ever heard him use. He touched my face and whispered into my ear. "You're beautiful. All of you."
Butterflies danced around my stomach and I felt so moved, tears welled up in my eyes. I loved this man. I turned toward his warm body, gazed into his brown eyes. He meant it. He really did think I was beautiful. I kissed him and almost heard the rain from that evening so many years ago hitting the pavement.
Thirty seconds later we were breaking our dry streak. It was fantastic—it always is, even with me insisting that the lights stay off lest my jiggles be seen. Afterward he hugged me tight, as if afraid to lose me again to the world of mother.
"I miss you," he whispered into my ear. Tears sprang into my eyes again. Dang hormones. I missed me, too.
I wished I could promise him that I'd be this person, this loving, giving, sexy person again tomorrow night or the next night, but I couldn't. I tried to squash the feelings of guilt swirling around my psyche.
I kissed his cheek. "I know."
He turned over and fell fast asleep. Normally I would, too, but I couldn't quit my thoughts.
I tried to think about something else. My very first playdate. Tomorrow.
I decided to dress Aubrey in her pale pink jumper and heather-gray top with the matching gray booties. She looked like a baby model in that ensemble. It was made by some fancy Italian designer. Joy gave it to me as her way of apologizing for #BabyNameGate.
I'd actually tried to invite Joy. After all, Emily Walker wouldn't be worried about Joy stealing her friends. Emily Walker would be secure in her friend-getting abilities and say, "The more the merrier!"
But, of course, Joy had to get all weird. "You met this woman while discount shopping and are going to her house?"
You'd think I was taking Aubrey to an abandoned meat warehouse at midnight. Classic Joy. She decided against coming, which was fine by me. Anyway, she had tons of friends from her scrapbooking club, book club and cookie swap. I'd asked if I could join the cookie club once, but all of the cookies have to be homemade so it wasn't a good fit.
I wiggled in bed a little, getting myself comfortable.
I was almost asleep when I heard David say, "Do you smell yogurt?"
Thursday, January 24, 9 A.M.
Isabel's party was in an hour and we were ready.
I texted Isabel and told her that though I'd invited my sister she couldn't make it and I'd be coming alone. She's so sweet, she offered to talk to Joy directly but I let her know it'd be a lost cause.
Aubrey looked absolutely adorable! I need to submit her photo to modeling agencies, seriously. I showered, brushed my teeth, and put on foundation, mascara AND lipstick. I was wearing a dress that fit like a (slightly tight) glove and I felt incredible. I should do this every day! I didn't have time to make the Lemon Poppyseed Cake, so I would be picking up a dozen doughnuts on the way there. Wish me luck!
11 P.M.
Well.
I'm not even sure where to start.
Aubrey and I arrived at 10:15, just a bit late. There was a long line at the drive-through for the doughnuts.
When I got to Isabel's house I rang the doorbell and was greeted by a woman with red hair holding a clipboard. She asked if I was Ashley, scribbled something down and gave me a name tag with my name already on it. That didn't immediately strike me as odd. I'd never been on a playdate. Maybe there are so many moms that they wear name tags when getting to know one another.
She led me to the living room where eight other moms with babies in their laps and toddlers walking around aimlessly were watching a video on the large flatscreen. The woman showed me to the only seat left available. At that point, I wondered what we were doing, but I saw Isabel smiling at me from the left of the television screen and figured this was some kind of chick flick movie time.
Then the film started. Wait no, the INFOMERCIAL started.
A woman in a bikini wearing some kind of linen girdle popped up on the screen. "Are you ready to feel sexy again?"
That's when I started to feel like an idiot.
"In just three hours you'll feel the YES Wrap start to shrink your belly fat and trim your waistline! Get ready for a lean, mean tummy! I love my YES Wraps and you will, too!"
I watched in stunned horror for the next twenty minutes as women mummified their abdomens while animated fat cells floated out of their bodies. Finally the video went to black and Isabel walked to the front of the room holding a green and white box with YES Wrap emblazoned on the sides.
"Does anyone have any questions?"
I knew I shouldn't have raised my hand, but I couldn't help it.
"Is this the playdate?" I asked.
Isabel fake smiled at me. "Absolutely! I've invited all of you here to make some friends and learn about a product that has helped moms around the world lose weight naturally."
I went on. "Right. So you invited me—no, targeted me—because you think I'm fat?"
The fake smile didn't fade but her eyes flickered.
She shifted her weight from one foot to the other. "I didn't target you. I shop at BabyOutlet all the time with my nephew."
At this point I may have snapped. "HE'S NOT EVEN YOUR SON? YOU'RE NOT EVEN A MOM?"
I don't know what came over me. The humiliation turned into hot, searing anger.
"I MAY NOT HAVE A TIGHT STOMACH BUT AT LEAST I'M NOT A LIAR. YOU CAN STICK YOUR WRAPS UP YOUR—" then I noticed the kids in the room "—BUTT!"
Isabitch started to speak but I ripped off my name tag and a patch of my dress at the same time, grabbed Aubrey's car seat and stormed out, but not before scooping up my box of doughnuts. I ate five of them this afternoon and another two after dinner. So much for a lean, mean tummy.
Joy texted to ask how the playdate went. I said it was a blast. She wants to come to the next one.
Just my luck that when a (fake) mom wants to get to know me it's because she thinks I could stand to lose a few pounds and she wants to make a few bucks off me in the process.
FML.
Friday, January 25, 10 A.M.
Visualize what you want out of your mommy life. Just because you've had kids doesn't mean you can't live the reality of your dreams. My five children, beautiful husband and I take two tropical beach vacations a year thanks to the power of intention.
—Emily Walker, Motherhood Better
I was shaking off the predatory playdate. I needed to move on. I needed to put my energy elsewhere.
Wishes For My Fairy Godmother.
* \- Take 25lbs off of my body. Not boobs or butt, please, and not via some playdate marketing scam
* \- Give them to Suzy Wexler (kidding)
* \- Make sure Aubrey grows up to be happy, healthy and safe (move that to the top)
* \- Make me a great housewife
* \- World peace (move that to second place)
* \- End famine (move this up, too)
* \- Delete Facebook.com
* \- Pass a law that all boxes of diapers should be accompanied with a Buy One Get One Free coupon for a bottle of wine
* \- Make me a nicer wife
* \- Remove all calories from wine but keep taste intact
* \- Organize my house
Impossible Goal of the Day: Improve my grocery shopping.
Speaking of the power of intention, I ran to the market today and actually took a list with me.
Grocery List
Kale (For Emily Walker's famous kale, quinoa, and fat-free feta salad with pomegranate vinaigrette.)
Quinoa.
Fat-free feta (Even though fat-free cheese should be illegal.)
One pomegranate.
Blueberries.
Radishes.
Organic milk (In Motherhood Better, Emily says regular milk can cause toddlers to go through puberty.)
Eggs.
Flour.
Butter.
Cream of tartar (For baking, because I'm going to start doing this any minute now.)
Cherries.
Apples.
Celery.
Chicken.
Oats.
Toilet paper.
Cheese.
Tomatoes.
Onions.
Red peppers.
Here's what I bought:
Kale (For rotting in the fridge. Let's be real—I'm never going to make that salad.)
Quinoa (I have no idea how to cook this. Is it rice? Is it pasta? Nobody knows.)
A pomegranate (For watching dry out in the fruit bowl over the next several weeks.)
I didn't buy the fat-free feta. It felt wrong.
Organic milk.
Eggs.
Cookie dough.
Honey Nut Cinnamon Crunch cereal.
A pound cake.
Toilet paper.
Gum.
Sugar-free fake strawberry poison liquid drink mix (for weight loss.)
6-pack glazed doughnuts.
Hot dogs (for snacking.)
Frozen Tater Tots.
Apples.
Cherries.
Strawberries.
Frozen onion rings.
Tortilla chips (for unexpected guests.)
Nacho cheese dip (also for guests.)
3 tank tops.
2 pairs black pants.
Running shoes.
Workout DVD.
Water bottle.
Ice cream.
Someone told me they named it "pound cake" because it contains a pound of butter. I prefer to think it's just honest labeling: you gain a pound per slice. But on the bright side, butter contains milk, which contains calcium, so in a small way, pound cake is helping fortify my bones. I also always eat pound cake with strawberries, which contain minerals and vitamin C.
Confession: I hadn't showered in four days and I was kind of okay with it. That's what deodorant is for, right? Right now, I had six layers of Lady Smells Bad antiperspirant on my underarms. It's strong enough for a man but pH balanced for a mom who can't find the time to wash her privates.
I smelled like a cross between sheets that were put away wet and very expensive cheese.
I checked my bank statement after this "grocery" shop, and do you know what stood out? Every third line was either for vanilla lattes or Burger Central. The only two food groups I consumed were caffeine and fast food. It wasn't my fault, though. Junk food and caffeine were all that were keeping me going. I needed these treats to make it through the day. I didn't get to sleep anymore, there was no "me" time, I didn't have friends—the value menu, sweet caffeinated beverages and wine were currently pleasure central and I would not apologize for it. My pants might, though, because they were stretched to capacity.
PS: Emily would announce the twelve Motherhood Better Bootcamp winners on her show in a couple of days. She said they received over 7,000 entries. Please fairy godmother, come through for me.
11 P.M.
Motherhood is an ashram; our religion is love, diaper changes and sleepless nights. This begins with pregnancy. Speak to and dance with your unborn baby every day—preferably to music that features either harps or Tibetan gongs.
—Emily Walker, Motherhood Better
Fun fact: Did you know that some women take their placenta home with them after giving birth? Some send it away to be freeze-dried into capsules and others eat it raw, like sashimi...supposedly it helps balance out the hormones and make you feel like a normal person again faster.
I was on the Mommy Chat online message board complaining about how tired and emotional I always am, as one does on a Friday night post baby, and someone asked if I'd eaten mine. I said no, and she responded with, "That explains everything."
Really? So motherhood would be easier for me if I'd just cooked up the afterbirth like Bolognese and served it over linguini with a side of garlic bread?
Joy's neighbor buried her placenta in their backyard under a tree. If you bury a placenta under an apple tree, are the fruits then an apple/placenta hybrid? If you bury it in a vineyard, would the wine have hints of afterbirth?
Sommelier in a fancy restaurant: "This full-bodied pinot grigio hails from Napa Valley. It was aged in maple oak barrels. You'll notice hints of elderberry and subtle notes of the placenta of a seven-pound six-ounce child."
Maybe I should have kept my placenta. The birthing center offered, but between figuring out how to install the car seat, heal my broken vagina and oh, yeah, trying to wrap my mind around the fact that a human baby was coming home with me, I'd felt like I had enough on my plate (no pun intended).
I was fascinated by the thing, though.
It was way bigger than I thought it would be. In my mind I imagined a pork chop but it was more like a blobby T-bone steak. It had all kinds of veins on it. An old high school friend on Facebook dipped her wet, bloody placenta into red paint and threw it against a canvas. The art now hangs in her family room.
No comment.
If I had taken my placenta, what would I have brought it home in? A freezer bag? Do they put it in a to-go box like restaurant leftovers? Wrap it in foil or maybe drop it into a Styrofoam box complete with utensils, and salt and pepper packets?
Mom to nurse: "Can I have this wrapped up? I'm taking it with me."
There was a whole section of the Mommy Chat website, I was discovering now, dedicated to placenta recipes. Smoothies, cakes, even stir fry. STIR FRY. Bok choy, onions, bean sprouts and thinly sliced placenta. Maybe a little Chianti on the side?
This was way too much for me. I should go to bed.
The contestants chosen for the Motherhood Better Bootcamp program would be announced tomorrow live on the show. If I hear my name I am going to absolutely freak.
Saturday, January 26, 10 A.M.
Of course Emily had to keep everyone on their toes until the last sixty seconds of her show. Well, I didn't make it into the Motherhood Better Bootcamp, but I wasn't going to let it get to me. Emily said something on her show today that really struck me. "I wasn't born a good mom, I willed myself into one." All I needed to do was try harder. I needed to put the same energy that I once put into my job into motherhood.
I had Emily's book. I could do this on my own. I decided to embark on a mission called Ashley the Perfect-ish Mom. First thing in the morning I was going to join a gym (or at least research gyms), eat healthy and be the best, most attentive mom ever.
It was time for me to stop living in dirty sweats and move up to the fancy $10 stretch pants from ShopMart. I was going to start dressing up Aubrey like a human and not a Les Misérables extra. I was browsing Etsy right then, picking out some bows. She needed them. I'm not saying she looked like a boy, but I swear she could be sitting in a pink stroller, wearing a pink and purple dress, with a fluorescent flashing sign that read, I'M FEMALE, and people would still ask "How old is your son?"
Anyway, maybe I'd even start juicing once I figured out exactly what that was and if mix-ins like tequila were allowed (tequila is from a plant).
I had this.
Impossible Goal of the Day: Get accepted into a group of mom friends, or at least make one awesome best friend sometime this century.
I joined three local mom Facebook groups but hadn't posted yet.
What would I even say?
Hey guys, friendless mom looking for a new bestie. Need someone to share secrets with? I'm your gal!
Maybe something a little more subtle.
Lonely, unemployed, reluctant stay-at-home mom looking for 2–3 moms for my mama bear pack. Must be cool, love complaining, not be a YES Wrap representative and be imperfect. Must NOT have a Pinterest account.
I know the last part sounds harsh, but I don't need a crafter in my life. You know why? Because it'll only be a matter of time before I've spent $500 on yarn, crotchet needles, puff paints and a glass-etching kit in a sad, futile attempt to become her. I'm too easily influenced to have these bad seeds in my emotional space. I need another sister in failure. Someone who not only fails to achieve resolutions but forgets she even made them. Yeah. Someone like that. A leader.
Being a new mom is like being a freshman in high school. You have just a few days to find your clique and commit to the corresponding lifestyle. So far, the available groups are:
1. Crunchy Moms
2. Stay-at-Home Moms
3. Working, Executive-Type Ambitious Moms
4. Moms Who Hate Their Jobs But Do Them Anyway
5. Wine Moms
6. Hot Moms
There's a bit of overlap here and there, but so far I haven't found one that I identify with and, therefore, still have exactly zero friends. It's getting a little old walking Aubrey through the park alone, especially when it seems like there are groups of moms gathered all over the place, laughing, smiling, being best friends and sharing stories about their kids. I want to share stories about kids. Someone should invent a match.com just for moms who want to find their life mom-mate.
It seems like once you're an adult, if you don't already have your friends picked out, you're screwed. Nobody makes new friends after twenty-seven.
I miss my office friends, but since I had Aubrey, they've all vanished. I don't blame them. Given the choice, who would want to spend an afternoon at the park with me and Aubrey when they could be getting manicures? I just wish they would have kept in touch more than the occasional "She's so cute!" Facebook comment.
All I want is one mom friend I can talk to about life. Is that too much to ask? In fourth grade my best friend was Ruthie Miller. We did everything together. We ate lunch every day in the cafeteria side by side, we played at recess, we even sat together on the bus. I was never lonely because she was always there. She was my default person. I need a Mom Ruthie.
Hospitals and birthing centers should assign every woman a mom friend the second they give birth. Then we wouldn't have to spend afternoons alone on the living room floor wishing we had someone other than people in mail delivery to chat with.
How amazing would it be to have a best friend who lived across the street? We'd talk about everything. How David has been working twelve-hour days, but I feel bad complaining because he's the only one bringing in an income right now and seems super stressed-out, even though I'm also super stressed-out. I'd tell her about how I feel like being a stay-at-home mom is amazing because I get to watch Aubrey grow right in front of my eyes and, while my heart is so full of love for her that it feels like it's going to explode, how I'd do anything for just one good nap. I'd also tell her that I feel like I matter less to David since having her. How I feel like he sees me as some kind of maid/caretaker to his child and not the woman he pined for desperately for years. I can't remember the last time he asked me how I am.
I'd listen to her rants, too, of course. Friendship, especially one based on complaining, is a two-way street.
David had worked through the last few weekends but took today off so we could all go to the FunsieLand play center together. Before becoming a mom I avoided places like FunsieLand like the plague. Every once in a while I'd get invited to a coworker's child's birthday party and would always make a point of sending a huge gift in lieu of my actual presence. The last thing I wanted to do was spend five hours in a loud, rave-like, plastic ball and E. coli petri dish, but since there aren't many places where parents feel 100 percent okay letting their kids be kids, that's where we were headed to this morning.
It'd be nice to do something as a family. David had been so busy lately. Every time I asked him how Keller & Associates was going, he would close up. I wanted to support him, but talking about work just stressed him out even more. A day of bonding as a family was just what we needed.
9 P.M.
I need three shots of vodka, a hot shower and a shot of penicillin. To think, for my entire adult life I've avoided play centers because of the kids, when the real monsters lurking in those places were the moms.
We made it to the play center at 10 a.m., and even though it'd just opened, it was already so loud that David and I had to scream in order to be heard.
"LET'S SET UP BY THE BABY AREA!" I yelled, one hand over Aubrey's ear as I carried her through the center that was packed with shrieking, running and crying children. Above us, a twisted spiral of tubes was filled with children, crawling like rats through plumbing.
I motioned to David, who had both hands over his ears and whose eyes were wide with terror.
"WHAT?" he yelled back. A five-year-old crashed into his legs and fell to the floor, laughing hysterically.
"THE BABY AREA!" I motioned toward the back of the sprawling center.
We navigated carefully around birthday parties, children who seemed jacked up on Mountain Dew and rock cocaine, and seemingly millions of small multicolored balls that were everywhere.
From atop a small stage, a band of large furry animals sang a song about a big blue boat. The music boomed across the entire arena.
We finally made our way toward a door in front of a clear Plexiglas wall. On the other side of it was a smaller version of a play center: a carpeted room featuring a small jungle gym. It was littered with stuffed toys and babies crawling around their parents.
David pulled the door open and I hurried through with Aubrey. As soon as it was shut there was silence. We took off our shoes (Shoes Off in Babyland, Please!) and let out a deep sigh of relief, as if we'd just narrowly escaped with our lives. David pointed back toward the chaos that was now a muted version of insanity. "We are NEVER having Aubrey's birthday party there."
"I agree."
We scoured the sides of the Baby Room and found a section of wall without a diaper bag leaning against it.
David and I sat cross-legged on the floor and placed Aubrey in front of us.
I bent down to her. "Okay, Aubrey, go! Play."
She sat up and stared out into the play area where other children were flailing on their backs and older babies were struggling to make their way up the small slide stairs.
She instantly burst into tears.
"Awww, Aubs," David reached out his arms and pulled Aubrey into them. "Don't cry, honey." He pulled her close and pressed her face into his chest with his hand.
My heart fluttered as I watched the two great loves of my life embrace. Nobody can prepare you for the magic that is watching the man you love become a father. I found myself swooning every time I caught him gazing at Aubrey, feeding her or just cradling her in his arms.
A woman's high-pitched voice cut through the moment. "She doesn't socialize much, does she?"
I turned to the mom on my left. She was in her mid-thirties and was wearing dark blue jeans and a pink sweater. Her hair was pulled back in a tight bun.
"What?" I said, looking around.
The mom crossed her arms. "Your daughter. She doesn't spend much time with other kids, does she?"
My mouth hung open. I didn't even know what to say.
"She doesn't have many friends or coworkers, no..." I said slowly.
The woman smiled tightly. "Funny. But it's not going to be funny when she's eighteen and still living in your basement. Let me guess, stay-at-home mommy?"
I tried to smile back. "...Yes."
The mom examined her nails. "I can tell. You're really going to want to get her socialized ASAP."
David, who had been listening quietly, cut in. "She's a baby, not a dog."
"David," I whispered, trying to calm him down.
The woman pursed her lips. "I was just trying to help." She collected her bag and walked away.
"The nerve of that woman," David said when she walked away.
"David," I hissed. "We're here to have fun."
"I know but—" He motioned in the direction of the woman.
I gave him a look before picking Aubrey up and carrying her over to the center of the room where several babies were playing with the communal toys.
Aubrey and I sat down with the other moms. I could feel myself starting to sweat. Hanging out with other moms always made me nervous. I was terrified of coming off as a parenting noob and highly conscious of how desperately I wanted the friendship of even just one of these women.
I sat Aubrey down and pushed a blinking jack-in-the-box toward her. Aubrey smiled and began tapping the buttons with her hands.
"Is that fun, baby?" Aubrey pressed another button and a rabbit popped out of one of the toy's hidden doors. She screamed with delight.
I looked up at the other moms. Surely people were taking notice of me and my adorable child having a Hallmark moment. Then, out of nowhere, Aubrey began to cry. I looked down just in time to see an eighteen-month-old little boy wearing a pair of brown cotton shorts and a red shirt toddling away with the toy she had been squealing over.
I scooped the hysterical Aubrey up and followed the boy to where he sat down to play. He was seated next to a young mom with blond curly hair wearing a flowing burnt-orange dress.
"Excuse me," I said, kneeling down next to her. "My daughter was playing with that toy when your son came over and grabbed it."
She stared at me blankly before pushing a stray hair out of her face. "I'm sorry?"
Her son was now happily playing with the toy Aubrey had had earlier while Aubrey sobbed.
"Your son, he grabbed that toy out of my daughter's hands." I pointed to the little boy sticking his tongue out at me.
The mom held up a hand defensively, "Please do not point at River. We point at places, not people."
"Okay..." I said, lowering my hand.
"And I'm sorry your daughter is having a shadow experience today, but we do not force River to share."
"You what now?" I asked, puzzled.
"We do not force River to share. River makes his own decisions. It's part of his journey," she said, smiling serenely.
"What? Lady—"
"Please do not gender me," the woman said, shaking her head.
"My daughter is going to need that toy back," I said flatly.
"Please do not gender your child," she said, staring at me.
"Okay, that's quite enough." I reached down and pulled the toy away from River. He let out a squeal.
The woman was livid. "How dare you?"
A play center supervisor wearing a white shirt with the center's logo on it walked over. "Is there a problem here?"
River's mom stood up and put her hands on her hips. "This woman just snatched a toy out of my child's hands!"
I struggled to stand while holding Aubrey. "Only after he took it from mine."
David popped up. "What's going on, Ashley?"
The employee, a man in his early twenties with a crew cut, spoke up. "It appears as if your wife took a toy from a baby."
David looked at me, startled. "Is this true?"
"Yes, but no, he took it from Aubrey first..."
David could barely speak. "Took a toy from a baby?"
The employee put a hand on my elbow, "Ma'am, we're going to have to ask you to leave."
"Fine. We don't want to be here with this kind of lawlessness anyway." I turned to River's mom. "This isn't over."
I took a step forward and felt my foot sink into something mushy.
"What the—" I looked down and saw that I was four toes deep in a soft turd.
"I eliminated, Mama," said River.
David laughed all the way home, and eventually even I had to giggle after replaying how I hopped through the play center on one foot to the public bathroom to wash off River's elimination.
"You do realize we can never go back there again, right?" said David, struggling to hold back hysterical laughter.
"Do you think there's a photo of me by the cash register?" I said, a smile playing on my lips.
"Hopefully it's not scratch and sniff," he said, dissolving into hysterics.
He reached over and took my hand. Our fingers intertwined as Aubrey slept in the backseat.
As we turned off of the freeway I stared at David. It felt so good to laugh again together. I studied his profile as he drove: his strong jaw, five o'clock shadow...he really was incredibly handsome. This is what I wanted when I found out we were pregnant—to just enjoy being together as a family. Sure, there was less foreign kid feces in my fantasy, but all in all, I considered the day a success. A poop-covered success.
Sunday, January 27, 4:30 P.M.
I spend every Sunday morning doing a deep clean of my home. My littles love to help with age-appropriate jobs like wiping down silk flowers, stirring the compost and watering our bonsai trees.
—Emily Walker, Motherhood Better
Impossible Goal of the Day: Declutter everything.
My closet is no longer a closet. It is a mini-secondhand store/storage space for all of Aubrey's things. How can a baby so small have so much stuff? I know it's my fault, but girl clothes are so cute. How am I supposed to not spend every last dime buying clothes I never put her in? I know for a fact that her wardrobe is worth more than mine. All of the money I used to spend on myself, I now spend on her.
My postpartum body doesn't exactly say DRESS ME UP! If it could talk, it'd probably say something like, STOP WITH ALL THE CHOCOLATE, or COVER ME WITH A BURLAP SACK.
In my closet are no less than four sizes of clothing that serve as a living monument to the old me, the pregnant me, the postpartum me and the postpartum-PMS-bloated me. I read in AllWomen magazine that your closet is a metaphor for your subconscious. If that's true, then my subconscious is a mess and needs to be taken out back and put out of its misery.
Confession: I hate cleaning.
Does anyone else find it entirely unreasonable that a human being should be required to cook AND clean on the same day? I woke up determined to get my kitchen in a state that doesn't make me shrink with shame. David ended up having to go into the office so I spent Aubrey's afternoon nap wearing ill-fitting rubber gloves scouring the stove top, washing dishes, organizing cabinets, sweeping, mopping, etc.
Ridiculous Things I Found In Our Pantry:
5 partially consumed boxes of cereal
3 cans of fortified shakes for pregnant women (I drank one. Don't judge me; it was chocolate.)
7 boxes of cake mix (I made a cake.)
3 tubs of frosting (I frosted the cake. See? I'm baking.)
3 one-pound bags of cashews from when I wanted to make my own cashew butter (Homesteaders. Don't ask.)
When I was done my kitchen sparkled like it never had before. Aubrey woke up and I honestly felt like an amazing woman and mom until I realized something. I had to start dinner. In an hour, the kitchen would be destroyed. It seemed like a waste of my hard work so I ordered Chinese food, instead.
As I bounced a cranky post-nap Aubrey on my hip while watching television in the living room, I couldn't help but wish David were home. It was Sunday, after all. I glanced around the room trying to think of something to do while waiting for the food to be delivered.
I wished parenting books talked about how utterly boring motherhood could be. I felt guilty for feeling it, but...I was bored. I tried to set Aubrey down on her foam mat, but as soon as her tiny feet grazed the floor, she let out a banshee scream. Like a good servant, I picked her right back up and headed into the kitchen to eat my feelings. Yes, food was coming any minute, but I needed calories to deal with my emotions.
I grabbed a clean spoon out of the dishwasher and made my way toward the pantry. It only took a few seconds to pop the top off of the industrial-sized tub of peanut butter and dip my spoon into its creamy goodness. It was like therapy for my mouth.
"Ah! Ah!" Aubrey begged for a taste. If she hadn't already had peanut butter at Gloria's house (even though I'd asked her not to give her any high-allergy foods—apparently peanut butter cookies don't count), I would have hesitated. I watched, amused, as Aubrey worked the Tic Tac-sized piece of peanut butter around her mouth.
"Pretty good, isn't it? One day you'll eat your feelings, too, honey," I said, closing the pantry and sitting with Aubrey on my lap at the kitchen table. I sighed. I pulled out my cell phone and considered texting David just for a little conversation. No, he was probably busy. I put the phone back into my pocket.
I don't think he will ever fully understand what my life is like. I'm with Aubrey pretty much every waking minute. Yes, he and I are equal parents in the sense that we share equal DNA with the kid, but I'm with her all the time. I just want to talk to someone who doesn't crap her pants every three hours.
I'd kill for some adult conversation. Last Wednesday I tried to spark up a convo with a barista at the café. I think she could sense my desperation because she nodded and smiled as if speaking to a child bragging about how old they were.
The other day the FedEx guy said, "How is everything?" and I went into a three-minute monologue about Aubrey's sleep situation before the weird look on his face told me he was just being polite and not applying to be my therapist.
I get the feeling that sometimes David thinks I'm being dramatic about how exhausting this all is. "Just get more organized." That's like telling someone who's drowning to simply learn the backstroke.
No, I'm not digging trenches all day, but motherhood is draining. I can't nail down exactly why it's so hard. Changing a diaper in itself isn't difficult. Neither is feeding Aubrey or taking her on a walk.
I think what makes being a mom so hard is that it never stops. It just keeps going in perpetual motion. It's a cycle with no end. The days of the week don't mean anything to me. I don't punch out. I'm never "off." David comes home at the end of a hard day and has a sense of completion. He kicks off his shoes, throws his socks anywhere but the laundry basket, opens a beer, and sits on his recliner and plays with Aubrey. I never have that moment because I'm never done. Even when Aubrey goes down for the night, I stay on alert. She could wake up at any time for any reason. Teething. A cold. A wet diaper. I'm always in a heightened state of awareness.
There's no paycheck as a sign of a job well done. No pats on the back from a manager. It just keeps going on and on, twenty-four hours a day, seven days a week.
I pulled out my phone again and couldn't resist sending a quick text to David. Almost done?
A few seconds later my phone beeped with a new message. PR crisis with the Loeman account. Don't wait up. Love u.
No problem. Love u too, I texted back, before returning my phone to my pocket.
I felt my eyes start to well up with unexpected tears. "What's wrong with me?" I asked, brushing them away.
I thought about calling Joy, but remembered that Sunday night is her book—i.e., wine and chatting—club. Even if I had a babysitter, her friends are the organized, always dressed perfectly, "Oh, look, I made organic blueberry muffins" type, and I don't need that kind of negativity in my life.
I'd call Mom but she's an hour and a half away, and hearing my tone would just worry her.
The idea popped into my head before I had a chance to stop it.
Gloria?
Was I desperate enough for company that I'd call the mother-in-law who once referred to my three-bean casserole as a "cute experiment"?
Yes. Yes, I was.
I stood up and switched Aubrey to the other hip. She squawked in protest.
Dialing the number, I tried not to notice that my fingers were shaking. I held the phone to my ear.
Ring. Ring. Ring. Okay, she's not there, I should just hang—
"Hello?" Gloria's voice caught me off guard.
"Gloria. Hi. Hi. Um. It's me, Ashley. Hi. Um..."
"Ashley? Is that you?"
I tried to remember why I was calling.
"Hi, Gloria. Yes, it's me. I'm just calling because... I just wanted... I wanted to see if you were free to pop by for dinner?" I bit my lip.
The line was silent.
"Tonight? Ashley, I..."
"If you're busy, I totally understand. I just ordered Chinese food, David's working, Aubrey won't let me put her down and..."
To my horror a lump started to rise in my throat blocking my words. New tears flooded down my cheeks without warning. I let out a heaving sob.
"Ashley? Dear, are you crying? What's wrong?" Gloria sounded more alarmed than I'd ever heard her.
"I'm just tired. And a little lonely. I'm so sorry..."
Gloria's voice was steady. "I'll be there in ten minutes."
She must have flown down the highway because eight minutes later there was a knock at the door. I'd had just enough time to splash some water on my face and pull my hair into a ponytail.
I opened it, and to my absolute surprise there was Gloria, in full makeup and hair with a black evening gown under an unbuttoned black faux-fur coat.
I gasped. She looked amazing. "Gloria! I..."
Gloria walked into the house and closed the door behind her. "I was getting ready to go to the theater with some friends from the community center but clearly you need me here."
"I had no idea! I wish you hadn't..."
Gloria waved in front of her face.
"Nonsense. I know a breakdown when I hear one. Tell me what's going on, at once."
In one sweeping motion, Gloria draped her coat over a dining room chair and took Aubrey from me. It was such a glorious relief to have my arms free. It was then I noticed that she was holding a bottle of red wine. My heart soared.
Gloria stared at me. "Well? Are you going to get us a couple of glasses?"
Ten minutes later we were sitting at the kitchen table surrounded by takeout boxes. Gloria placed a chunk of white rice in Aubrey's waiting mouth. I took a sip of my wine.
She cleared her throat. "So, if I understand correctly, you're exhausted, tired of being alone with Aubrey all of the time, you miss David, wish he'd help you more and want to lose twenty pounds but are unwilling to exercise."
I stared at the ceiling trying to remember if I'd missed anything.
"That's about it, yes." I nodded furiously, taking another long sip. "It's just that, I thought motherhood would be more fulfilling. I'm here with Aubrey every day, watching her scoot around on the floor or holding her all over the house—and there's nowhere I'd rather be—but I'm bored. I have no one to talk to. David is busy with work. I'm just..."
"You're just a mom," cut in Gloria. "You feel useless and essential at the same time. You feel like everyone is doing a better job than you and that nobody understands what you're going through."
I stared at Gloria with my mouth agape.
"Yes," I said quietly.
Gloria reached her chopsticks into the Kung Pao chicken and popped a bite into her mouth.
"Dear. We all felt like that." She sipped her wine. "David was the first baby I'd ever held. I remember being so surprised when the nurse let us take him home after I had him. I was terrified. Back then, dads made the money and moms did all of the child raising, so I was completely on my own. Then, when David Senior passed away when the kids were just ten and eight...well...I was really on my own."
I looked into my wine. I tried to imagine what that must have been like, raising two children on your own while navigating your own personal tragedy and theirs.
Gloria coughed. "But do you know how I got through it?"
I took a sip of wine. "You pulled yourself up by your bootstraps?"
Gloria scoffed. "No. Vodka. One shot every day at 5 p.m. on the dot."
We dissolved into laughter. I couldn't believe I was actually bonding with my mother-in-law, who only an hour earlier I thought didn't much care for me.
Gloria picked up a stringy piece of chicken with her fingers and placed it in Aubrey's waiting mouth. "Ashley, there's no way around it. Motherhood is hard. And you young moms put more pressure on yourselves than we ever did, with your crafts and your activities. Do you know what we called crafts when David was young? Chores. We didn't play with our kids, we sent them outside. All day. They'd only come back in when the streetlights came on. You moms have it different. You're expected to be on 24/7 and look good doing it. My advice is this. Stop being so hard on yourself. And drink more vodka."
I giggled again, this time with a mouthful of noodles.
Gloria and I watched as Aubrey gummed the chicken.
"When are you going to get some teeth, baby girl?" Gloria teased.
I shrugged.
Aubrey began to fuss and I realized it was almost her bath time.
I stood up. "I should get her ready for bed. Feel free to keep eating. I'll bring her out after her bath."
Gloria stood and held Aubrey close. "Absolutely not. This is your time. Put your feet up and eat your dinner. I'll put her down to bed tonight."
I was speechless. I blinked back the wetness that was rapidly rising behind my eyes.
"Thank you, Gloria. For everything. Thank you for coming tonight."
Gloria smiled and squeezed my shoulder. "You're welcome. I know I'm not your mom, and I know you wish she lived closer, but I'm here for you. Remember what I said. Stop putting so much pressure on yourself, and don't forget..."
"The vodka," we said together.
Gloria kept her word and didn't leave until Aubrey was breathing heavily, her chest rising steadily. We stood together, mother-in-law and daughter-in-law in the darkened doorway, and just watched her, splayed out in her pink bunny sleeper.
I peeked over at Gloria, and for the first time wondered if I'd gotten her all wrong. She had come through for me.
As we walked down the stairs I felt the need to say something. I needed to cement this moment in history as the turning point in our relationship.
She was putting on her coat when I cleared my throat.
"Gloria, I just wanted to say thank you...thank you for coming tonight. It means a lot."
"Think nothing of it," she said, slipping her arm into her enormous fur coat. "I'm actually glad you called. From now on, whenever David is working late, I'll be right here with you."
What?
She continued. "Don't worry, I'll get David's schedule directly from him so you don't even need to call next time. I'll pop right over."
I tried to keep my mouth affixed in smile formation. "That's...great, Gloria. Okay. Thank you."
What had I gotten myself into?
When Gloria left, I sank onto the couch and opened up my phone, hoping to see a text from David. It was already 8 p.m.
Nothing. I clicked through to Instagram and pulled up Emily Walker's page.
She'd just posted a photo of herself with the twelve moms in Motherhood Better Bootcamp and their kids. They were standing in the lobby of her New York office, a gaggle of excited mothers, babies in strollers and a few older children. I've seen her office plenty of times on her Instagram; it's baby pink and white, and has silver accents. She calls the lobby "the Pavilion" and has posted loads of photos of her two youngest children, Sage and Willow, eighteen months and three years, crawling around on the Shibori Jasmine wood floors next to celebrities, chefs and athletes. The moms all looked so happy in their pink shirts monogramed with Emily's EW logo in white calligraphy.
I wasn't jealous at all. No really, good for them.
Maybe I should make myself a T-shirt for Operation Perfect-ish Mom. No, that's just pathetic. And it means more laundry.
I sat on the couch and pulled out Motherhood Better.
Too many moms depend on alcohol to relax and let off steam. I prefer yoga and sunbathing.
I took a long sip of wine. I was about to turn the page when the home phone rang.
"Dang!" I hissed, running toward the kitchen receiver. I'd forgotten to put it on silent for the night. What if it woke up Aubrey?
I skidded into the kitchen and breathlessly picked up the phone.
"Hello?" I said, annoyed.
"Is this Ashley Keller?" a woman's voice asked.
Oh, no, was this about my credit card?
"Um, no... I'm...her nanny...may I take a message?"
"Yes, this is Rebecca Anderson, assistant to Emily Walker."
I dropped the phone. Or threw it, rather. Rebecca Anderson? Emily Walker? I had to be dreaming. This was a dream.
I ran over to the sink where I'd thrown the phone and picked it up.
"I'm so sorry. Um, Ashley actually just walked through the door. Let me get her. One moment, please." I put the phone down on the counter, and with my heart beating out of my chest, tiptoed over to the kitchen table. I then stomped over to the counter, pretending I was just entering the room.
"Hello? Ashley Keller speaking," I said, trying to sound casual even though my voice cracked.
At this point, my heart was pounding so loudly I was afraid she could hear it.
"Hello, Ashley. This is Rebecca Anderson, assistant to Emily Walker of The Emily Walker Show. I'll get right to the point. I'm calling you today because a spot in the Motherhood Better Bootcamp just opened up and you are next on the list."
I think I passed out. She kept talking but I didn't hear anything she said. At one point the line went quiet.
"Hello? Are you there? Can you do it?"
"YES, YES, I CAN DO IT. YES, PLEASE!" I scream-whispered into the receiver.
I still can't believe any of this happened. Turns out, one of the moms was a "dog mommy" and didn't have a human child, which got her disqualified.
I'm in. I'm actually in. I missed the kick-off party at Emily Walker's studios, but the program officially starts tomorrow so I didn't miss anything!
I slid down to the kitchen floor. It was happening. I was in.
"Hello? Are you there?" Rebecca's voice spoke through the receiver.
"Yes, yes, I'm here," I said, struggling to compose myself.
"As a member of the Motherhood Better Bootcamp, you're required to attend weekly video chats with Emily Walker and the rest of the team. You missed the introductory one, but the first real chat is tomorrow morning at 10 a.m."
"Uh-huh," I responded, brilliantly. I felt like I was in a dream. Could I be dreaming? I looked around the kitchen at the empty takeout boxes. No, if I were dreaming my kitchen would be cleaner.
Rebecca kept talking. "In six weeks, you'll be flown out to the gorgeous Napa Valley in northern California for the closing reception and a special taping of The Emily Walker Show. The $100,000 grand prize winner will be announced live. Is all of this something you can do?"
"Yes. I can do this," I said, trying not to float away.
"Great. I'll send the details to your email shortly."
"Okay, thank you, Rebecca. Please hug Emily for me." Did I just say that?
"I, um, okay. Goodbye." The phone clicked off.
I sat there on the living room floor trying to make sense of what had just happened.
Tomorrow I would talk to Emily Walker face-to-face. Tomorrow was the first day of my new life.
Thank you, fairy godmother.
Monday, January 28, NOON
The first video conference was this morning at 10 a.m.
I showered, even though no one would be able to smell me, and even did my hair and makeup. What to wear was a harder decision. My daily hoodie didn't seem right. It was my first time meeting Emily Walker, so looking like a slob wasn't an option. I settled on a long-sleeved purple cotton T-shirt.
I was searching through the laundry pile on my bedroom floor for pants and clean underwear when I realized the call started in three minutes. I plopped Aubrey in her bouncy chair and grabbed the only remaining piece of clean underwear from my drawer, which just happened to be my wedding night white lace thong. It wasn't like anyone was going to be seeing me from the waist down. Maybe I'd keep them on and surprise David tonight. Maybe.
All of the participants were already logged on to the Motherhood Better portal before I signed in. With a little beep my name and face popped up in a pink-outlined square on the screen next to eleven other faces. It was almost like the Brady Brunch opener.
The other moms were so lovely—they were all smiles and excited waving. It was like being part of an exclusive club. It was, in fact, an exclusive club. We were all better mothers. Or, at least, we would be.
The moment Emily Walker's face illuminated the screen was pure magic. I couldn't get over the fact that Emily Walker, blogger turned media darling, could see me. Sure, I was just one of twelve little faces at the bottom of the screen with the other moms, but she could see me. She was just as beautiful in video conference as she was on Instagram. Her makeup was that "natural" style that I can never get quite right—the kind that looks like you aren't wearing any at all but are just blessed by the gods with a flawless, dewy complexion and soft, tinted lips.
In the V of her plush, white (moms can wear white?) cashmere V-neck sweater was a gold heart pendant held by a thin platinum chain. Emily's jet-black hair was in an immaculate topknot and her face was framed by sparkly diamond earrings. She looked like a princess. There was something about her that almost looked like an oil painting come to life.
"Hello, mommies!" Her voice was like a bell ringing. "Welcome to the first of six Motherhood Better Bootcamp video chats. Who's ready to change their life?"
There it was. The dazzling Emily Walker smile. Two rows of perfect white teeth. We all cheered! Aubrey stirred a little in her bouncy seat from the noise but didn't wake up.
"As you know, the Motherhood Better Bootcamp program is divided into six challenges. Every Monday, we'll discuss the week's challenge via video chat. Last week's challenge was to reflect on the mom you've been versus the mom you want to be. The next five challenges are as follows. Week two, create a physical fitness regimen. Week three, find a hobby you truly love. Week four, put the spice back in your marriage. Week five, find your village of moms. And week six, turn your house into a home.
"Okay, does everyone have their copy of Motherhood Better with them?" Emily asked, holding up her book.
I did. So prepared. I felt like a Girl Scout. Minus the pants.
"This week's challenge is to shake off the shackles of baby weight and find a fitness routine that works for you. Please open it up to the first chapter, 'Your Mommy Body: Your Mommy Temple.' Who's ready to get in shape?"
The cheering was noticeably quieter this time, but everyone was still all smiles.
Emily lifted a transparent water bottle monogrammed in black calligraphy with her initials.
"If you follow me on Instagram, which I hope you do, you already know that every day I drink no less than seventy ounces of water infused with lemon, stevia and fresh-pressed ginger. I call it my 'mommy tonic' and it's what helps me stay on top of my five kids and bustling business!"
Emily took a dramatic sip from the bottle.
"Yummy! The recipe is on the Motherhood Better online communication portal. By the way, don't forget to check into the forums daily and let us know how you're doing!"
I made a note to myself to buy a cute water bottle and make some mommy tonic. Hopefully it tasted something like a gin and tonic.
Emily put the bottle down. "Okay, this week, your challenge is to focus on your health by adopting a fitness routine that works for you. Every morning, I spend forty-five minutes with my personal trainer, Sven, and we..."
My mind wandered. Oh, we all knew about Sven. He was the Norwegian Hercules who graced Emily's blog regularly, and always in some kind of graceful but intimidating yoga pose. Most of the time he donned only a pair of skintight elastic short shorts. The way his skin glistened in Emily's photos, it looked like he'd been freshly oiled up for a body building competition. All of Emily's followers were obsessed with him, and posts featuring her trainer always were flooded with comments.
Is he available for sessions out of state?
What are his rates?
I snapped myself back to reality.
"Sven and I prefer to exercise in nature and barefoot. It promotes a mind/body/Earth connection. Look, ladies, if I can get my body back after birthing five littles, so can you!" Emily continued. "Now, I'd like to hear from some of you. What are your personal body goals?"
A mom with long, wavy brown hair, a glittery tank top and expensive-looking sunglasses perched on her head spoke up. "Yeah, hi. I'm Kimmie from Los Angeles." She popped her chewing gum. "My personal body goal is to lose the last one-and-a-half pounds of baby weight and complete the last abdominal skin laser treatments from my plastic surgeon. It's painful, but I know I'm worth it."
Emily smiled sweetly into her camera. "Those are all very good goals, Kimmie. Would anyone else like to share?"
Two more women shared their goals. Fiona, a mom with two dark brown braids that hit just past her armpits, said she wanted to start every day with yoga. A woman named Lillian with a short blond bob talked about joining some kind of stroller exercise club.
"These are all so fantastic," Emily said, clapping her hands. "I just know this week will be a turning point. Remember, it's not about being a size two, it's about having the confidence of a size two."
The call ended in a way that I couldn't have ever imagined.
"Before we go, I'd like to introduce the group to our new member, Ashley Keller. She's replacing Mellie."
She said "Mellie" like the name tasted bitter in her mouth.
"We're so excited to have you, Ashley! You do have a human child, right?" she asked, with a slightly annoyed giggle.
I was frozen with shock that Emily Walker was addressing me by name but managed to sputter out an embarrassed, "Yes."
"Tell us a little about yourself, Ashley!"
"Um, my name is Ashley..."
Duh! She just said that! I could feel my face getting hot. I rubbed my sweaty palms on my shirt. "My daughter, Aubrey, is, um..."
My mind went blank. I couldn't remember how old Aubrey was. Everyone was staring at me, Emily included. She has five kids and probably never forgets how old any of them are. How could she? She throws them massive fabulous birthday parties every year. If anything, her kids' ages are marked in AmEx bills.
"She's...less than a year old."
Less than a year? A tiny bead of sweat formed around my temple. I brushed it away with my hand.
Emily smiled warmly. "Is she there with you?"
Emily Walker wants to meet my baby. The Emily Walker. I broke out in a dopey grin.
Of course! I jumped out of my seat and bent over to pick up Aubrey. It wasn't until I heard the audible gasps that I realized I'd just mooned the entire group. Eleven people, including the woman I want to be when I grew up, had just seen my thonged, practically naked backside.
I ducked down immediately under the desk and out of frame. No. No, no, no, no. No. This wasn't happening. This couldn't be happening. Every last member of the group and Emily Walker—my mom crush, future bestie and mentor—did not just see the bottom back half of my birthday suit, including the Minnie Mouse tattoo I got when I was eighteen that only David and a handful of others know about.
No, no, no, no. I held a now-fussing Aubrey under the table for what felt like an eternity and tried to melt into the floor and wish my existence off of the planet.
"Ashley?" I heard Emily say through the speakers. "Are you there?" Behind her I could hear a muffled snicker.
I crawled back up to the chair with Aubrey.
"I'm... I'm sorry about that. I forgot I wasn't..."
A booming, confident female voice cut me off, "I'm not wearing pants, either, Minnie Mouse," said the brown-haired, burly mom who had earlier identified herself as Josie from Iowa.
Everyone broke into laughter and I sheepishly smiled, relieved. I mouthed "thank you" to Josie.
"Well then! That was exciting," continued Emily, tersely. "This must be Aubrey! She's darling! We've run out of time but I just wanted to thank all of you for your commitment to being the best moms you can be. Remember, great moms are made, not born. Good luck with the challenge!"
Before I knew it, everyone was saying goodbye and the screen went black.
Well, it could have been worse. I could have done a full frontal.
I decided not to let my peep show get me down. Yes, it was humiliating, but I had three huge things to be grateful for: I just had a meeting with Emily Walker, in six weeks I'd be going on a three-day vacation with her and I was on the path to becoming the mom Aubrey deserves. A mom who wears pants.
Now I just had to figure out how to do it.
This week's task was to exercise. I wondered if stretching to reach the candy on top of the fridge counted as Pilates.
My first step in the Fitness Challenge was to make Emily's mommy tonic. It only called for water, lemon, stevia and fresh ginger, but the only ingredient I had on hand was H2O. I was not 100 percent sure what stevia was. Hopefully it was some kind of Russian vodka I'd never heard of. With any luck this tonic would be more of a cocktail than something I'd have to choke down all day like cough medicine.
It was already 7 p.m. when I realized I was missing two ingredients for Emily's magic elixir and David had just texted me, letting me know he was on his way home (he worked late AGAIN), so I asked him to pick them up. You would have thought I'd asked him for a pound of flesh from his passive aggressive, I'm exhausted, but sure, text. I can count on one hand the number of times I've asked him to go to the grocery store since Aubrey was born. Was I supposed to put a freshly bathed and pajamaed Aubrey in the car and take her to the store? I don't know if it's work stress or what, but asking him for anything these days results in a huge man tantrum that is starting to get on my last nerve.
I never wanted to be the type of wife that nags, but if I need something done I have to say it a minimum of six times to make it happen. The kitchen faucet was spraying me in the face from the base for two weeks before he finally fixed it. Over those fourteen days I must have brought it up twenty-eight times. If that's nagging, I guess I'm a nag. Excuse me for not wanting to look like I'm about to enter a wet T-shirt contest every time I wash my hands.
At 7:45 p.m. David walked through the door and angrily tossed me a small shopping bag. It turns out stevia is not a Russian vodka but an all-natural sweetener that he had to go to three stores to find. I would have felt worse for him if he hadn't had such an attitude about it.
"You're welcome," he uttered sarcastically after kissing me on the cheek.
I pursed my lips and used the sing-song tone that means I'm trying not to snap.
"You're welcome, too, for me taking care of the baby all day, cleaning, changing the worst diaper I've ever seen in a six-inch by six-inch public bathroom, doing the laundry, and..." I almost said "making dinner" but stopped myself. The frozen chicken tenders, mashed potatoes from a box and canned corn waiting for him on a plate in the microwave probably wasn't a meal I wanted to brag about.
He set his briefcase on the kitchen table. "And you're welcome for my working an entire day so that we can have a house to live in and food to eat."
I took his lunch container out of his bag and placed it in the sink. "You're also very welcome for my doing everything at home so that you're free to work and interact with other adults while I sit at home all day like a hermit with only dirty dishes to talk to."
He began to walk upstairs toward the bathroom. I followed him, my plastic grocery bag still in hand.
David sat on the bed and kicked off his shoes haphazardly, knowing full well how much that annoys me.
He sighed. "If you hate being at home with Aubrey so much, why don't you get a job?"
I felt like I'd been stabbed in the chest with a jagged icicle. I walked slowly toward him. Suddenly he wasn't my husband, he was the enemy.
"First of all, I do not hate being home with Aubrey. She's my entire life. It's hard. Every single day it's hard. Why aren't I allowed to say that? My life isn't easy."
David stood up and loosened his tie. He leaned into me. "Neither is mine."
Without another word he walked into our bathroom and shut the door. I heard the shower start. I went downstairs to clean up.
I felt conflicted. I never thought his work was easy, but if I were to be honest, it did seem more interesting and less...tedious than being a stay-at-home mom. I love Aubrey with all of my heart and wouldn't change a thing which in some ways makes it worse. How can my life be exactly how I want it to be but feel like such a daily struggle?
I turned on the microwave and set it to two minutes to warm David's gourmet meal. Hopefully he'd see it as a peace offering. A slightly overcooked peace offering with a side of ketchup.
I walked over to the kitchen counter and opened the plastic bag. It contained a small bottle of stevia, lemonade, and ginger ale. Lemonade? Ginger ale? I asked for stevia, a lemon and fresh ginger. I slammed the bag down on the counter and tried to control my rising anger.
This would have to do for the night. I mixed three drops of stevia and a splash of lemonade into a glass of ginger ale and took a big swig. Not bad.
I walked upstairs to my bedroom with my not-so-healthy elixir and settled into bed with my computer in my lap. I could still hear David in the shower.
I clicked through to the Motherhood Better message boards. Rebecca, Emily's assistant, had sent me login information for the portal late last night. Apparently, it was some sort of private online journal where all of the Motherhood Better Bootcamp members were supposed to update each other with their progress. Scanning the page I saw that there were already over a hundred posts.
Hello ladies! Today I jogged for six miles while pushing my three-month-old twins in their jogging stroller. I felt incredible. I'm training for a half-marathon to raise funds for a local charity.—Heather from New Jersey, mom of two
Hi moms! Oh, I have had the best day ever! Our video chat with Emily really lit a fire underneath me. I have three children three and under, but that didn't stop me from signing up for my city's intramural lacrosse team! My husband is so supportive and is bringing the kids to every game and practice.—Naomi from Wisconsin, mother of three
Gosh. The most physical thing I'd done that day was break a sweat trying to open a particularly difficult bag of potato chips during Aubrey's nap. At least I was drinking the mommy tonic. I sipped the sweet, carbonated beverage, hoping the core ingredients were melting away my cellulite.
I needed to up my game. This was a competition, after all, and Emily was probably reading all of these posts. I jumped up and checked my face in the mirror. I looked alright. Standing in the light of my bedroom next to my closet, I opened my phone's camera and held it at a flattering angle, making sure to hold up my glass of tonic. I snapped a photo.
I had dark circles under my eyes and my hair was noticeably slick, but it would have to do. I quickly uploaded it to the Motherhood Better Bootcamp portal with the caption, I'm loving the mommy tonic! I can feel my body getting detoxified already. Thanks Emily!
It was only after I was admiring my brilliant post that I noticed three loads of unwashed laundry, including my inside-out panties with the crotch section facing up, were in the background. I scrambled to delete the photo but there was no option to do so.
Typing quickly, I added, Photo taken at my best friend's house.
As my eyelids became heavy I checked Emily's Instagram one more time. I thought Bare-Butt-Gate had been long forgotten, but she'd snapped a photo of a small purple bottle of some kind of body cream on top of her Egyptian cotton sheets with the caption, Perfect for keeping arms, legs, AND BOTTOMS smooth.
I fainted. Good night.
Tuesday, January 29, 12:30 P.M.
Too many mothers rely on caffeine to keep them going. What they don't know is that motherhood comes with its own natural pick-me-up: love! When your heart is wide open to the miracle that is your blessings, you'll no longer need sugary coffee drinks to make it through the day.
—Emily Walker, Motherhood Better
I made it to noon without a cup of coffee, but after almost falling asleep on the living room floor three times this morning while Aubrey banged a plastic octopus on my head like a judge's gavel, I knew I had to get some coffee in my body. It was in Aubrey's best interests. I'd never made it to the café that quickly—on the way, I almost ran over an elderly woman with my stroller, but if I slowed down, I risked dozing off in the street. The smoky black liquid tasted like heaven in my mouth and I downed it in less than six greedy gulps. A few minutes later I had that familiar buzz.
The café was mostly empty, except for two women chatting together in the corner. They'd lean into each other, whisper something and then laugh raucously, as if they were sharing the most hilarious stories anyone had ever heard. I tried not to watch them.
It was a recurring theme, but ever since Gloria came over, I'd been thinking more and more about how desperately lonely motherhood is. I ran through the different times in my life, teenage years included, and had to admit I'd never been this lonely in my entire life. David could be right next to me in bed and I still felt like I was by myself. I just didn't feel like he understood me anymore. I didn't feel like anyone did.
Ever since Aubrey was born, I'd felt like I lived on a deserted island of baby television shows, chores and diapering accessories. I had one teeny finger based in reality and the rest of me was stuck in an oblivion of sleepless nights.
I loved being a mom. I loved Aubrey, but I wished I had real friends to talk to every day. I couldn't open up to David. He'd just go on and on about how I needed to start making to-do lists and getting things done while the baby slept. I wanted a friend who would just listen and complain, not make reasonable suggestions.
David was as involved as he could be, but at the end of the day he'd never know what it was like to hate his flabby stomach but love the cause of it. I knew he worked hard, but whenever he said, "I'm tired," I wanted to cut him a little bit. Tired? You get to sleep through the night. I give 100 percent of myself but still feel like I'm failing at the most important job I've ever done.
Before I knew it, it was time to take Aubrey home and put her down for a nap. Even with the cup of coffee coursing through my veins, I knew I'd probably have one, too.
Looking around at the empty tables, and longing for connection, I pulled out my phone before leaving the café and logged into the Motherhood Better portal.
Motherhood Better Bootcamp Journal Entry
From Ashley Keller, mom of 1
Today I enjoyed a brisk walk with my daughter to a nearby café. I really worked up a sweat. I'm still adjusting to the mommy tonic and indulged in a small coffee, but instead of my usual chocolate cookie I opted for fruit-based apple pie.
3 P.M.
When I met Sven I was like most of you: unhappy and overweight. I couldn't shake the last six ounces of baby weight. Within three weeks, he whipped my body into the best shape of my life. My high school cheerleading uniform is too big for me now.
—Emily Walker, Motherhood Better
I'm tackling the Exercise Challenge today. Guess what? I joined a gym. I signed the contract for a year and paid the first three months up front. The very fit personal trainer guy at the front desk asked what my fitness goals were. I don't think "general thinness" is what he was expecting so I added "muscle building" in at the last minute.
Want to hear the best part? The gym has childcare. You can drop off your baby for an hour at a time. I feel a little bad leaving Aubrey with strangers, but I checked it out and they've all been background checked, fingerprinted, have at least thirty early childhood education college units and are CPR certified. Come to think of it, they're probably more qualified for motherhood than I am.
I start tomorrow. Today I'm going to get my new fitness clothes: a few pairs of stretchy black pants, two sports bras, a new water bottle, indoor running shoes and four sporty tops should do it. Maybe I should get some of those electrolyte drinks that look like they glow in the dark. And some granola bars for energy. Peanut butter, too. I have a coupon for the new kind with swirls of chocolate. Yum!
I can't wait.
Wednesday, January 30, 2 P.M.
Always incorporate your children into your exercise routine. It's important to model healthy living. My five love to join me on my 5 a.m. walks. The baby fits snugly in my wrap and I pull my middle two in a wagon. More weight means a better workout!
—Emily Walker, Motherhood Better
I love the gym. Aubrey and I got there at 8:30 a.m. today and she was the first baby in the Kid's Korner (don't ask me about the double K. I'm trying to ignore it). After dropping her off I headed to the locker room and changed into my new, very cute ensemble. I felt fitter already!
Then I saw it: the hot tub. I didn't spend the entire hour soaking. Just forty-five minutes to warm up my muscles before a very brisk ten-minute speed walk on the treadmill. The machine said I burned thirty calories, which is probably half of a granola bar, but it's not just about calories burned, it's about the changes to your metabolism and muscle building. That's what I overheard a personal trainer saying. I'm learning so much.
Aubrey slept the entire time. Can't wait to go back. I'm such a gym rat already. I'm going to be such a MILF: Mom I'd Love to Feel good about. #SoFit.
Thursday, January 31, 9:30 A.M.
Salad makes a wonderful breakfast! My breakfast salad bowls include baby arugula, six organic grapes, red onions, cucumber slices, fair trade walnuts, ¼ cup of quinoa, and a generous serving of aloe and mango juice vinaigrette.
—Emily Walker, Motherhood Better
Not only does this gym have a hot tub, it has a steam room and free WiFi. I walked once around the track today. I did two sets of three pushups, as well. I've gained a pound but muscle is heavier than fat so I'm not worried.
After my pushups, whew! I fired up my laptop and watched two episodes of Hillside Heights in my nook. What's my nook, you ask? It's a private changing room where I sit with my feet up on a bench in the corner and just focus on being present, like in yoga. Naturally I use my headphones so as to not disturb anyone. It is extremely similar to yoga.
Amazing Fact: This gym has a snack bar with the most delicious creations. The Chicken Tucson wrap is to die for. It has only 300 calories without the Southwest sauce. I added the sauce, of course, but just for a bit of flavor.
I also jogged for almost six minutes. #FitnessFreak.
I took a gym selfie and sent it to David. He replied with a heart-eyes emoji. He's so incredibly proud of me, but not as proud as I am of myself.
You'll be happy to learn that I've changed my eating habits entirely. No more ice cream, only frozen yogurt. There's a new place two doors down the street and it has all kinds of mix-ins: breakfast cereals, chocolate chips, almonds (healthy), and coconut caramel flakes (also healthy). When you buy four cups you get the fifth one free. Guess who's getting a freebie tomorrow?
Friday, February 1, 11 A.M.
Don't feel pressure to lose the baby weight too quickly. After the miracle of childbirth, for me, it takes between 10–15 days.
—Emily Walker, Motherhood Better
Quick update: I felt bad monopolizing the changing rooms, so after I dropped Aubrey off in the gym childcare today, I watched Hillside Heights in my car. If I pull up right beside the back entrance the WiFi is still incredible. I didn't have time to work out, but I really do need the downtime. Aubrey is doing great in the Kid's Korner.
I think I'll come back this afternoon for another workout.
2 P.M.
We have a snitch. When I returned to the locker room today after watching two episodes of Celebrity Style Scoop in my car, there was an envelope tucked into my locker. Inside was an official letter.
Dear gym member,
Please be advised that the use of the Kid's Korner is for active gym members only. We require all guardians to stay inside of the fitness center while their children are being minded.
Warmly,
The Management
How dare they? My car is only a hop and a skip away from the treadmills. It's barely on the other side of the glass. They're acting like I went on a shopping spree in the next city. Relaxing one's mind is just as important as working on your body. Emily always says that. How do they know I'm not meditating in my car or doing laps around the building? How do they know I don't have a medical condition and need to give myself injections in the privacy of my vehicle? If that were true, I could probably sue for discrimination.
I am furious.
I am determined to find the source of the information leak. My top suspects right now are:
#1: The super-skinny blonde who runs the gym café. Sometimes I order a chocolate protein smoothie to go before popping off to my car.
#2: Yolanda. Yolanda is another Kid's Korner mom. She drops off her two-year-old, Jasper, at the same time I drop off Aubrey. We're usually in the changing room together. She's asked me if I'd like to weight train with her once—be spotting buddies—and I turned her down not just because I don't want to lift weights but because "spotting buddies" sounds like some kind of mutual agreement to discharge blood between periods together and that's gross.
I've seen Yolanda give me side-eye more than once as I saunter back from my car, relaxed and happy to pick up Aubrey. It's not my fault that I've figured out a way to enjoy my life while she gets sweaty and punishes herself.
Update: It's definitely Yolanda. As I tucked the letter into my bag she walked past me and gave me a half I-told-on-you smile. Wench.
Tomorrow I'm going to try some yoga if the class isn't full.
Saturday, February 2, 11 A.M.
Sven is a licensed massage therapist. I highly recommend that mothers treat themselves to a massage once a week to work out some of that stress.
—Emily Walker, Motherhood Better
Yolanda is watching me. After I dropped Aubrey off at the Kid's Korner, I headed over to the elliptical machines and saw her peeking at me, not once but TWICE, from the free weights area. How childish of her to tattle on me just because I wouldn't be her period partner.
The upside is that I burned a hundred calories, which means I can stop by the froyo place and treat myself on the way home.
Aubrey cried a little when I dropped her off today. She could probably sense my stress from the situation. Thanks, Yolanda.
In more uplifting news, I signed up for a Mommy & Me yoga class. A Bikram (that's yoga-speak for "unnecessary torture") studio a few minutes from my house has a few openings and I thought, why not?
Someone on Facebook said it helped them bond with their one-year-old and connect their souls or something. I don't know what that means, but I'd love for my soul to be connected to Aubrey's.
I know it sounds crazy, but I'm already worried about what her teen years will be like. If she's anything like me, she'll be absolutely insane and risk her life twelve times before breakfast. I'm hoping that if I keep an open dialogue and attach chains to her ankles, it won't be so bad. The yoga can't hurt, either. Maybe by the time she's thirteen we'll have bonded so well that she'll confide in me, come to me when she needs advice... A mom can dream, right?
Our first class is this afternoon. Wish me luck and flexibility.
10 P.M.
The decision to move Sven into our pool house was a natural one. He's like a member of our family now. Our kids call him Uncle Sven! It's my solemn prayer that every mom finds a trainer and friend like him.
—Emily Walker, Motherhood Better
How did Mommy & Me Yoga go? Thanks for asking. It started off a little rocky. We were running late and I didn't have time to change, so I just Febreezed my yoga pants in case we had to sit with our legs open.
I must be doing something wrong because all of the other babies seemed much calmer than Aubrey. She spent the entire time crying and trying to squirm out of my arms. She wasn't at all interested in Baby Crane or Downward Facing Puppy. A mom in white linen pants to my left kept eyeing me like I was failing some kind of Zen-ness test.
Near the end, we were supposed to meditate "third eye to third eye," with our faces pressed against our baby's faces. I leaned into Aubrey, who was sitting on her green mat, and she head butted me. Right in the nose. Stars exploded behind my eyes and I almost blacked out. Before I could think, six or seven curse words flew out of my mouth. Loudly. Aubrey and the babies on either side of us burst into tears. White Linen Pants picked up her son and held him to her chest like I was holding a machete.
The yoga teacher tried to salvage the tattered calm vibe in the room, "Okay, accidents happen. Draw in the good air, breathe out the bad."
I'm pretty sure I was the bad.
We left shortly after that.
We weren't banned for life but I'm not going back. Aubrey can head-butt me in our living room for free.
I canceled my gym membership. I decided that I don't want to be part of an organization that discriminates based on how people choose to interpret "working out" or uses a K to spell Korner. But I am going to miss those wraps.
Fun news: I checked into the Motherhood Better Bootcamp online portal today.
Bad news: There's a thread for updating everyone with your progress, and seven of the moms have already lost weight, toned up or done things with their bodies other than stuff them with frozen yogurt and get knocked out by their infant.
I can't mess this up. Today I did ten pushups (over a three-hour period) and three sets of four sit-ups. For dinner I'm making cheese tortellini, but I'm only eating a baby bowl-sized portion with just once tiny piece of buttered French bread.
Progress.
Sunday, February 3, 9 A.M.
Not every meal you eat needs to be solid food. I replace at least two a day with juice made of vegetables from my garden. For enhanced vitality, add a teaspoon of heart-healthy colostrum.
—Emily Walker, Motherhood Better
Today is my last day to make some progress before the bootcamp video chat tomorrow.
I started a new diet. It's called Ship Shape Shake, and according to the infomercial, I should start seeing dramatic results in just seven days. I bought the box after the failed yoga class yesterday, and I haven't read through the literature yet but I'm excited.
Full disclosure: I may have messed up just a teeny bit. I didn't realize that each silver packet of strawberry flavored powder was supposed to be a meal REPLACEMENT. I thought it was a kind of fat-melting solution that would enter my body, bear hug the cellulite and then carry it out.
Apparently, I'm actually supposed to mix the powder with cold water to make some kind of sad watery shake and drink that instead of eating actual food.
I downed the first shake with a bowl of cereal, one hard-boiled egg and a vanilla latte with whipped cream.
I'm totally on board for lunch, though.
For dinner you're allowed to have a shake and a "reasonable dinner." The picture of the dinner in the brochure was a romaine salad, chopped tomatoes and grilled chicken but David is working tonight so I'm going to finish the last slice of pepperoni pizza in the fridge for dinner before it goes bad. People are starving all over the world and it feels wrong to waste food at a time like this.
10 A.M.
Today started out rough. I was so hungry I started eating almonds to curb the pangs. Forty-five minutes passed and I was still starving.
10:45 A.M.
I'm not sure, but I believe the diet is starting to affect my cognitive functions. As hard as I tried I couldn't remember what bagels taste like. I would've killed for a bagel and cream cheese. Okay, maybe not kill, but I would have definitely slapped someone for one.
10:50 A.M.
I ate six of Aubrey's baby cheese puff things. Not on purpose. I gave her one and then before I realized what was happening, six were in my mouth half chewed. Yes, I could have spit them out but that's insane. Who spits out food?
10:54 A.M.
I broke down and had an apple with peanut butter. It's not on the meal plan, but apples are fruit and peanut butter is just nuts which have omega 3s, I think.
11 A.M.
Took Aubrey on a walk for some cardio. Bought a low-fat mocha with no whip at the café. I would have opted for nonfat milk, but that's against everything I believe in. Have you seen nonfat milk? It's blue.
I bought a croissant but gave most of it to Aubrey to gnaw on. May have had a few bites for energy for the walk.
11:30 A.M.
I drank my second shake in less than ten seconds. I was supposed to wait for lunch, but I couldn't. My stomach felt empty and acidic. I ate twenty more almonds. If I have to see another almond in my life I will immediately barf. Unless it's a chocolate-covered almond, I love those. I wonder who discovered chocolate-covered almonds? That person should have a national holiday named in their honor.
11:45 A.M.
I kept walking in and out of the kitchen like a lost child. I ate a cherry tomato in desperation.
11:47 A.M.
Just ate a plate of sliced red onion dipped in fat-free dressing with six shakes of pepper. I pretended it was a steak. Did not work.
SUNDAY, NOON
Aubrey was having a jar of pureed butternut squash, apple and beef for lunch. Normally the dark orange mush wouldn't appeal to me, but after warming it in the microwave for twenty seconds, I tested it on my tongue. It was like heaven. I took one more mini bite. Then one more. I ate half of the jar before coming to my senses. This was a new low.
2 P.M.
CraigsPage.com
New Listing
For Sale:
Almost complete starter kit of Ship Shape Shake Meal Replacement Diet Kit.
Strawberry Flavored.
Only two pouches missing.
Note: You can't eat actual food. The shakes are the food. Just thought you should know.
11 P.M.
Aubrey just went back to sleep for the second time, so I decided, since I was up, I'd update my Motherhood Better Bootcamp online journal before tomorrow's call.
Motherhood Better Bootcamp Message Board Entry
Hello ladies and Emily! So far I've joined a gym and taken up yoga with my daughter. She's such a strong little girl. Very headstrong. She inspires me to see stars in the mundane every single day. I love her. I'm eating more consciously and really savoring my meals. Thank you for the Ship Shape Shake recommendation. They're delicious and really changed the way I look at food. Xo Ashley
I shut the computer and sat in the dark of my bedroom next to David, who was sleeping soundly.
I was just settling into bed when I heard Aubrey wail again. She sounded wide awake. "No, no, no," I wailed internally.
Moments like this I wish I had sister wives. Surely my sister wife would hear my baby's pitiful wails from the next room and help me. She'd float in, wearing a long, modest ivory Victorian nightgown and smile sympathetically at me before picking up my baby and whisking her away. Before she left I'd pretend to protest her help, and she'd put a finger to her lips and mouth, "No. Sleep. You deserve it."
I threw my feet over the side of the bed and quickly made my way down the hall. I opened Aubrey's door to see her sitting up, sleepily. She could barely stay upright as she rubbed her eyes with a chubby hand. My heart melted.
I carefully laid her on her back and rubbed her stomach. Without warning she let out an enormous burp. She sighed, closed her eyes and within moments was breathing deeply again.
That's all it was? Gas? I stroked her fine hair.
Suddenly, a sister wife didn't seem like a brilliant idea anymore. As utterly exhausted as I was, seeing Aubrey's still face in the moonlight, I knew I wanted this moment to myself.
Monday, February 4, 11 A.M.
It's important for every mom to have a passion. Your calling is motherhood, but you must have something yours alone that lights a fire under you every day. My hobby is crafting. Whether I'm monogramming organic T-shirts for orphans in Russia or simply making sustainable and aromatic sachets for friends, creating beautiful things with my hands is what makes me excited to wake up in the morning.
—Emily Walker, Motherhood Better
The Motherhood Better Bootcamp video chat had started promptly at 10 a.m. Despite being jetlagged in Australia as part of her book tour, Emily looked fantastic. Her shiny black hair was pulled into a side French braid and she wore a long-sleeved cashmere shirtdress. Her eye shadow and lipstick were both a luxurious deep plum and her skin was flawless.
"Hello, mommies!" she said excitedly, her sparkling pearl-like teeth shining in her camera's light. "I've been reading all of your online journal entries and am so proud of the progress you made during the Fitness Challenge! Brava to each and every one of you! Now, who's ready to get crafty?"
I sat at the kitchen table staring at my computer and bouncing Aubrey in my lap, trying to look enthusiastic. I don't exactly have the best history with crafts. Joy tried to get me on the DIY bandwagon but quickly gave up when she realized I didn't know my macramé from my marzipan.
Emily leaned into the camera. "Having a hobby is so important when you're a busy mama. It gives you something to do that's just for you, nobody else. Right now I'm working on a needlepoint of my entire family." Emily held up a thick three by three white sheet showing a half-completed—but clearly expert—embroidery of her family of seven.
"Oh, my freaking—" I stopped myself before I cursed aloud.
The other moms oohed and aahed.
"This week, the challenge is to flex your crafting muscles. I want you to dig deep and get those creative juices flowing. Does anyone have a project they're currently working on?"
Josie from Iowa raised her hand. She was a stocky woman who wore lots of flannel. I recognized her from her journal entry photos. As down to earth as she seemed, I'd hate to cross her, as I was sure she could break a grown man in half.
Josie cleared her throat. "I'm building my kids a playhouse out of reclaimed wood from the lumberyard. I'm laying the concrete foundation later today."
Emily's face froze. "Wow, well, that's certainly a...craft, I suppose. Anyone else?"
Kim from LA raised a finger before speaking. "I'm having my nanny make a quilt out of Connor's old onesies. She's really good at those things."
Emily blinked. "That's wonderful, Kim, but the challenge is to make something by yourself."
Kim's mouth hung open. "I made Connor."
Emily paused before continuing. "If you're stuck and need craft ideas, check the message board. I put a few links up to some of my more popular crafts including the papier-mâché mold of your child's hand that everybody loved a few months ago."
The ladies oohed and aahed.
I didn't manage to get in any face time with Emily during the call so I knew I'd have to knock it out of the park this week. If I couldn't get her attention, I had no chance of winning the competition.
After the call was over, I put Aubrey in her stroller for a walk to give myself time to think.
As we sauntered down the sidewalk, I made a resolution.
I decided to not only learn to craft but to learn to LOVE to craft. I always pictured myself as the kind of mom who made every sweater, spent the afternoons dipping candles and was always up to some adorable project.
So what if I almost burned the house down two years ago trying melt crayons onto canvas with a blow-dryer (RIP blow-dryer)?
Fact: Blow-dryers cannot be propped up for several minutes using a stack of paper plates while on full blast.
I've learned that crafting is a great bonding activity with children. I can't open Facebook without seeing what my high school friend turned perfect mom Penny McConnel is crafting. Today her status was, "Found a vintage olive oil bottle at the recycling center. Turned it into a fun lotion dispenser." The photo looked like something out of the Anthropologie catalog. I bet her four daughters (yes, four daughters) all wore matching aprons and made their own mini homemade coconut-oil lotion and lotion infused with freshly picked lavender. I want that for me and Aubrey.
I noticed that Aubrey had fallen asleep so I parked the stroller at one of the patio seats outside the café. I pulled out my phone and spent a few minutes scrolling through Pinterest, and even though I hated the website from the bottom of my soul, Ashley the Perfect-ish Mom was going to learn to tolerate it. I'd feel differently once I had a few successfully pulled-off crafts under my belt.
To really impress Emily Walker, I was going to choose three crafts to master over the next few days.
Potential crafts:
1. DIY watercolor coffee mugs (Yes, they sell beautiful mugs at the store, but why would you want to buy one for $3 when you can spend $20 in supplies to make one that will stain your cuticles?)
2. DIY stain remover (All you need is a little borax, vinegar and salt, and you no longer need to be dependent on drugstore laundry products. As a bonus, you get free chemical burns.)
3. No-bake cake batter truffles (These would be wonderful for holiday gifts or eating in the kitchen in the dark.)
4. DIY mason jar etching (These are gorgeous! I could already see them filled with wildflowers and decorating my home.)
5. DIY ruffled baby romper out of a pillowcase (For Aubrey. I should really just sew all of her clothes.)
I put a shopping list together and just had to go get the supplies.
Who's a slacker? NOT ME!
3 P.M.
A Crafting Essentials starter list can be found on my website. The 67 items listed will get you started on your crafting journey. You'll find they are more than affordable and add up to only around $600. My children and I begin a new craft every morning at 7 a.m. on the dot. We begin by changing into our matching aprons on which I hand-embroidered our initials. We enjoy crafting by the light of the sun on a project table made from reclaimed lumber that I sanded and stained myself over a lazy weekend.
—Emily Walker, Motherhood Better
I decided to wait until Aubrey woke up from her nap to start crafting. Yes, she's just a baby, but I was sure Laura Ingalls Wilder's mother passed down all of her canning and quilting skills to her at a young age. I felt like it was important for Aubrey to grow up in a homemade environment and see me take charge of the home or something.
To get into the mood, we even wore matching aprons, just like the ones Emily and her kids wear. Unlike Emily, though, I didn't make them; they sell them at Michelle's, the home base for all crafters. It's a huge chain. I'd never been in there before today, and after I'd spent a house payment on supplies I was still confused by the prices. Was everything supposed to be that expensive? I actually had to double-check the currency with an employee. "I'm sorry, but what money is this in? Turkish lira? Pesos?" Maybe everything was blessed, like kosher food but by Martha Stewart.
Wasn't the whole point of making things to save money? I was pretty sure Laura Ingalls Wilder wouldn't have stepped foot in a Michelle's.
Michelle's lures you in with the promise of a better life and then empties your checking account. It's like one of those fraudulent emails from an overseas "prince" promising you an inheritance you don't deserve. Michelle's has the same business model as movie theaters: offer you a good time, and once you're trapped inside charge $12 for a small popcorn—or, in Michelle's case, $200 for an old-timey popcorn maker. I almost bought it, too. That is, until I pictured David's face when I told him that I spent a car insurance payment on the promise of buttery snacks.
There was an entire aisle just for glue. GLUE. And one for cake stands. Since when did people get too good to eat cake out of the pan it was baked in? I bought one anyway. I've decided I'm going to make Aubrey's birthday cakes every year. I also picked up some piping bags, a book about cake decorating and some fondant for snacking while I learn. Unfortunately, they didn't sell baking skills, but I have a couple months to learn.
I've already completed my first craft! After we returned from giving all of our money to the craft store, I placed Aubrey in her high chair and got to hobbying! The first craft up was the DIY watercolor mugs.
Outcome: Moderately successful.
The instructions said to fill a plastic bowl with water and gently dump in whatever colors of nail polish you'd like. Then you're supposed to swirl around the colors with a toothpick until they're "dreamy looking." Technically, I did this correctly because last time I checked, nightmares are considered dreams. Maybe I shouldn't have purchased so many blacks and blues.
After that, you carefully dip your white mugs that cost $6 each at Michelle's in the water, creating beautiful designs. I bought eight so that I could give them as gifts to the family.
You should see Joy's Pinterest profile. She has more than thirty pages and half of them are crafts she invented. I know I can't outdo her, but at least I can prove I'm not completely useless.
Back to the crafting. Maybe it was the colors I chose, but my mugs look less "a starry night" and more "acute skin damage." They look like they're emo. I'm going to call them Mood Mugs Inspired by Xanax and hope they're not interpreted as a cry for help.
Other than that, totally nailed it.
Next I was going to try my hand at the DIY stain remover that's supposedly a staple in Emily Walker's laundry room, but Aubrey was getting fussy. I threw a handful of fruit puffs down on her high chair. She inhaled them. Like mother, like daughter. I decided we needed a break and picked her up for a little bit of play (and reality television) in the living room. Before leaving the kitchen, I looked back at the colossal mess I'd created. For a lot less money, time and effort, I could have purchased eight mugs that didn't look like they'd been in a fight. As hard as I tried, I just didn't get the point of crafting. Maybe I just had to give it some time.
After that, I put Aubrey down for her nap and felt the familiar fatigue and boredom of late afternoon setting in. I wondered what David was up to.
The phone rang three times before he answered it.
"Hi, Ashley." He sounded stressed.
"Hi, David, how's work?" I yawned, exhausted.
"It's busy. What's up?"
"Oh, nothing. Just wanted to say hi. I hit up the craft store this morning and—"
"Is that where you spent $300? I just saw it come out of the bank account."
Well wasn't he Mister On Top of the Finances.
"Yes. But David, I'm learning that it's very important for me to flex my creative muscles. Crafting is my outlet."
"Well, it's also a bit of a drain. Just don't go crazy. Things might get tight soon."
My ears perked up. "What? Why?"
"We were just underbid on two accounts I was counting on. It's a lot rougher out here than I thought."
I tried to think of some words of encouragement for my brave entrepreneur husband. "I know you can do this. You're smart."
"Yeah. Thanks, babe. I'm trying." He sighed softly. "I'd better let you go."
"Okay. What time are you coming home tonight?"
"After dinner. Sorry."
I felt a tug in the pit of my stomach.
"That's okay. Do what you have to do."
I hung up the phone and collapsed onto the couch. Even though I'd only intended to rest my eyes for a few minutes, I found myself waking up two hours later to Aubrey whining loudly.
I checked my phone. It was 4:45. Time for the second shift. Motherhood had a way of making one day feel like two. Or three.
I was just picking Aubrey up out of her bed when the doorbell rang.
"Did I order a package?" I thought to myself as I galloped downstairs with a sleepy Aubrey on my hip. David wasn't going to love that.
I could see the cheetah print through the glass window on the door and knew who it was before I even opened the door.
"Hi, Gloria!" I said, puzzled. "What are you, um...what are you doing here?"
Gloria walked past me and into the house. She was wearing a cheetah-print tracksuit. "I called David and found out he'll be working late again today. I knew you might be too shy to call me, so I figured I'd come over and help out."
I wasn't sure what to say but "can you leave?" didn't feel appropriate. It's not that I minded the company, it's just that I was looking forward to relaxing in various stages of undress for the rest of the afternoon and evening.
Gloria set her purse down on an end table and made her way into the kitchen. I followed her. It wasn't until I heard her gasp that I remembered the mug mess.
"What happened here?" she asked, her hand over her cheek as she stared at my crafty watercolor tornado.
I handed Aubrey to her. "Oh, I was just getting creative." I rushed over to the sink and started cleaning up.
I was happy I'd put the mugs in the oven to dry. I didn't want her to see her gift before I could present it to her.
"Well, you're certainly getting into it. Is this for the motherhood program you're in?"
David must have told her. I dumped a large plastic bowl of nail polish-colored water down the sink.
"Yes. It's going really well," I said convincingly.
Gloria sat at the kitchen table with Aubrey. "You young moms. Always up to one thing or another. Is this the book?"
Gloria picked up my copy of Motherhood Better from the kitchen table and, before I could stop her, opened it.
She put on her glasses and began reading. "Forget juice or soda, give your child kombucha." She looked up at me. "What's kombucha? Is that some kind of vaccine? Witchcraft?"
I tried to take the book away but she playfully held it away from me. "It's a type of fermented tea..." I said.
Gloria's eyes grew wide. "Rotten tea! What's wrong with milk these days?" She flipped a few pages and continued reading. "Enjoy my recipe for gluten-free beet muffins with a date-coconut oil glaze."
Gloria lowered the book. "Are you allergic to gluten?" I shook my head. "Is this Emily person allergic to gluten?" I shook my head. "Then why the hell are you avoiding it? When I was a kid we were afraid of the hydrogen bomb. Your generation is afraid of gluten." Gloria handed me the book.
"Yes, some of the ideas are a bit radical, but Emily's actually quite amazing."
"Amazing at what? Getting moms to buy books full of half-baked ideas? Oh, I'm sorry, half-baked, gluten-free ideas with a coconut-date glaze?"
Even I had to laugh. Gloria couldn't understand. She was from a different time.
"That reminds me." Gloria stood up and handed Aubrey to me. "I have groceries in the car."
"Groceries?" I asked, confused, following her to the front door.
"Yes, groceries."
Gloria slipped out the front door and returned carrying two bags full of food.
I followed her into the kitchen.
She began pulling out ingredients. A large bag of shredded cheese. Two huge bags of corn chips. Canned corn. Sour cream. Salsa.
"What's all this?" I asked, watching more items come out.
Gloria stopped and looked me dead in the eye. "I'm going to teach you how to cook—starting with my signature recipe, Frito Pie."
Frito Pie. I knew the name because David had asked me hundreds of times to make the dish that featured the popular gas station snack, but I'd refused.
"It's David's favorite and an easy weeknight recipe. Your Emily Walker friend probably wouldn't approve, but it's a big hit at parties," Gloria said, searching for a casserole dish in the cupboard.
"What's that smell?" she asked, as she closed in on the section under the sink where my ill-fated potato farm had once grown.
"A plumbing problem," I said, handing her a casserole dish from the top shelf.
Gloria preheated the oven to 350 and began mixing cheese, chips, and globs of cream cheese. Within fifteen minutes it was ready to go into the oven.
"That was fast," I had to admit.
"What's that smell?" Gloria asked again, sniffing the air.
"It's just the plumbing," I lied again, hoping she'd finally drop it.
"No, it's something else. Something's burning."
As soon as she said that, I began smelling it, too. It was coming from...oh, no, the oven. I'd forgotten that my mugs were drying on the brand-new plastic platter I'd purchased earlier.
I practically threw Aubrey at Gloria and opened the oven. A cloud of toxic black smoke billowed out. Gobs of hot melted plastic were melting from the top rack onto the oven floor. It was a disaster.
"What IS that?" Gloria asked, backing out of the room with Aubrey. "Did you try to bake?"
I opened the back door and all of the windows, but not before the smoke alarm went off.
"It's a craft. I crafted," I shrieked.
Gloria played in the living room with Aubrey while I fanned under the smoke detector. I then poured cold water all over what looked like a radioactive mess in the oven. Thirty minutes later I was still chipping burnt plastic out of the oven with a knife. The mugs themselves weren't too damaged. Once I pried the burnt plastic off, they looked almost post-modern. I decided not to give them as gifts but to definitely keep them. They were artistic and smelled of the struggle.
Gloria walked into the kitchen.
"I put the casserole in the fridge," I said. "I'll make it when I finally get this clean. Sometime next week, I anticipate."
Gloria laughed. "Don't worry. I ordered pizza. You know, you really shouldn't use your oven as a cabinet. Even if you don't use it often."
I cringed.
I heard the front door open.
"Anybody home?" called David cheerfully.
He rounded the corner into the kitchen, and upon seeing his face Aubrey screamed happily. He kissed her on the cheek before hugging his mom. Last, but not least, he gave me a quick peck.
"What a treat to come home to all three of my girls! What's that smell?"
I was really getting tired of people asking me that.
"There was a slight problem with the oven," Gloria answered. "Ashley's still learning how they work. But it's all better now. Are you hungry? I ordered pizza!"
I bit my lip.
David looked at me sympathetically. "Rough day, hon?"
"I'm okay. How was yours?" He looked so confident standing there holding Aubrey and she looked so perfect in his arms. I stared at them, feeling like the odd person out—the obvious screwup. I shook the thought out of my head.
"Work is work," he said, but I could tell he was worried. "Just let me know before you do any more expensive craft store runs. How did it turn out?"
"It turned out!" I answered, hoping the questions would end with that.
Later that night, after David had fallen asleep, I took my phone off the bedside table and peeked into the Motherhood Better Bootcamp portal.
There were already eight journal entries in the craft challenge section.
Josie from Iowa, mom of two
I'm setting up indoor plumbing in the playhouse I put together for my kiddos today. We're inviting local foster children to spend their afternoons here.
Tanya Gregory, mom of three
In the past 24 hours, I've knitted six sets of baby booties for newborns born in my hospital's maternity ward. The mommies were so grateful when I dropped them off this afternoon. I used organic, fair-trade yarn.
I quickly shut off my phone. Who were these women? How could I ever stand out when they were all mini Marthas? Tomorrow, I'd need to bring my A game to the crafting table.
Tuesday, February 5, 11:30 A.M.
I don't use any mainstream chemical cleaners in my home. From my tabletops to my bathroom floors, every surface in my domain is gently cleansed with essential oils and natural products that ensure that babies' bodies can grow healthily. Even the rags I use to clean come from old organic-cotton T-shirts. One can never be too careful.
—Emily Walker, Motherhood Better
Aubrey had just gone down for her nap and I was ready to take a crack at making my first DIY natural cleaner. I took the recipe right from Emily's blog. Apparently, she uses this stuff to clean every nook and cranny of her giant home and it serves double duty as a laundry stain remover. I figured this would be a pretty simple way to show her that I'm a huge fan and therefore deserve to win the $100,000.
Supplies:
* • Vinegar
* • Baking soda
* • Water
* • Lemon essential oil
* • Eucalyptus oil
* • Blue dishwashing soap
The only things I didn't have were the essential oils. I feel like their title was a little presumptuous, anyway. Essential oils. Shouldn't they let us be the judge of that? It's like if I called myself Best Ashley. Hello, everyone, my name is Best Ashley. Nice to meet you. What's so essential about these oils? And if they are essential, why is it in their title? It screamed of insecurity. We don't say "essential sunlight" or "essential water." We don't even say "essential oxygen."
Truth be told, the whole essential oils industry bothered me. They had mobsters in Lululemon peddling the stuff with a hard sell in every city. I had one mom at the park try to convince me lavender oil would get Aubrey to sleep through the night. Of course I immediately bought six bottles. Aubrey smelled like a Bath & Body Works but she didn't sleep through the night no matter how much I put in her bottle. (Joke.) But seriously, it didn't work. The same mom sold me a Himalayan sea salt lamp, three amethyst crystals to help with my non-existent milk production (something about past life trauma affecting my confidence) and eight bamboo-cloth diapers for the low, low price of $39.99 each.
Did I mention I did a brief cloth-diapering stint? It was all fun and games until I realized that they needed to be washed. Who has time for that? I guess I got sucked into visions of beautiful multicolored diapers line-drying in the sun. And when she told me that disposable diapers took a hundred years to biodegrade it was a no-brainer. I only lasted three days before I got behind on laundry and our house started to smell like a porta-potty. I decided to use disposable diapers and offset my carbon footprint by recycling all of my wine bottles.
I still feel bad about all of the cloth diapers I ended up buying, but it just wasn't for me. I could barely stay on top of the essential laundry (note the proper use of "essential") much less deal with a wet bag overflowing with sewage-soaked nappies. I was a little jealous of those moms who have it down. Those photos of chubby babies in cloth diapers running through flower fields, their amber teething necklaces blowing in the wind, are adorable.
It took me only three minutes to put together the DIY cleaner. After mixing the ingredients (minus the essential oils) I poured them into an empty spray bottle and affixed a cute little label I'd printed off of Emily's blog to the front. There. I was officially a natural earth mother!
When I was done, I plopped down on the couch with a bag of the remaining Fritos from Gloria's casserole and logged on to the Motherhood Better Bootcamp portal. The previous night I'd posted photos of my Emo Watercolor Mugs but hadn't had a chance to read the comments. I headed straight for my notifications.
Aubrey did such a great job! These will make wonderful keepsakes for grandma and grandpa!
Wow, your little one has talent! Great job!
Beautiful work! I'm a preschool teacher and might have my kids make these for the holidays! Hats off to your budding artist!
Um... I made those. But I played along. No need to let people know that I have the creative skills of a toddler.
I polished off the bag of Fritos but was still hungry. For something sweet. Something about naptime made me want to eat the whole house. I flipped through Motherhood Better for an easy but impressive recipe to pass the time.
Coconut-Flour Cherry Spelt Cookies... No. I didn't even know coconuts could make flour. Does it taste like piña coladas?
Banana Quinoa Loaf with Gingerroot Lemon Glaze... No. That sounds less like dessert and more like some weird foot cream.
Date, Macadamia Nut and Dandelion Energy Bites... Never. Energy bites? Desserts are supposed to make you comfortably sleepy, not ready for a run. I'm pretty sure running and dessert are sworn enemies.
I opened up my computer and pulled up Pinterest. There it was: No Bake Chocolate Cake Batter Truffles. And I had all of the ingredients. My stomach rumbled in anticipation.
I almost ran into the kitchen and started pulling out the ingredients I'd need.
I was all set. I scanned the recipe and felt my mouth watering. This recipe was easy. Even for me. All I had to do was mix a frightening amount of butter, chocolate chips, powdered sugar and vanilla together until it formed what I think my thighs are made out of. Then I formed half of it into balls to set in the fridge and ate the other half while watching daytime talk shows.
The next step was supposed to be to melt a brick of white chocolate and dip the truffles into it with toothpicks, but I opted out of that step. "No bake" meant "no cook" in my mind, and I wanted to stay true to the heart of the recipe.
The recipe made twelve truffles, not including the handful of dough I ate while watching 30-Minute Dinners with Robin Ray.
They were cooling in the fridge when the doorbell rang. Guess who? Gloria and her little poodle mix, Terry. It'd been a while since she brought him over so I didn't mind, although I wished she had called first. I'd have to ask David to say something. I love all animals, but you'll excuse me if I can't overlook the fact that Terry looks like a rodent. A drooling rodent who constantly yaps and barks.
I'd just gotten Aubrey to sleep, so the idea of that little rat dog making a racket was less than ideal.
"Do you mind leaving Terry outside, Gloria?"
"Would you leave Aubrey outside?"
I held myself back from saying, "If she were an animal, yes."
As soon as we were inside, I tried to get to the bottom of today's visit.
"So, what brings you over today?"
"Oh, nothing, I just wanted to see how my granddaughter was doing," she answered while looking around the house, probably searching for evidence that I'm somehow unfit to parent her precious grandchild.
She bent over and placed Terry on the floor. He immediately started banging into walls and yapping. Five seconds later I heard Aubrey crying in her crib over the downstairs monitor.
"Oh, good, she's awake."
Good? I wanted to strangle Gloria but she'd probably fill Aubrey's head with all kinds of lies about me when I was in jail. "Your mother didn't know a sieve from a strainer!" Okay, that one is true.
I went upstairs to get Aubrey and the next thing I knew, Gloria was screaming.
I flew down with Aubrey in my arms to see Gloria sitting on the kitchen floor, tears running down her cheeks, with a suspiciously quiet Terry in her lap.
"What is it? What's happening?!"I asked, shaking.
"Ch-ch-ch-chocolate," she sputtered, and then I saw the remnants of one of my truffles and several chocolate chips beside Terry.
Oh, no. I must have dropped one.
Several hours and a visit to the emergency veterinarian later, I'm happy to report that Terry is fine. Gloria caught him before he had a chance to eat all my chocolate chips. David spoke to his mom before bed. She wants me to doggy-proof the house before she comes over. Well, that would require a phone call, wouldn't it?
I pretended not to hear her yell, "I didn't even know she baked!" through the receiver.
Wednesday, February 6, 3 P.M.
My all-time favorite craft was my lake house in upstate Washington. What started off as six acres of lush wildflowers is now a gorgeous cabin that my family escapes to whenever we can. My husband, a world-renowned architect, built the home from the ground up. I planned the décor of each room by myself.
—Emily Walker, Motherhood Better
Today was glass-etching day. What's glass etching? It's when someone who doesn't know what a Target is uses acid to burn designs into glassware. I don't know why I tried to do this. Okay, that's a lie. I do know why. I had this vision of burning "Keller" in some swirly but respectable font onto all of my casserole dishes. Then, when I took dishes to family events and all of the potlucks I'd surely receive invitations to once I made friends, I could show them off.
"Who made your custom casserole dish, Ashley?"
"Oh, I did! I get invited to so many of these functions that I thought it would be a simple way to keep tabs on my dishes."
"Genius! I never knew you were so crafty! I mean, I knew you were a fantastic homemaker and amazing mother, but creative and skilled, as well? Can we be best friends? I'd also like to formally apply to be your intern."
It sounded simple. "Keller" going across the long side of the casserole dish with a few accent hearts. Except it wasn't.
Supplies:
* • Glass dish.
* • Etching cream.
* • Stencils.
* • Brushes.
* • Tape.
In my defense, I watched three YouTube videos and read no fewer than five blog posts by annoyingly bubbly moms before starting.
Can I share something? I have a theory that crafters have conspired together to make crafting complicated. There are secrets and tips that they're not sharing because deep down, they want to see us normals fail. This shouldn't have been as hard as it was. I'm a smart person.
1. Glass Etching Mistake #1: Not wearing gloves. Don't be fooled by the word "cream" in etching cream. This isn't Lady Loves Her Face lotion; it's acid. I knew this going into the craft, but figured since it was sold at Michelle's that it couldn't be that toxic. Wrong! I'm pretty sure I burned two of my fingerprints off. So, if you're an international spy and looking for a way to burgle the royal gems from the Queen of England or whatever, get yourself a glass-etching kit and take care of your fingerprints the old-fashioned way!
2. Glass Etching Mistake #2: Thinking that I was detail-oriented enough to pull this off. I ruined three, that's right, THREE casserole dishes in the following ways:
* \- Getting distracted and leaving the etching-acid burn cream on for too long. Aubrey woke up from her morning nap earlier than she should have so I ran upstairs to settle her. Fast forward to me lying on her bedroom floor with one arm in her crib and, yes, I fell asleep. When I woke up forty minutes later, the dish broke in half when I tried to wash the cream off. I like to think it was symbolic of my broken craft dreams.
* \- Focus. Wait—what? Focus. Casserole dish two out of three was ruined when I spelled my own last name wrong using the stencils. I guess I could petition David to change our last name from Keller to Keler. Why not go through the court system to make our name reflect this casserole dish that I put an hour of my life and $200 in craft supplies into? Makes sense to me.
* \- Getting too excited. Casserole dish three out of three was broken due to sheer enthusiasm. I lined up the stencils just right. I left the etching cream on for just enough time. But you know what I didn't do? I didn't factor in my limited grip due to the burned-off pads of two of my fingers. During my celebration dance I dropped the dish on the kitchen floor.
The shattering casserole dish startled Aubrey, who instantly began crying. I picked her up.
"It's okay, honey. That's just the sound of Mommy being a hot mess." It was time for her afternoon nap, anyway.
I changed her diaper and, after rocking her in the glider for almost half an hour, she finally settled down and fell asleep. As I lowered her into her crib, my arms burning from fatigue, I took in her beautiful little face. I fought a cascade of tears. She really was just so gorgeous.
Does every mom get lost in their child's face like this? I wondered. I studied her eyelashes, the bow of her lips and her soft cheeks. She really did deserve the best of everything. I had to try to be the mom she needed.
I crept downstairs and cleaned up the broken glass, sweeping every corner of my destroyed kitchen. Afterward, I sat at the kitchen table with my computer and my third cup of coffee.
Scrolling through Pinterest, I stumbled across a photo of a little girl who couldn't have been more than Aubrey's age sitting in front of a window. She was wearing the most adorable little dress with ribbons on the shoulders. The sunshine poured through the window behind her, creating little flecks of light that caught in her curly hair, giving the impression of a crown. Underneath her, the text read: No-Sew Pillowcase Dress Tutorial: 30 Minutes and EASY!
That's it! I felt hot determination creep up my back. I remember Emily sharing on a blog post a few months ago how she makes pajamas for all five of her children. I'd probably learn Mandarin Chinese before I could learn to operate a sewing machine, but this dress was right up my alley.
I ran to the linen closet and found the perfect pillowcase. It was part of a bedroom set I'd purchased months ago for the guest room we'd surely have one day. The off-white satin pillowcase was decorated with little purple, pink and yellow flowers. It would make the perfect dress. I found a roll of ribbon in the garage in the Christmas supplies box.
I sat on the living room floor, hunched over the pillowcase, with the ribbon, scissors, and a needle and thread.
All I had to do was lay the pillowcase flat, cut out the head and armholes and hem them (my stiches were a little shaky but you could barely make them out and they were more rustic that way). Then I threaded the ribbon through the armhole hem. The ribbons served as the straps, ensuring a custom fit every time.
This dress will really grow with her, I thought, as I held it up, impressed with my work. It was a bit big...maybe I should have used a smaller pillowcase, but it was so pretty. Who knew, I might just be the new face of baby clothing design. Okay, maybe that's a bit of a stretch, but I'd just successfully made a piece of clothing for Aubrey and I felt great about it.
I could barely wait until Aubrey woke up, and when she finally did, we did a small (big) photo shoot. I must have uploaded twelve photos of her in the dress from all angles to Facebook. Then we were off to the park. I had to show her dress off to the world!
5 P.M.
I hate crafts. I was walking on air over the amazing dress I'd handcrafted for Aubrey for about ten minutes. That's when, with Aubrey sitting innocently on my lap—maybe I was showing her off a little—a mom in shorts and a pink tank top pushed her jogging stroller next to me and sat down. I thought she was going to ask me where I got Aubrey's fabulous dress, and had already prepared the look of surprise and gesture I'd make (my hand to my neck) as I said, "Oh, this is just something I made this morning!" But the words out of her mouth were, "I want to bless you today."
At first I was confused. Bless me?
"Bless me?"
She put a hand on my hand and leaned in. "Yes, honey. We all go through hard times. You know, my youngest daughter just turned two and I have a bag of clothes at home that I think will fit your little one just right until you get back on your feet."
I was speechless. I literally could not speak. I tried, but all that escaped my mouth was a weird honking cough. She kept talking.
"No, no, it's fine. You just give me a call and tell me where to drop it off and I'll come to you. I'd love to bring you and your daughter dinner, as well."
She then put a piece of folded paper with her number on it in my hand and walked away, to spare me some dignity, perhaps.
Apparently, my pillowcase dress is so terrible people think I'm struggling to clothe my child. I wonder if this happed to Maria in The Sound of Music when she made the children playclothes out of the curtains.
I could barely move for ten minutes I was so embarrassed. Aubrey did not look that bad. I mean, okay maybe the stitching was a little crooked, but that gave the dress character. I suppose I did make the armholes a little big. And the ribbon was slightly frayed.
And then I finally came to my senses. Who was I kidding? She looked like a cross between The Real Housewives of New Jersey and Oliver Twist.
Then I remembered. FACEBOOK. I had shared photos.
I pulled out my phone and saw that I had twenty-five notifications. Twenty. Five.
The comments.
Joy: Ashley, is this a Halloween costume? Baby calf? I don't get it.
Mom: Very cute...this is an indoor outfit I'm assuming?
David: LOVE IT! (He types in all caps when he's lying.)
Amelia Davis (high school frenemy): Wow.
I didn't read the rest. I just deleted the photos and hoped that I'd somehow erased them from everyone's minds at the same time.
I've learned my lesson. Level II crafts are not for me. I need to stay in the shallow end of this pool. I aimed too high. Wish I had more of those truffles.
Dear Pinterest,
When we first started dating, you lured me in with Skittles-flavored vodka and Oreo-filled chocolate chip cookies. You wooed me with cheesy casseroles adjacent to motivational fitness sayings. I loved your inventiveness: Who knew cookies needed a sugary butter dip?
You did. You knew, Pinterest. You inspired me, not to make stuff, but to think about one day possibly making stuff if I have time. You took the cake batter, rainbow and bacon trends to levels nobody thought were possible. You made me hungry. The nights I spent pinning and eating nachos were some of the best nights of my life.
Pinterest, we can't see each other anymore. You see, it's recently come to my attention that some people aren't just pinning, they are making. This makes me want to make, too. Unfortunately, I'm not good at making, and deep down I like buying way more. Do you see where I'm going with this? I'm starting to feel bad, Pinterest. I don't enjoy you the way I once did.
We need to take a break. I'm going to miss your crazy ideas (rolls made with 7Up? Shut your mouth). This isn't going to be easy. You've been responsible for nearly every 2 a.m. grilled cheese binge I've had for the past couple of years, and for that I'll be eternally grateful.
Stay cool, Pinterest.
PS. You hurt me.
PPS. I'm also poor now.
Xo
Me
10 P.M.
On the plus side, David made it back from work before dinner tonight. He came home with a bouquet of red roses for me. If I hadn't been so exhausted I would have made it worth his while.
Watching him walk through the door with flowers was like watching a unicorn jump over a leprechaun—the stuff of fantasies.
I made the Frito Casserole and he devoured two-thirds of it himself. There weren't even leftovers for him to take to work. I'm ashamed to admit that I felt jealous. He'd never eaten anything I'd made like that.
Then, of course, he tried to get frisky as soon as Aubrey fell asleep. I'm no prude, but it's hard to jump into bed with someone you've barely spoken a paragraph to over the past few weeks. He's just been so busy... I mean, okay, he bought some roses before he came home. But I need actual romance, I need ulterior motive–free seduction. I tried explaining to him that it was impossible for me to get in the mood after two seconds of kissing and while he said, "It's fine," before rolling over and going to sleep, I felt bad. Maybe I should have tried harder.
Note to self: Craft yourself a libido.
Motherhood Better Bootcamp Message Board Entry
Hello ladies and Emily: I took a good stab at crafting this week and I definitely feel different. My family and friends couldn't believe that I was behind some of my creations! The mugs I made were en fuego. The pillowcase dress I sewed for my daughter turned so many heads. And the truffles I made were to die for. Some of you have asked for the recipe and I'll get it to you ASAP (do any of you have pets?). I hope everyone is doing well! Can't wait for our call tomorrow. Xo, Ashley
Thursday, February 7, 9 A.M.
Working from home is the best of both worlds: you get to spend time with your precious children, flex your creative muscles and bring in an income. My first year blogging at Motherhood Better by Emily Walker, I made six figures and that was while my babies slept.
—Emily Walker, Motherhood Better
Aubrey woke up at 4 a.m. this morning which gave me time to think about what's missing in my life: purpose. Of course Aubrey and David will always be my #1, but I need something outside of them to fulfill me. I've decided that since crafts aren't for me, I'm going to get a work-at-home job. Emily started her empire when she was a stay-at-home mom to three kids, and if she can do it, why can't I? The only difference between us is that she's organized, driven, resourceful and...never mind.
It only took two hours searching online, but I found something. It was like magic and just goes to show you that when you want something enough, it will happen. I replied to an ad on an online job board with my résumé and they called me within half an hour. Something about my work experience must have really impressed them. So this is what the Law of Attraction is all about!
My official job title is Customer Satisfaction Specialist for a company called Dreamstar Direct. They didn't have a website, but when I worked for Weber & Associates we held focus groups to understand consumer trends all the time. I figured this was the same thing—just over the phone. It's a step down from what I used to do, but I have to start somewhere. The plan is to dazzle them with my skills and work my way up. Six months from now, who knows, maybe I'll be a team leader with a squad of super work-at-home moms under me. We'll have conference calls, I'll convert the garage into my office, and all with Aubrey steps away from me. I'll have it all.
I may have fibbed a little during the interview. When the raspy-voiced regional manager, Wanda, asked me if I'd ever done work like this before, I said yes. I mean, I have talked on the phone. What could be so hard about doing it from the comfort of my own home? She asked me when I wanted to start and I said "yesterday" to which she replied that I must really need the money.
I would have explained that while the money is appreciated, it's really just about feeling useful in a capacity that doesn't have to do with wiping dried yogurt off a high chair, but that seemed unprofessional.
The stars must have been aligned in my favor, because my very first shift starts tomorrow at noon! It's a short one, just four hours. Wanda didn't give me much instruction other than that the customers would call me with their needs. These marketing types are so secretive. She was probably worried about my feeding info to a competitor. I've made it my mission to earn their trust.
I found a little notebook in the hall closet for writing down customer feedback. I'll keep impeccable notes and ask open-ended questions like, "How do Dreamstar Direct products make you feel?" and "Do you think Dreamstar Direct values you as a human being?" My shift would fit in perfectly with Aubrey's schedule. I'd feed her an early lunch, get her down for her nap by noon, and go back and forth between playing with her and taking calls for the last hour or so of my shift.
I'm making $20 an hour. If I work five days a week, that's $1,600 a month.
I can't wait to tell David.
It just goes to show you that with positive thinking and a proactive mindset, you really can do anything you want. I'm officially a work-at-home mom! It sounds like the best of both worlds and I'm so excited.
Friday, February 8, 11 A.M.
Working from home is simple. If you don't have a spare room for an office, create a space for yourself at the kitchen table or in the corner of your children's playroom.
—Emily Walker, Motherhood Better
Thirty minutes before my first call, I was still working through the paperwork Wanda sent me the night before. The plan was to wake up before Aubrey and learn all about the company, but she woke up no less than four times last night and I was beat. So there we were, at the kitchen table, me with my open computer on one side and a screaming, tired baby waiting for her next spoonful of mashed rigatoni on the other. I could feel the stress rising.
I pushed the spoon into Aubrey's mouth, and she hungrily chewed while banging her hands on her high chair.
I turned my attention toward my worksheet. Wanda said filling out the New Hire questionnaire would help me learn what made Dreamstar Direct so special.
Some of the questions were a little odd.
"What's your favorite fantasy?"
If I were being completely honest, I would have written down "Free nanny and a bedroom with a built-in hot tub," but instead I said "Being part of a fantastic team and making the world a better place." It was a little Miss Universe, but I supposed they'd heard worse.
"What's your secret passion?"
Secret passion? I supposed the truthful answer would be "Making s'mores on the stove at midnight while my husband and daughter sleep." I wrote "Success."
An email notification popped up on my screen. It was Wanda.
To: Ashley Keller
Ready? We've routed your phone with your own 900 number. First call is in 20 minutes. I'll be listening in. Remember to write down customer requests so we can log the changes in the market. Don't forget to use a fake name.
Log customer requests. Check. Fake name! I'd completely forgotten. Wanda said that in customer service, pseudonyms are often used. Probably so that if a client starts yelling, they can't actually insult you accurately.
I didn't remember her telling me that she'd be listening in. I turned to Aubrey who wasn't even halfway through her lunch. If I cut her off now, she'd turn into an angry baboon baby and I'd be fired on the spot.
I knew what I had to do. I picked up my cell phone and punched in the number.
"Joy? I need you. Right now."
Seven minutes later, Joy rang my doorbell. I met her at the door with Aubrey.
"Take her, now. My call is in five minutes!"
Joy juggled Aubrey and Ella, who was dressed in a pale pink crocheted ensemble with white tights and a matching white beret. On her feet were delicate cream-colored plush booties. I kissed my niece on the head.
Joy sputtered, "Ashley! Okay, okay! Since when do you even have a job? I can't do this every day, you know. I'm busy." Joy headed toward the kitchen to finish feeding Aubrey.
"Busy doing what? Dressing Ella in perfect outfits?" I would have said if I hadn't needed my sister so much.
"Thank you, thank you, thank you!" I said instead, leaping upstairs with my phone and notebook in hand.
When I was finally sitting down, cross-legged on my bedspread, my home phone, notebook and pencil in front of me, I took a deep breath. I'd done it. Joy was probably in my kitchen judging the number of dirty dishes in the sink, but I'd done it.
I waited.
And waited.
And waited.
I could hear the dishwasher whirl downstairs. Typical Joy.
The phone rang. I answered it immediately.
"Dreamstar Direct, how can I help you?"
A hoarse male voice answered. "You're supposed to tell me your name."
I flushed. He was right. And Wanda was on the line.
"Thank you for calling Dreamstar Direct. My name is Tiffany."
"Hi, Tiffany. I'm Greg. What are you wearing?"
My mind went blank. What am I wearing? Is Dreamstar Direct some kind of fashion hotline?
I looked down at my red and gray checked pajama pants and oversized black T-shirt.
"Sir, I'm wearing a designer black dress and Gucci sling-backs."
"Take it all off," said Greg, his voice thickening.
"EXCUSE ME?" I yelled into the receiver. I heard a click and Wanda's gravelly voice interrupted.
"Greg, we're going to redirect this call to Cinnamon, your regular girl."
Another click.
Wanda came back on the line.
"Ashley. You're fired."
The line went dead. I sat with the phone to my ear in disbelief. What just happened?
Standing up, I made my way downstairs and into the kitchen in a fog.
Joy was standing at the counter chopping pears and dropping the pieces into a mini blender with FirstFoods written across the side. Neat little jars filled with pale green puree sat on the counter beside her. She was wearing a sleeping Aubrey in the baby wrap. She must have found it balled up in my laundry basket in the living room.
Ella sat in Aubrey's bouncy seat, jumping up and down. In her formal day outfit, she looked like some kind of little duchess.
Joy takes care of two kids better than I can take care of one.
"Already done, Ashley? This wrap is divine. Do you ever use it?" Joy gushed without looking up.
I sat down at the kitchen table behind her and put my face in my hands as hot tears slid down my cheeks. Within moments, they turned into sobs.
Joy rushed over and put her hand on my shoulder. "Ash, what happened? What's going on?"
I sniffled and raised my head. "I got fired."
"Fired? On your first day? Did you sign a contract? They can't just fire you without notice!" She pulled out her cell phone. "I'm calling Grover. He plays racquetball with an employment lawyer. What's the name of the company?"
I wiped my face with my arm. "Dreamstar Direct... Joy, don't, it's f—"
Joy's face went red and she plopped down in the seat next to me. "Did you say Dreamstar Direct?"
My face flushed with embarrassment.
"Ashley. Why were you working for a phone-sex hotline?" she said and I felt like a fifteen-year-old being scolded by her mother after being caught smoking.
I blew my nose into a paper towel. Ella laughed at the sound. I'm glad someone was finding this funny.
"Because I didn't know it was a phone-sex hotline! I thought it was a customer service agency!"
Joy looked at me incredulously. "How could you not know? Their ads run nonstop all night! When I'm up nursing Ella, it's the only commercial on!"
I blew my nose again. "Yeah, if only I were breastfeeding, I wouldn't have accidentally become a phone-sex operator," I said sarcastically. I knew I sounded immature, but did she have to mention breastfeeding in every conversation?
Joy sat up straight. "That's not what I said."
I stood up. "I know. Sorry. Well, I'll take it from here, I guess. Thanks for coming over."
Normally I wouldn't have rushed Joy out so quickly, especially not before bumming a jar or two of organic baby food off her, but I needed to wallow alone.
Before heading out the door with Ella, she touched my arm. "Don't let it get you down, Ashley."
I smiled and kissed my niece again before closing the door.
8 P.M.
I personally have never needed a nanny, but when you need help, don't be ashamed to get it.
—Emily Walker, Motherhood Better
I had a realization this evening as I was standing in the kitchen trying to do dishes while holding a screaming Aubrey because David was working late for the 300th week in a row: Mary Poppins isn't a child's fantasy, she's a mother's. Isn't it your dream to have some maternal figure float in out of nowhere, no background check needed, and take your kids away for an indefinite amount of time? All of this and your children come back better people with no money exchanged.
I've decided to hire a part-time babysitter so that I can...wait for it...start freelancing again! I miss the marketing world so much. The whole phone sex debacle was a wake-up call (no pun intended). I need to do something in the field I love. I know I can do this. Maybe David and I will end up doing business together! Just the thought of us brainstorming client product launches over hazelnut-flavored coffees got me excited. Finally, I'd be in my element again!
We don't really have extra money, but if I cut back on spending we should be able to swing five hours a week. Now I just have to find someone with the right qualifications.
I know I want someone younger than me. Not too much younger. I want them to have common sense, experience and a good head on their shoulders.
No one under twenty-six. I know someone in their early twenties can be responsible, but I want the person to have seen enough terrible things in life that they know to be alert with a baby around. In your early twenties you still think life is all good and that nothing terrible can happen. By twenty-six a person starts to get a sense that bad things don't just happen to other people, they happen to babysitters who leave babies in high chairs unattended. By one's mid-twenties, some of the glitter has worn off of life, leaving behind a matte finish.
Also, I don't want some hot young thing running around my house. Not while my stomach looks like some kind of front butt hanging out of my tank top. My fragile ego can't handle it.
Yes, there are lots of hot women in their late twenties, but they're less willing to lose their jobs for making a pass at their bosses' husbands, I think.
And the butt-stomach thing.
In summary, I need someone who is capable and not too hot.
David's working through the weekend so it's just me and Aubrey. I'm never going to get any work done if I can't find someone to watch her.
Saturday, February 9, 9 A.M.
Don't feel bad about needing domestic help. Not every woman can do it all, and until you can, the services of others bridge the gap.
—Emily Walker, Motherhood Better
What's so hard about finding a babysitter? When I was a kid the babysitter was the girl on the street old enough to stay home by herself but too young to date. And since when do babysitters make $12-plus per hour? When I was seventeen I made $2 and all the snacks I could eat.
So far I've email interviewed:
* \- a Russian au pair who was very interested in why Aubrey wasn't sleeping through the night and suggested I incorporate more ground beef into her diet
* \- a twenty-two-year-old very lovely young woman with a degree in early childhood education who suggested that I not let Aubrey have any screen time until she's twelve and even then only twenty minutes a day and preferably Claymation
* \- a seventy(?)-year-old grandmother who asked if I offered a retirement package
After this, I'm considering hiring a dog to watch Aubrey, like in Peter Pan. I'm sure Nana wouldn't charge more than $10 an hour and the occasional Milk Bone. Maybe she'd work for stomach rubs.
Wish me luck.
10 P.M.
I found her. She floated in from a nanny website. Joy couldn't have been happier when I told her I was getting a babysitter. She was proud of me for getting "the help I needed." I made sure to tell her it's only part-time.
"Oh, it starts like that," was her response.
What does that mean? A month from now I'll be parenting Aubrey via Skype? I don't think so. And I can only afford three weeks' worth of babysitting without having any money coming in.
Chelsea, my twenty-eight-year-old angel sitter nanny starts tomorrow at 9 a.m. I interviewed her, will check her references tonight, and Aubrey seemed to take nicely to her. I can't wait!
Sunday, February 10, 9:20 A.M.
People ask me all the time how I run a successful company with five children. The answer is: naps! My littles are all on a regular sleep schedule, and while they doze, I take conference calls, fulfill orders for the Motherhood Better line of maternity wear and sign contracts. Where there's a will, there's a way.
—Emily Walker, Motherhood Better
I was sitting in the bushes at the park.
Okay, let me explain.
Chelsea arrived at 9 a.m. on the dot, and Aubrey was a bit fussy so I suggested she take her on a walk. Six seconds after they left I realized that while I interviewed this woman and checked her references, she could be anyone. What if she's an international child smuggler? What if those references were just her accomplices?
Bottom line: I realized I don't really know her and had just sent my child off with a potential criminal. I don't know if it's all of the episodes of Crime Files and Gone Without a Trace, but I pictured Aubrey's car seat in a van somewhere, off to her new family—or worse.
I threw a black sweatshirt over my black sweats and put a black beanie on my head so that I could follow them without being noticed. In hindsight, dressing up like a bank robber in broad daylight may not have been the smartest move but nobody could see me. This bush was thick. And there were three different toddler shoes behind it. So this is where they lose them.
Okay, back to Chelsea, aka Potential Baby Thief.
She was sitting on the bench near the swings with Aubrey in the stroller next to her. No sign of a van anywhere. She was looking around suspiciously—wait, that might just have been boredom. Wasn't she going to play with Aubrey or something? I know a baby can't do much, but she could at least sing to her. I mean, she was on the clock.
OMG.
No. Freaking. Way.
She was pulling out her phone. SHE WAS CHECKING HER PHONE. Instead of engaging my infant in age-appropriate play she was on her phone and...taking a park selfie? Was she serious? What was the caption? "Just neglecting my charge on this beautiful day at the park! Isn't being a half-assed babysitter awesome! Look at my youthful skin and hair that isn't falling out by the handful!"
Her phone rang. She answered it. This was insane. Aubrey was sitting in her stroller rotting away and Chelsea was laughing on the phone? What if someone grabbed Aubrey while she was distracted? Sure, she had one hand on the stroller, but this wasn't what she was getting paid to do. I was paying her to participate in the development of my daughter, not throw her social life in my face.
I was just about to jump out from behind this bush...
8 P.M.
The craziest thing happened today.
No, not the part where I was tailing my nanny and child through the park.
No, not the part where I was staking them out.
I'm talking about the part where I almost got arrested by a police officer for behaving suspiciously around small children.
Yeah, THAT PART.
Just as I was about to bust Chelsea for neglecting my child, a six-foot-tall officer yelled, "HEY, YOU! WHAT ARE YOU DOING OVER THERE IN THAT BUSH?" causing the whole park, Chelsea included, to turn their heads while I tried unsuccessfully to shush him. Hasn't he ever been on a stakeout? First rule: inside voices.
Apparently police officers don't like to be shushed because he pulled me up by my arm. I know. Crazy. Aubrey immediately recognized me and started crying. I was horrified, but a little touched that she recognized Mommy in her all-black cat-burglar ensemble.
Chelsea rushed over. She looked a bit confused, then angry when I explained to the officer that I was supervising my babysitter from afar. I thought it was completely inappropriate for the officer to agree with Chelsea that "spying" was a better word.
Chelsea quit and called me a crazy b-word in front of Aubrey, which pretty much proves she's not cut out for this job. The police officer laughed at me.
I now have no babysitter and no dignity.
I give up. I'd try another nanny, but I'm obviously not ready to let anyone else watch Aubrey yet. It doesn't make any sense. All I could think about for the past few months was getting a break from her, but the second I did, the moment freedom peeked over the horizon, I sabotaged it. Is this what motherhood is going to be like? Spending all day dreaming about getting a break and then, when it comes, wanting nothing more than to be with Aubrey?
I felt dread wash over me. I'd never be content again, would I? I love Aubrey more than I've ever loved anything or anyone, but when I'm with her, I feel smothered. And when I'm not with her, I feel incomplete, like a piece of me is missing.
How do other moms do it? Maybe it'll be easier once she gets older.
Maybe I need to stop resisting motherhood and just dive in headfirst and learn to "live in the beauty of the moment" like Emily says. I'm going to turn around and Aubrey will be eighteen, moving out, and I'll have spent her entire childhood wishing I was somewhere else.
The thought of Aubrey living somewhere else made my chest seize up. So this is motherhood. You pour your entire life into someone and then they just leave? It's insane. I'm insane. I keep watching those crime dramas and eating my weight in peanut butter. Since becoming a mom, I simultaneously have no stomach for these shows, but feel as if I need to watch every episode to know exactly how terrible the world is that I brought my child into.
Confession: Last night Aubrey barely slept and I cursed motherhood at 1 a.m. I cursed motherhood as in, "I hate this so much."
Now, watching these detectives break the news of a son's death to his elderly father, I felt so guilty. I love you, Aubrey. I'll try to protect you in every way that I can. I want you to have a happy, full life. I get tired sometimes, but I love you.
What kind of mother curses motherhood?
I'm awful.
PS. I think the elderly father is the perp.
Monday, February 11, 11 A.M.
Your lover should be your #1 priority. Every Friday night, my husband and I go out on a date to keep our fires burning brightly. We also go on a no-kids vacation three times a year and, after five kids, we're closer than ever!
—Emily Walker, Motherhood Better
Today's call was even better than the last one. When Emily popped up on the screen everyone gasped—she was wearing a sparkly gold-sequined gown and her hair was swept into a fancy updo. Her makeup was done with dramatic smoky eyes and deep red matte rouge on her lips. She looked straight off a Hollywood red carpet.
"Hi, everyone! I'm coming to you live from my photo shoot with SHE magazine! They've chosen me as one of the twenty women in their Sexy Entrepreneur Women edition!" she said, her sparkly white teeth gleaming through the monitor.
Looking down at the faded pink Gap sweatshirt that I was wearing, I felt a dull twinge of embarrassment. I'd fed Aubrey raspberry yogurt that morning and half of it was smashed into my chest. I did my best to wipe it off before the call, but it just looked like a giant bird had made me its poop target. I leaned in to conceal my dishrag of an outfit. That, coupled with my hair being days from its last washing, made me look especially homely next to dazzling Emily. I tried to focus on her words and not the fact that I looked like I'd been put away wet.
"If you follow me on Instagram, you already know that my incredible husband, Thomas, is with me on the set, taking care of the children while I work. He and I are not only a team, but we're best friends and—" she leaned into her webcam and lowered her voice "—passionate lovers."
I felt my face get hot. Passionate lovers? With five kids? David and I have one baby and our sex life is in the crapper.
"It's so important to keep the fire in your marriage burning with hot, sizzling embers of desire. Having children is no excuse for letting the spark that brought you together smoke and fizzle out."
Yeah, I'm pretty sure that, in my marriage, the "fire" is actually a pile of damp, charred sticks.
Emily went on. "I want all of you to read through Chapter Four, entitled 'Keeping Your Marriage Red Hot,' and then put into action some of my tips. Does anyone have any specific goals for their marriage?"
A shy-looking mom with short blond hair raised her hand.
"Yes, Lillian?" asked Emily.
Lillian look petrified to be the center of attention, "Hello everyone. I'm mom to three-year-old twin girls. I've been married to my husband for ten years. I'm just trying to figure out how to jump-start our sex life. He works so much and I'm exhausted after a full day staying home with the girls. They run me ragged."
Emily nodded sympathetically. "I totally get it. What's your main objective?"
"Ideally, we'd have more...you know...relations. Right now our encounters are dwindling. On a good week we only have sex three or four times."
"WHAT?" I screamed aloud unintentionally. Three or four times a week? David would be in heaven!
Emily held up a hand. "Now remember, this is a safe space for Lillian. Lillian, I totally understand. My husband and I used to have sex multiple times a day and we're down to just once per day. Read the chapter and let me know if it helps."
I couldn't believe what I was hearing. Compared to Emily and Lillian, I was living on a passion iceberg.
Something caught Emily's attention off camera and she made a thumbs-up sign before continuing. "Okay, they're ready for me so I have to go, but this week is the Marriage Challenge. Find that spark you and your partner in childrearing used to have and let it burn!"
All of those "burning" and "fire" metaphors were simultaneously making me think of yeast infections and BBQ. I was grossed out, hungry and completely overwhelmed at the task of turning my laundry-strewn bedroom into a lover's den. Sure, I wanted my marriage to have fireworks, but after spending an entire day wiping down counters and shuffling around braless, it was easier said than done. Not to mention, I was always tired. Where was I supposed to find the energy to stoke the embers of this "love furnace"?
I stood up and studied myself in the full-length mirror behind my bedroom door, trying desperately to find any signs of a vixen lurking beneath, but all I saw were dark circles, a dingy outfit and a mom who would give her left butt cheek for an afternoon nap.
"I'm more of a spaghetti squash than a seductress," I said to no one. Aubrey laughed and jumped up and down excitedly in her zoo animal-themed exersaucer, causing it to sing a catchy but annoying song about bears.
I picked her up and grabbed my keys off the counter.
I needed coffee.
11 P.M.
It is always so hard to fall asleep after Aubrey screams me awake. Somehow she always knows when I've just entered the most delicious REM sleep. Thanks, honey.
I didn't want to wake David with my tossing and turning, so I sat on the couch in the living room with my laptop and a cup of tea. While I'd rather be sleeping, it was nice to sit down for a minute knowing the phone wouldn't ring, a meal didn't have to be made and Aubrey (hopefully) wouldn't need me for a few hours. I looked around the darkened room and sank deeper into the buttery leather.
Yes, I thought. This is the life. Motherhood may be the hardest thing I've ever done, but it sure makes a few moments of silence feel like the most luxurious of vacations.
Then the thought hit me: the Marriage Challenge. Maybe I should check into the portal and see how the other moms are doing.
I opened my computer and after my eyes adjusted to the glare, clicked my way into the website.
What on earth...?
We hadn't had this challenge for twenty-four hours and some of the moms had already posted updates.
Tonight after our son went to bed I surprised my husband with chocolate-dipped strawberries that I'd made that afternoon during naptime. He was absolutely delighted and, after the evening we just had, so am I.—Samantha Davidson, mom of 2-year-old Henry
Girls! My hubby and I are about to hit the town and have a date night! I picked up a strappy red number and he made reservations at my favorite Italian restaurant. We're definitely making this a weekly thing. Can't wait!—Kimmie Reardon, mom of four
Strappy red number? The closest thing to a strappy red number I'd worn since Aubrey was born was when I wore a pair of black tennis shoes with red laces.
I thought these women were supposed to be underachievers, like me.
"These moms are frauds!" I whispered angrily, shutting my laptop with more force than necessary.
I needed to think of something and fast. Tapping out on the second challenge was not an option, especially when this program meant everything to my whole family.
I opened my computer again and began to type.
Hi ladies! I'm thrilled to see all of you doing so well. #SexyMamas. I had a busy day of yogurt-making, but I can't wait to start this challenge tomorrow! Get ready, hubby!—Ashley Keller, mom of one
So maybe I stretched the truth a little on the whole "yogurt-making" part, but it's not all false. The yogurt cultures on my sweatshirt must have multiplied throughout the day due to my body heat, so technically I did make yogurt.
I looked at the clock—11:25. Time for bed. Tomorrow was a new day and I was determined to make it a sexy one.
Tuesday, February 12, 8 A.M.
My husband and I met at a fundraiser supporting the preservation of antique teacups. It was early in my modeling career and I'd been escorted to the event by a rising designer watch model, but as soon as our eyes met, I knew I wanted him to be the father of my children. His face was so symmetrical. I wanted that for my babies.
—Emily Walker, Motherhood Better
I love my husband, but sometimes I want to scream in his face. These days all it takes is one of his insensitive remarks, and I start picturing my life as a single mother, the two of us passing Aubrey between us at mutually agreed upon locations like a highway truck stop. Naturally, I'd be thin by then, due to all of the stress.
Let me tell you what happened.
Aubrey has been waking up at 2 a.m. on the dot for the past few days. Teething, growth spurt, I don't know. But last night I woke up my doting husband and asked him to go get her. Just this once. For the first time EVER in the eight months since OUR baby was born. Did I mention how this is OUR baby? The one we made together? Do you know what the man who promised to be there "for better or for worse" said to me?
"I have to work in the morning."
I have to work in the morning.
I know there is no salary for stay-at-home moms, but is this not a job of some kind? Isn't what I do work? I know I'm not getting paid, but it's not like I can just pop a squat and have a nap whenever I want.
"I have to be up in the morning, too," was my seething response in the dark.
"Yeah, Ashley, but you can sleep when the baby sleeps," he said through a yawn.
Sleep when the baby sleeps? And am I supposed to wash dishes when the baby washes dishes, fold laundry when the baby folds laundry, and sweep the floor when the baby sweeps the floor?
If it weren't for the marriage passion fire challenge, or whatever it's called, I would have flipped on the lights and told him exactly what I thought of his "sleep when the baby sleeps" idea.
All I asked was that he get up with her, just this once, and he threw his important job in my face.
I feel like I've gotten a glimpse into his subconscious. I'm the nonworking stay-at-home mom who should get up nights because he's an oh-so-important contributing member of society because obviously I don't need a good night's rest every now and then. Motherhood can be run on fumes alone. Good to know.
So far the only thing burning in our love furnace is any chance that he'll be getting any of this spaghetti squash before Aubrey's eighteenth birthday.
8:45 P.M.
My husband is my best friend. He understands exactly what I'm going through as a mom. Sometimes it's like we're twins!
—Emily Walker, Motherhood Better
I was prepared to be in a huff when David got back from work. The plan was to barely speak and close the fridge too hard until he asked me what was wrong five billion times. Five billion times I'd say "nothing" until he let his guard down. Only then would I unleash a heartfelt torrent of emotional diarrhea. That's how we do things. But I never had the chance.
He missed dinner entirely without even calling. This has never happened. Ever. Not in our entire marriage.
I texted my standard What time today? at 4 p.m. when I was at my brink. Aubrey had been screaming every time her favorite episode of VeggieFriends ended, meaning I'd been watching it on a loop for forty-five minutes.
His reply? Late.
One word.
I typed, Okay, what time?
He replied, Not sure busy.
He knows Estimated Times of Arrival are the only things that get me through afternoons. Could it be possible that he's angry about last night? That would be rich. But coming home late isn't his anger style at all. Usually he just gets quiet until I gently coax him with rapid-fire questioning.
When he hadn't come home by 7:30, I called him. Aubrey was fresh out of the bath and squirming in my arms as I balanced the phone between my shoulder and ear.
"Where are you?"
His voice was curt, "Work. Where else would I be?"
Excuse me? I let it slide because Aubrey was thirty seconds away from wiggling out of my arms and onto the floor. What is it about being naked that makes babies so athletic?
"What's going on?"
I heard a muffled side conversation. He wasn't listening.
"David? I said what's going on?"
He finished talking to whoever needed his attention more than I did. "Pepperoni and olives," he said.
"Are you ordering pizza?" My voice was shriller than I meant it to be. Aubrey glanced up at me, probably wondering if I was yelling at her.
"Ashley, I really need to go. We're swamped. I worked through lunch and, yes, we're finally getting some dinner."
"Who's we?"
"Barry, the partners and myself," he said slowly, as if speaking to a three-year-old.
I felt stupid for having asked. What, did I think he was having a romantic candlelight pizza with a woman in his office? Some hot twenty-one-year-old intern who has nothing else to do but burn the midnight oil with my husband? An intern who showers daily and whose healthy, fragrant hair isn't in a greasy half bun? An intern who isn't on day three of the same pajama pants? Of course I didn't.
"Oh, sure. I know. When are you getting home? I made lasagna but since you're eating..." I hadn't meant that to come off like a guilt trip but as soon as the words came out of my mouth I knew they sounded like one.
Silence.
"Probably around nine. We're swamped with the DentaFresh proposal."
Duh. His firm has been trying to land the toothpaste conglomerate since they launched a year ago. This deal, if they get it, would be huge for them.
"Of course! I totally understand! Work as late as you need to. I'll be here. Aubrey just got out of the bath. Do you want to say hi?"
He sighed into the phone. "Ashley, I'd love to but I really have to—"
"Go—no problem, honey. Good luck. See you later."
"Good night." Click.
Good night? I guess they'd be later than I thought. An hour ago I thought he'd be apologizing to me, and now I felt horrible for wanting him to get up with Aubrey the night before such a big day at work. How was I supposed to know? He doesn't tell me anything. I tell him everything. Twice. Three times if I'm feeling particularly chatty.
I placed the phone in my pocket and stared at Aubrey. Her still-damp hair framed her cheery face, making her look like a drenched cherub. She giggled, her eyes squinting and cheeks forming small apples. Something in her mouth caught my eye. Using my finger to examine her gums I could see two bumpy white nubs smack dab in the middle of her bottom molars.
First teeth! I squealed, which made her smile even bigger and then laugh. I couldn't stop staring at them as if they were ruby-encrusted gold nuggets rather than a couple of barely-there baby chompers.
Just as quickly as it came, the wave of excitement turned bittersweet. It was all happening so fast. My baby was growing up. First teeth, then braces, then I'll turn around and she'll be filling out college applications. I can almost see her driving away in a car packed to the brim with boxes, off to start her life...away from me. Only to come home on the odd weekend. Tears sprang into my eyes and I hugged her tightly. The moment was interrupted when a strange warmth flooded my midsection.
"Aubrey, did you—" Pee. I pinched the soaked edge of my T-shirt with my free hand and looked down at Aubrey. She glanced back at me innocently, as if to say, "Are you sure that was me?"
It's only pee, I said to myself as I made my way to her bedroom to get her ready for bed. I read somewhere that it's sterile, anyway.
As I walked down the hallway, I couldn't help but wish David were with me. He'd love to know that she'd gotten her first tooth. I could imagine him laughing as I told him that she'd marked her territory on me yet again. But I didn't want to disturb him—again.
"Sorry, business partners, I need to take this call. My eight-month-old just grew two teeth and pissed on my wife." Yeah, that screams professionalism.
Wednesday, February 13, 11 A.M.
David didn't make it back home until after 1 a.m. Right after he pecked me on the cheek and collapsed into bed, Aubrey started fussing.
My hopes that the arrival of new teeth finally popping through would settle her sleep nonschedule were in vain. It took me half an hour to get her back down. I've spent the morning researching the "cry it out" method.
Here's what I've learned so far.
Half of the internet thinks crying it out is hard to carry out but a perfectly healthy way to get babies on track to becoming fantastic sleepers for their entire lives, which in turn will lead to happy, successful adults who excel both at work and in their personal lives.
The other half of the internet believes that if you let your baby cry it out you will permanently damage their spirit and their brain, and they'll end up selling their bodies down by the train tracks for illicit drugs and dying of an overdose before they hit thirty.
What. Am. I. Supposed. To. Do?
I was desperate for sleep at this point. This morning I wore two different shoes to the café. I didn't even realize it until a five-year-old loudly asked her mommy if it was "crazy feet day" while pointing at them. I replied, "Why, yes it is, darling," in the sweetest voice I could muster, in case you're wondering where I'm operating, maturity-wise.
I bought a book called Love Sleep Repeat, which sounds like the insomniac's guide to the Kama Sutra, but it is really the go-to manual for learning how to do the whole crying-it-out thing. The book was written by a medical professional, Dr. Faber, who, according to the internet again, is both the best and most evil man to ever walk the planet.
Aubrey was hell-bent on eating the prologue, so I only managed to read the first few pages, but I get the idea. Instead of rocking your night screamer to sleep, you simply give them what are called "verbal assurances" until their dependence on you to soothe their night wakefulness vanishes. I hope Dr. Faber is right, because these double vanilla lattes are getting expensive.
Speaking of beds, I have four more days to get Operation Love Furnace up and roaring hot, but between Aubrey keeping me a zombie mom and David working around the clock, what's a mother to do?
Then I remembered. Emily said that if we need extra help to just ask. I mean, what could an international TV host, businesswoman, mother of five and jet-setting author have going on that would prevent her having the time to help me with my love shack problems?
It's better than flunking out.
Private Message
Hi Emily! I know you're busy with the book and your kids and your life (that, by the way, is the stuff dreams are made of, you inspire me every single day, thank you so much for having me in this incredible program, I'm learning tons), but I was wondering if you could give me some advice. I'm having a bit of a time lighting my passion fire. Any easy tricks to share? Thank you so much! Xo Ashley
* * *
A month ago if you'd told me I'd be asking Emily Walker, my momspiration, for relationship advice, I'd have said you were crazy. And yet here we are.
I pressed Send. Looking over at Aubrey, I saw that she was doing her telltale squished-up, breath-holding poop face. How a baby on a mostly liquid diet can create such horrifyingly large emissions, I'll never understand.
Five minutes later I was done changing her and heard a little ping from my laptop, which was still open on the couch. One new message.
Private Message
Dearest Ashley,
I feel so honored that you trusted me with such an intimate inquiry. Progress in the Motherhood Better Bootcamp depends on the openness and earnestness you've shown. When Thomas and I were new parents to our sweet twins, we had a little ritual. Every night after they drifted off to sleep, we would take a bath together. Essential oils and sustainable beeswax candles transformed our bathroom into a Sharing Lair. We'd pour our hearts out to each other, cradled in the warm waters of life, a womb keeping our love aglow.
Never hesitate to reach out to me.
Love, Emily
I'm doomed.
9 P.M.
David is working late again. He let me know via a very personal text message: Late night. No dinner.
He sent the text at 5 p.m., which meant I'd already started cooking. I wish he'd let me know earlier. Does he think I'm cooking for myself? I'd be perfectly happy eating a couple of frozen waffles slathered with chocolate-peanut butter spread. They pair beautifully with cheap red wine. I'm certainly not cooking for an eight-month-old who takes ten minutes to polish off a single cracker.
I dutifully finished up the spaghetti and meatballs I'd been working on for the last hour and dined alone with Aubrey. I know technically that if Aubrey is there I'm not alone, but infants aren't known for their dinner conversation.
I may not have been alone, but I was lonely. Very lonely. He had to have been planning a little something for Valentine's Day, I hoped. Though, at this point, I'd be thrilled to receive a box of drugstore chocolates.
Maybe if I'd tended to our love furnace earlier, the nights David works late wouldn't be so hard. The furnace would be hot enough to keep me warm or something. The metaphors were starting to irritate me.
All I kept hearing from everyone—Joy, my mom and strangers at the grocery store—is how lucky I was to be a stay-at-home mom, but I wondered, if people knew how much time I spent by myself, whether they'd still say that.
I missed David. I looked forward to him getting home, not just to throw Aubrey at him the second he walked through the door, but to have him here with me. I really, really missed him.
An unexpected tear slid down my cheek just as Aubrey glanced up at me from her pile of shredded noodles. She cocked her head to the side like a puppy trying to understand, and then returned to pounding the pasta into her high chair tray with her bare hands. At least someone was having a blast.
Thursday, February 14, 2 P.M.
Date nights are a must for all couples with children. You don't have to make them elaborate: dinner, a movie followed by drinks, can make for a very special night out. I like to buy a new outfit to really get myself excited. If you don't have time to shop, many boutiques will send over a concierge with samples.
—Emily Walker, Motherhood Better
Happy Valentine's Day! I couldn't be happier than I was at this moment. David had just called me from work. Not only was he coming home early, but Gloria was babysitting tonight because he was taking me out to dinner!
"I've been working late and I know you're exhausted with Aubrey. Things haven't been easy. I appreciate everything you do." Those words came out of my husband's mouth.
I felt like the high school quarterback had just asked me to go to prom.
He'd be home at 6, which left me four hours to tidy up (hide everything I didn't want Gloria to see), shower, do my hair and makeup, and pick out something that fit.
The timing couldn't be better, I was all out of ideas for this week's challenge and had two days to write my journal entry.
Can I just say that I have the sweetest, most intuitive husband ever?
5:55 P.M.
The house was clean (enough), and Gloria should be here any second. But none of my prebaby dresses would zip up completely, so I'd ended up running out just before dinner with Aubrey and finding a simple yet elegant three-quarter-sleeve black wrap dress. It was on sale for $49, marked down from $220. Score. The saleslady was quick to tell me that the gathered fabric over the midsection was "very forgiving" and "great for postpartum mommies."
Ugh. Thanks, size zero college student. I'm sure she was just parroting sales copy, but maybe a little less emphasis on my stomach? I'm surprised she didn't ask me how far along I was. Postpartum? I don't think I qualify for that exemption anymore, although I have heard it takes a full year for internal organs to reposition themselves correctly and for bloating to subside 100 percent. See? My thirty-two-week post-pregnancy pooch isn't my fault. My stomach doesn't know where to be. And my fluids haven't gone down. But you wouldn't know about that would you, body-shaming saleswoman?
Or so I thought.
Before I walked out of the store, the associate ran over to me with another coworker in hand.
"Doesn't she look just like Melissa?" she said, gesturing at Aubrey.
I smiled. "Is Melissa your sister?"
She grinned. "No, she's my daughter! She's six months old."
I coughed to prevent myself from cursing at the stranger. How dare you look so good and have a baby younger than mine? is what I wanted to say.
"Oh, how nice! You look fantastic...and rested."
"Thanks," my new lifelong enemy said, running her hands down her sides. "I still have a few more pounds to go. And Melissa's been sleeping through the night since she was two weeks old, bless her."
With that, I walked away for her own safety.
I wasn't letting anything get me down, though. Tonight was my night!
6:30 P.M.
David still wasn't home and hadn't returned any of my five texts or two voice mails.
"Leave him be, darling. He's hard at work. He'll get here when he gets here," Gloria said from the living room couch, bouncing Aubrey on her lap.
I tried the office line. No answer.
I couldn't stop pacing. What if he'd gotten into a car accident? What if something happened? My calls were going straight to voice mail. What if he was robbed going to the ATM machine and the thief forced him to chuck his phone into an ocean or something? Aubrey's never going to see her daddy again. I could feel the tears start to rise again.
7 P.M.
Did you know that 911 doesn't consider anyone a missing person until they've been gone for twenty-four hours? Insanity.
10 P.M.
David walked through the door at 9:30, fifteen minutes after I had insisted Gloria go home.
"He just got caught up with work. I'm sure of it. A mother can sense these things," she said, lingering at the front door.
"Normally he'd call. I'm worried."
"In my day, you know, during the war, we wouldn't hear back from our men for months at a time," she said, waving a finger at me.
I didn't say "These aren't war times," because all I really wanted was for her to leave so that I could try David's phone again.
"Okay. I'll call you as soon as I hear anything."
Fifteen minutes later the door opened and I felt my heart jump into my throat.
I practically ran toward him.
"Where were you? What happened? Are you alright?"
"I'm fine. My phone died."
It was like someone punched me in the chest. "Your phone died? Your phone died?" I couldn't stop repeating it over and over.
He walked over to the kitchen and put his briefcase on a chair, then took off his coat.
"Yes," he said, rubbing his eyes with his palms. "Didn't you get my email?"
"Email? I haven't been on my computer all day. Why didn't you call me from the office?"
"I've been in back-to-back meetings all day. I left as soon as I could."
I stood in the kitchen, unable to process what he was saying.
"I'd love to talk, but I'm exhausted," he said, kissing me on the cheek before walking past me.
I followed him into the bedroom and watched him undress and lie down. His eyes were just about to close when I blew a fuse.
"David." My voice was so calm it scared me. It was scary calm. The kind of tone only serial killers use. "David, do you see what I'm wearing?"
His eyes fluttered. "Yeah. A dress. You look good."
I was dumbfounded.
"Do you know why I'm wearing a dress?" I felt like a kindergarten teacher quizzing her students on their ABCs.
He raised his hands, exasperated. "Ashley, I'm tired, okay? I don't have energy for whatever it is you're getting at. Can you just spit it out?"
I felt a searing heat creep up my spine like a volcano about to explode lava, destroying everything in its path.
"Date night. Valentine's Day. Need I go on?"
His face went blank and then...recognition. He jumped out of bed and walked over to me cautiously. "That was tonight. Oh, my—I completely forgot. I completely—it's work. It's been so stressful, Ashley. I will make this up to you."
I took a step back. "Stress? Do you think you're the only one stressed out right now? I haven't had eight hours of continuous sleep for over a year. I'm overwhelmed every single day. Yet somehow I don't forget to show up for the first date we've had since Aubrey was born."
I tried my best not to raise my voice and my words came out like hissed accusations.
David cupped my face with his hands. "I'm so, so sorry. You have no idea how sorry I am. It's this DentaFresh proposal, at the last minute they let us know their marketing initiatives for the calendar year were changing and—"
"Is this how it's going to be?" I interrupted.
He froze, confused. "How what is going to be?"
"Am I, are we, going to come last after your job? Will I always be waiting at home for you to toss me whatever crumbs are left over from your important life in the outside world?"
David's face fell. "No. It won't be...it's not like... I'm not tossing anything—"
I narrowed my eyes at him. "I plan my entire day around you and Aubrey. I cleaned all afternoon today. I bought a dress."
His eyes flickered. "You bought a dress? For dinner? You have a closet full of dresses."
"Yeah, and none of them fit me," I retorted painfully, each word feeling like it burned on its way out.
David crossed his arms. "Then work out!" he erupted.
As soon as he said it, he looked shocked by his own words.
The air felt like it was sucked clean out of the room with one of those infomercial vacuum sealers, but instead of raw cuts of rib eye, two people were suspended in time.
He started to speak. "I didn't mean... I'm tired...you look..."
I held up a hand. "Just stop."
I turned around and walked toward the door. Before leaving, I turned back and said, "Happy Valentine's Day." His shoulders dropped. I headed for Aubrey's room. Once the door was closed behind me, I switched off the baby monitor on the dresser and peeked at her. She lay still and I didn't move until I saw her take a deep breath.
I closed the door gently and made my way downstairs. I felt like a zombie curled up on the couch. The fight with David and his words sat in my chest, heavy and hollow. A few tears slid down my cheeks and I pulled my phone out of my pocket.
Motherhood Better Bootcamp Journal Entry
Hi everyone. This week has been really busy but I did my best with the challenge. My husband planned a date night and I won't get into the details, but I got to see a new side of him. Xo Ashley
Friday, February 15, 6:30 A.M.
I woke up at 6:30 on the couch with a blanket over me. David must have put it there. I just didn't feel like sharing a bed with him, not after how we'd ended things last night.
His words still stung.
I sat up. Something felt strange. Something was off. Then it hit me. Aubrey. She hadn't woken up all night. My heart started pounding. Was she okay? As I stood up and flew upstairs I prepared myself for the absolute worst. Pure terror pounded in my chest.
I pushed her door open and it hit the back of the wall with a bang as I lurched toward her crib. "AUBREY!" She was still there. I put my hand on her chest and felt it rise while I tried to control my still-shaky breathing.
She was fine. Just sleeping. I stared down at her face in disbelief. Did she sleep through the night?
"I got up with her," whispered David's voice behind me. I jumped, startled, and turned around to see him standing in the dark doorway. "She woke up at one and then again at 3:30. I don't know how you do it."
I turned once more to Aubrey. A peaceful half smile played on her serene face. She sniffled in her sleep. To think I almost woke her up. I crept toward the door and shut it, being careful to catch the latch with the doorknob before it clicked.
I turned to face David. He stood there, looking down at me with his I feel so bad but I don't know what to say face. I can't resist that face. He opened his arms.
Without speaking, I fell into his hug and he wrapped it around me. I closed my eyes and let the side of my face soak up the warmth of his cotton T-shirt against his hard chest.
"I'm sorry," he murmured into my hair. "I'm a jerk. I didn't mean that you need to exercise, I was just trying to think of something to say... I'm an idiot."
"I know," I breathed out.
He took my hand and led me to the top step, where we sat, side by side. "You're perfect. You've been doing everything around here while I've been trying to keep the business going."
The gravity of his tone startled me. "Keep it going?"
His brow furrowed, "Work has been hard lately, Ashley." His face was serious. I studied his face and saw...was that fear?
"Companies aren't hiring new marketing firms the way they used to and our start-up cushion is almost gone." His voice shook.
I took his hand. "David, it's going to be okay..."
He drew his hand back. "It's not. Not unless I can land this DentaFresh deal. If we don't get this business..." His voice trailed off, and from the way he looked around the house, I understood.
I felt helpless. Maybe I should have looked harder for a job. No wonder he blew up about the dress. "I'll spend less money. I can take the dress back."
He rubbed his forehead. I'd never seen him this stressed. "I'll figure something out. In the meantime...if I have to work late—"
"It's no problem. Work as much as you need to. I'm here."
I rubbed his back. Everything was going to be okay. It had to be okay.
I took his hand and looked him dead in the eye, "David. I believe in you."
He stared at me for a moment before putting his hand gently on my cheek.
"I love you. And your body," he whispered into my ear.
He kissed me. I leaned into his kiss and felt my heart flutter the way it used to. I heard him sigh and we both giggled.
He rested his temple on mine and drew me close. "Why, Mrs. Keller... I don't think we've kissed like that for a while."
I lifted my arms over his shoulders and locked them around his neck. "I guess you should stand me up more often."
He laughed his deep quiet laugh and wrapped his arms around my waist. "May I interest you in a date right now? Party of two."
"Maybe," I said, teasing.
"Fair enough. But first, I have something for you." He reached into his pocket and pulled out a rectangular black jewelry box. My eyes grew to the size of dinner plates. I thought he'd forgotten.
"Happy Valentine's Day, Ash."
I blinked back a few tears as I opened the box. Inside was a gold locket attached to a gorgeous braided-gold necklace.
"David," I said, holding the necklace up. "It's beautiful."
I opened the locket. Inside, the date was engraved and three sparkling stones gleamed in the dim light of the hallway.
"Those are our birthstones. You, me and Aubrey. So that we're always together and right next to your heart."
That did it. A waterfall of feelings poured out of my face. I blubbered while he helped me put the necklace on.
He spun me toward him and kissed me again. I felt a tingle run up my spine.
"So," I began coyly, "how about we have that date right now, but skip straight to dessert."
Saturday, February 16, 11 A.M.
Marriage is a partnership. My husband has supported me on my journey to creating a worldwide brand from day one. He even helps me pick out Instagram filters.
—Emily Walker, Motherhood Better
Aubrey clapped her hands and jumped up and down in her exersaucer as I played peekaboo with her. Every time my eyes closed behind my hands I fought the urge to fall asleep right there on the floor. She woke up four times last night and the day was creeping by. I was on my third cup of coffee, but my mind was still a thick fog.
All I could think about, other than how utterly exhausted I felt, was David. How could I be so blind? And selfish? Here David was trying to get his company up and going, and I was angry because he wasn't home for dinner. I couldn't imagine the amount of pressure he was under every day to make this work. He was so brave—he could have stayed at Paulson International and eventually become CEO, but instead he chose to build something for himself...for all of us.
Aubrey squealed as I popped out from behind my hands and made a silly face. I pulled her out of the exersaucer and put her in her Pack 'n Play surrounded by toys. Maybe she'd entertain herself for a few minutes while I sprawled across the living room floor.
No dice. As soon as I put her down she started wailing, her arms outstretched. I picked her up and fought back tired tears. It wasn't even noon.
My thoughts returned to David as I sat on the couch, Aubrey squirming in my lap, trying to pull my hair out of its messy bun. I hoped he got the DentaFresh account.
I feel so useless at home, just frittering the day away with Aubrey when I could be helping him succeed. There has to be something I can do; after all, this business is the family business and it's not like I don't have experience in marketing.
"Think, Ashley, think," I said to myself. After a night of almost no sleep, my mind felt like a muddy pond, but I was determined.
And then, an idea.
When I was with Weber & Associates, one of the ways I used to encourage potential clients to sign with us was by hinting that a competitor was interested in our services.
Maybe that's what DentaFresh needed: a little healthy encouragement. I grabbed my laptop.
It took me all of two minutes to find their press contact and make up a bogus email account.
To: Cynthia Burton, cburton@dentafreshco.com
From: Rebecca Squash, mssquash123@mail.com
Subject: Upcoming Dental Seminar
Hello Cynthia,
My name is Rebecca Squash.
I'm a reporter with a small regional newspaper looking for a quote from DentaFresh regarding marketing trends in the oral hygiene industry. Do you have any news you'd like to share? We're reaching out to the All White toothpaste brand, as well. According to reports, they're collaborating with new firms such as Keller & Associates to come up with innovative campaigns next quarter. We would love to hear your thoughts on the matter.
Best,
Rebecca
I smiled at the screen. So, is this what spies feel like? I felt both satisfied and utterly pleased with myself. It was just like old times in the office, except this time I'd completed a task with a baby batting at my face. Back in the day, my superiors used to praise me for my resourcefulness when it came to making things happen. It's just like Emily always says, "Opportunity waits for no mom."
The day felt like it couldn't get any better. The only thing left to do was stop by the grocery store.
8 P.M.
Grocery stores should have signs in front of them for new moms that read like this:
Dear valued shopper, if you are entering this store with a young child, please know that you will lose your mind. If you should find yourself in an aisle having a complete nervous breakdown, find a customer service agent who will promptly hand you a square of our finest chocolate and small glass of pinot grigio. You will then be led to one of our several massage rooms while your child is taken to our state-of-the-art nursery. We will happily finish your shopping for you and deliver your groceries to your home.
I made the mistake of taking Aubrey on a post-nap errand today. Aren't naps supposed to relax babies? Aubrey woke up the Chucky-doll version of herself.
I should have known things were going to be bad when Aubrey screamed the whole fifteen-minute ride to the store. By the time we arrived my nerves were already fried. After parking the car I did my best to do what Emily Walker calls "be present for your child's needs." She didn't want her pacifier. She didn't want her blanket. Her diaper was dry. She didn't want a teething cracker. I even waved my phone in front of her face and she took it alright, then threw it out of the open car window. The screen now has a tiny crack up the side. Fantastic.
"Do you want to stretch your legs, honey?" I cooed to her as she let out another feral holler. Yes, that's it. Once we're inside, she'll calm down.
For my baby shower I received one of those huge shopping cart covers that are supposed to prevent your child from getting cholera from other people's kids. I've been using it religiously, but even that had to go horribly wrong.
Aubrey was still screaming like her hair was on fire for the few seconds it took me to grab an abandoned shopping cart. As I opened the trunk to pull out the cholera-prevention cover, I must have been frazzled, because it slipped out of my hands and onto the cement.
That wouldn't have been such a terrible thing, but of course I had to have parked in the only spot that was directly over a huge puddle of brown, murky water with a thin gasoline-film rainbow over the top and what looked like a plastic bag full of vomit. I picked up the cover as quickly as I could, but it was already half sopping wet with putrid muck. No way was I putting my kid in that thing. Who knew what was in that water? Flesh-eating bacteria? I couldn't leave it in my car. I stuffed it into a nearby garbage can.
By that time, Aubrey's wails had settled down to desperate little hiccups, so I quickly cleaned the cart handle with a baby wipe before placing her inside. By "placing" her, I mean practically forcing her squirming, defiant little body to sit down and then doing my best to strap her in.
My luck continued when I noticed that not only was one side of the strap hard, caked with some sort of film, the other one was broken.
It took three more tries before I found a cart with functioning straps. Who are all of these kids breaking shopping cart straps with their Hulk muscles and bare werewolf teeth? And what are you spilling on them? Glue?
Aubrey's hiccups started to gear back into an angry cry as I sprinted through the store, haphazardly throwing things into the cart. Between speeding down aisles and yelling "No" every time she tried to peel off her shoes, I had no idea what I was buying. I'd made a grocery list, but it was in the car and there was no way I was starting all over.
Twenty-five minutes and two family-sized bags of tortilla chips, produce I'll probably never eat, overpriced chicken breasts, two frozen lasagnas and who knew what else later, we were done.
Standing in the line, Aubrey began looking at me strangely. Her eyes went blank and her head fell back a little before...she barfed. Projectile vomited, all the way down my shirt. Everyone in my immediate vicinity gasped and leapt away.
Ten to fifteen seconds passed before I could fully absorb what just happened. Aubrey just stared at me, looking somewhat relieved.
"Ma'am? Can I...get you a paper towel?" said the checker who couldn't have been a day over seventeen. He can thank me later for the free birth control.
"Yes," I stammered, fully aware that I had an audience of close to twenty people who seemed unable to look away. "A few would be great."
I did my best to clean myself up. All Aubrey needed was a dab on the chin; she'd managed to keep herself completely barf free. After the paper towels were all in a plastic garbage bag, a friendly mom shopping with her two toddlers handed me a container of disinfectant wipes.
"Keep them," she said, smiling sympathetically at me.
When we finally got home, I peeled off my shirt and called the nurses' hotline.
"If she doesn't have a fever, you don't have anything to worry about," the nurse told me matter-of-factly. "These things just happen."
"How often, do 'these things just happen,' exactly?" I asked dryly, sipping a cold glass of white wine as Aubrey splashed her bathwater with her palms. "I'd like to be prepared next time."
She laughed, not realizing I was serious.
When David arrived home a few minutes after I put Aubrey down, I was sitting on the couch with another glass, dazed out in front of a reality show featuring moms as rich as they were childish.
"Hi, babe, how was your day?" He leaned down and kissed me on the cheek, then scrunched up his nose. "What's that smell?"
"Motherhood."
Sunday, February 17, 1 P.M.
Positive Affirmation of the Day: Mama-hood fills me with joy! I am a goddess who radiates hope, wisdom, and maternal beauty!
—Emily Walker, Motherhood Better
Almost a full month into the Motherhood Better Bootcamp I have lost no weight, my hair is still falling out like it's offended by my scalp, and Aubrey knows zero sign language while Ella is up to forty-five words and has her own YouTube channel. Joy says she has 300 subscribers and is being scouted by baby modeling agencies.
I am a complete loser.
Off to drown my sorrows in a bag of chips. Chips always understand.
Monday, February 18, 10 A.M.
I don't know what I'd do without my group of mommy friends. There are ten of us in our village and we aren't just best buddies, we're sisters. We spend so much time together that even our housekeepers are friends now.
—Emily Walker, Motherhood Better
The fourth Motherhood Better Bootcamp video conference is this morning. Aubrey woke up at 4 a.m., so by 8 a.m. she was in a deep sleep. I placed her in her crib and by some miracle she didn't wake up. If it were any other day I'd immediately lie down on the couch and pass out until her cries woke me up, but I rushed to put on a bit of foundation and lip gloss.
Over the past few calls, I'd noticed something: each time, the other moms looked more and more put together. For the first one, everyone was in raggedy ponytails and had the same dark circles under their eyes I know so well. For the second one, hair was brushed and clean, lips were tinted. And then, suddenly, the moms looked like they'd been airbrushed: straightened or expertly curled hair, full makeup, no clutter in the background. We looked better, but I couldn't help but wonder if we felt better. We were in full-blown silent competition with each other.
I looked in the mirror and decided that a moderately clean black tank top, sweatpants that nobody would see, powder and plum gloss were going to have to do it today. I pulled back my hair into a bun. Not bad.
I opened my computer and logged in. It was only a few seconds before I heard Emily Walker's voice sing over my speakers.
"Aloha everyone!" The camera zoomed into focus and there was Emily, lying out on a beach chair in a gold bikini. She was holding some kind of selfie-stick-type camera that allowed her to pan right and left. Beside her were three other women in blue, red and white barely-there swimsuits, looking perfect.
I glanced down at my sweats.
"I'm coming to you live from the island of Kaio! My three best friends and I are here for the next few days enjoying a little break from my whirlwind book tour! The dads are officially on duty—am I right, ladies?"
They hooted and giggled. Hot jealousy pumped vigorously through my veins.
Emily took off her sunglasses and looked deep into the camera. How are her eyelashes so long? I wondered.
"My family is everything to me, but I wouldn't be able to survive without my mama village. These three women mean the world to me. That's why, whenever we can, we hop on a jet and go somewhere where we can connect."
A mystery gloved hand holding a platter of champagne flutes, appeared from the side.
The women cheered. Emily took a glass.
"This week, the challenge is to find your village of moms! Join a playgroup. Make a best friend. You can do it!"
She clinked glasses with her friends and took a long sip.
"I believe in you! Oh, and before I let you go, remember that you only have three more weeks before our trip to Napa together! I can't wait to make all of you my besties for life! Who knows, maybe next year we'll be on vacation together. Make today a great one!"
With that, the connection switched off.
Now that's the life. I tried to imagine jetting off to spend a few days with Emily Walker and her cast of mom models to drink sparkling wine on a secluded beach. I can already see the conversation.
"Gloria, can you take Aubrey for a little while? My best friend and television host, Emily Walker, and I are going resort hopping in Jamaica."
Could that really be my life? A shiver of excitement ran up my spine.
2 P.M.
Breastfeeding is the first and best gift you can give your child. It's not just perfect milk that's flowing through you into your child, it's perfect love. Some of my best memories are of being a young toddler and breastfeeding from my own mother.
—Emily Walker, Motherhood Better
Aubrey woke up soon after Laundrygate, so I popped her into the stroller for a coffee run. I've learned that staying home in the afternoon makes the day go by even slower than it usually does, so we often run errands (i.e., buy things we don't need or ice cream) to pass the time. If I'd known what was going to happen at the café, I probably would have stayed home.
It was quiet, the early afternoons just after lunch and before the later afternoon slump rush always were. There were plenty of tables to choose from, but I made a beeline toward the one with a stroller. It was empty—the owner must be in the bathroom, I theorized. Being a mom means being on the constant lookout for friendship, a listening ear, or just someone to complain to who gets it. I've found grocery checkers aren't the best listeners.
I quickly purchased my vanilla latte and gingerbread loaf with a madeleine for Aubrey and sat down, practically trembling with anticipation. Who was the mom? Or dad? Was I about to make my lifelong best friend?
Then she emerged from the bathroom, juggling her diaper bag and a baby wearing a blue romper who looked no older than six months. I cleared my throat in anticipation. The café was almost empty but I'd chosen a seat one table over so as not to come off as too desperate.
She crouched down and grabbed a lightweight blanket before sitting down, cradling her baby in her lap.
I stood halfway up, preparing to introduce myself, before I saw her slip one strap of her tank top down and flop the blanket over her shoulder. She was nursing. Oh. I'd been down this road before. When Aubrey was three months old I joined a mom group for about five minutes. That's how long it took me to figure out that I was the only one not breastfeeding. It's not that the moms were judgmental—the pitying, sympathetic smiles every time I pulled a bottle out were too much. Maybe it'd all been in my head, but watching them cradle their babies on their giant nursing pillows while I measured formula was more than I could take on a regular basis.
I didn't realize I was staring until I snapped to and saw the nursing mom looking at me. I smiled and she returned it.
I busied myself opening Aubrey's package of madeleines and handed her one. "Here you go, honey," I whispered, trying not to notice the stark difference in what we were feeding our babies. Aubrey snipped off a tiny bit of the soft cookie with her gums and grinned.
I couldn't resist peeking at the mom again. She and her baby were lost in each other the way breastfeeding moms always are. She gazed down at him with a serene smile on her face. What does that feel like? I wondered to myself. The feeling of knowing you're doing the absolute perfect thing for your child without a doubt. She looked so calm and serene. The baby reached up from behind the blanket and touched her face. They were like a commercial. I gathered our belongings and headed for the door. When the daylight hit my face, I was grateful for the distraction.
One hand on the stroller, the other clutching my sweet coffee, I took Aubrey for the longest walk we'd been on so far.
4 P.M.
I was sitting in my living room watching Aubrey, who was currently fascinated by the twirling monkey mirror on her exersaucer. She was adorable. I was obsessed with her. But I was bored.
I really did need friends, but when you're a mom, that's easier said than done.
Yesterday at the park I tried to chat up a couple of moms who were having what looked like a really interesting conversation. They were whispering and everything. You should have seen how slick I was as I complimented one of the moms on her stroller and tried to use that as a segue to introduce myself. They looked at me like I had six boobs and an infant breastfeeding on each one.
They were polite enough, but it obvious that they wanted me to keep moving.
You know what really surprised me about motherhood? The slow realization that mothers aren't anything I thought they were to each other. I thought once you entered the mommy club they brought you into the fold with open arms. Look guys, my vagina/stomach/overall body got torn up just like yours and I'm pushing a stroller here, we're all going to be best friends, right? No. Maybe it was naive of me to think that just because we shared the experience of never feeling rested that we'd be blood sisters for life, but I wanted that. I needed that.
It killed me that one of the hardest parts of being a mom was sometimes dealing with other moms. The judgments, the looks, the advice that feels like a slow plunging of a knife into an already sore spot. They were supposed to understand better than anyone. They were supposed to be the only people I didn't have to pretend for. They should have been my safe space, but they weren't.
Anyway. If someone needs me, I'll be talking to the nine-month-old in my care.
9 P.M.
I met my best friend, Alexsis, at the Rainbow Orchid Spa in Napa Valley, California. We were both taking a little R & R. The minute our eyes connected over the steam in the sauna, I knew we'd be best friends for life.
—Emily Walker, Motherhood Better
I took some decisive action to find my "mama tribe" today, and even by my standards it helped me achieve a new low.
Okay, so I was at the café, like always. It took me almost a full three minutes to cram my T. rex of a stroller through the door. The Mitax Marathon is trendy, but why, oh why, are the wheels so far apart? I felt like the business people on their phones and students tapping away on their computers enjoyed watching me almost dump Aubrey out onto the floor as I tipped the stroller to an angle to finally get myself in.
"No, no, don't get up," is what I hope my eyes said at the 20-plus people who remained glued to their seats staring at me while I struggled. I don't expect help just because I'm a mom, but what happened to the whole "it takes a village" thing?
Back to the story.
Ten minutes later I was sitting down, vanilla latte in hand, when Aubrey started to fuss the way she always does when I've reached a pre-baby state of relaxation. A few twenty-year-olds turned to look at me and I could tell they were irritated. Obviously they were never babies and were born fully grown, so the sound of a human infant is completely foreign to them.
Or maybe they think a good mother would sedate her baby with tranquilizers before taking it out in public so no one would be subjected to the torture of hearing a baby get upset.
Either that, or my child's cries were distracting them from their oh-so-important Facebook posts.
After one of them sighed loudly for the third time, I took the hint and started preparing to leave. But then I thought, Why should I have to vacate the premises every time Aubrey makes a sound? It's not like she's screaming her head off. No. I decided to handle it right there.
I picked Aubrey up out of her stroller and could tell right away that she was exhausted. It's hard for me to get her to nap at home much less in a loud coffee shop full of judgy twenty-year-olds probably live tweeting my every move, but I was determined.
I cradled her firmly in my arms and draped a blanket across my shoulder and over her head to block out some of the light and started bouncing her. The Motherhood Gods must have smiled upon me because she fell asleep in ten seconds flat. I couldn't believe it! I was finally becoming the kind of mom I'd always wanted to be: capable. My arm fell asleep and started to burn, and I was pretty sure it was going to fall off, but my kid was asleep and I had coffee. All was right in the world.
Then they walked in. The moms I'd seen at the park a few days earlier. My dream mommy group. My dream village. There were five of them. They all wore their babies and toddlers in a rainbow of amazing carriers: long strips of tie-dyed cloth, gorgeous prints. One of them pushed a double stroller. They held the door for her. See? Mom friends are a must. They walked in and sat at the table directly behind mine. I could barely breathe.
I knew it was my chance. I needed to say something. But what? Introduce myself? I took a few very nervous sips of my latte and tried to think of something to say. I took a deep breath and, right as I was about to turn around, a woman standing in front of me cleared her throat loudly.
I assumed my stroller was blocking her way.
"Sorry, do you need me to move my—" I began.
"Do you mind not doing THAT in here?" She twisted her lips and pointed at sleeping Aubrey.
I was legitimately confused. Let my baby sleep? Drink lattes while looking like a Dumpster? What was she talking about? And it dawned on me. She thought I was breastfeeding. My boobs have been drier than a raisin for months but she thought I was breastfeeding.
My mind raced as I tried to find just the right words, but before I could speak a voice behind me boomed, "SHE'S NOT GOING ANYWHERE."
The moms. They came in like a wrecking ball and swarmed me before I could utter a single word.
A redhead in a maxi dress stood between me and the woman. "She has every right to feed her baby here. Breastfeeding in public is protected by law, or didn't you know that?"
A mom in a blue sweatsuit chimed in, her arm protectively around a curly haired toddler in a yellow-and-green checkered wrap. "She's not going anywhere and you have no right to ask her!"
People were turning around in their seats now. The whole café was watching and I think I saw one teenager filming with his phone.
Business lady clicked her tongue and shook her head disapprovingly. "It would really be more appropriate if you did that kind of thing in the bathroom."
I still hadn't said anything. I knew that this was the moment to say that I wasn't even actually breastfeeding but two things popped into my head.
If I WERE breastfeeding, this woman was way out of line for asking me to leave.
THE MOMS NOTICED ME. THEY NOTICED ME AND MIGHT WANT TO BE MY FRIENDS.
I'm not sure where the voice came from but the words, "I'm not going anywhere. Breastfeeding is natural," came out of my mouth before I could stop them. I may have hugged sleeping Aubrey closer to my chest area, also. I also may have said, "It's my right."
Business lady whipped around in a huff and stomped away. Of course I immediately thanked the other moms. Maxi Dress (whose name is actually Lola) put her hand on my shoulder and asked me what I was doing tomorrow. I said "Nothing," and they invited me to their playgroup. The only problem is...it's a La Lait meeting. For breastfeeding moms. And I'm not breastfeeding.
I said yes.
The good news is that I now have friends. The bad news is that it's based on a small (HUGE) lie.
Tuesday, February 19, 9 A.M.
I breastfed my first children, Eleanor and Gregory, until they were 4.5 years old. They're rarely sick and read two grades above their age. Breast milk can cure many common ailments including sore throats, the flu, eczema, burns and even hangnails."
—Emily Walker, Motherhood Better
What am I going to do? I'm a formula mom in a breastfeeding world. Just my luck that the first serious mom-group prospect I get since the pyramid scheme playdate is based on a huge lie. Maybe once they get to know me they can overlook the whole "I lied about breastfeeding and my baby is really living on the stuff you think is pure evil" thing.
Today was my first La Lait meeting. Operation Pretend to Breastfeed to Make Friends was in full effect. I wore jeans and a button-down shirt because I read on the MilkMums.net message board that they're the easiest to nurse in. I wasn't proud of myself, but I knew blending in was going to be important until I worked up the nerve to tell them the truth.
There was a small possibility that I also wore a nursing bra, but only because I had one lying around from before Aubrey was born. I'd given all but one of them to Joy after it was cemented that I wouldn't be breastfeeding. To be honest, I was still a little raw that she'd had the nerve to ask me for them.
"I mean, it's not like you need them," she told me while I was holding six-week-old Aubrey and still crying every time I made a bottle.
Aubrey was quiet as we drove to the meeting. She was ridiculously cute in her lavender overalls and white shirt. As we made our way out of the suburbs and toward the La Lait meeting in the hip part of town that was inhabited by college students, organic grocery stores and independently owned coffee shops, I reflected on how I found myself in this utterly ridiculous predicament. Technically, I never lied. My exact words at the café were "I'm not going anywhere. Breastfeeding is natural. It's my right." All of those statements are true. I wasn't going anywhere. Breastfeeding is totally natural. And it was my right. I just wasn't doing it.
They're the ones who assumed I was breastfeeding. If I'd corrected them in the café in front of that wretched woman I would have hurt the movement.
My heart began to race as I pulled into the community co-op parking lot. It was adjacent to a public garden with a hand-painted sign that read, "Come one, plant all." A few people, a young woman in a long patchwork skirt with a toddler strapped to her back, a man with an elaborate beard and wearing denim shorts, and an older woman wearing a mechanic-style jumpsuit, were harvesting the land.
I sat in the car for a few moments with my hands on the steering wheel. "I can't pretend to breastfeed Aubrey," I said aloud. "That's insane. It's deranged. Who does that?" I peeked at Aubrey in the rearview mirror. She gummed on a silicone teether in the shape of a giraffe. I'd received three of them at my baby shower. Apparently they were the hot must-have for moms. As I stared into her sweet brown eyes, I knew what I had to do.
Opening the door gingerly, I walked to her side of the car. I grabbed the diaper bag and undid her straps. With Aubrey on my hip and the diaper bag (with a bottle hidden in a tangled mess of pacifiers, toys and changes of clothes), we made our way toward the door.
"I'm not going to pretend to do anything," I decided. "I'm just going to show up to the meeting I was invited to." Anyway, I thought, who says it's for breastfeeders only?
A sign on the door in swirly script read: Welcome to La Lait—A Safe Haven for Breastfeeding Mothers.
Oh.
11 A.M.
Breast milk isn't just wonderful for children. I pump and feed for premature shelter puppies once a month.
—Emily Walker, Motherhood Better
Lola, the outspoken redhead from the café, was waiting for me in the lobby of the co-op when I walked in.
She wore her two-year-old son, Donovan, in one of those woven wraps that are way more expensive than they look. Maybe she'd be able to teach me how to wrap Aubrey. That is, if she can't tell just by looking at me that my girls are as dry as a bone.
"Ashley!" she squealed as she glided over to me. "You made it!"
She reached out and grabbed me into her arms, squishing Donovan against my chest. She held my arms.
"The ladies are so excited to meet you."
I forced myself to smile and hoped that I wasn't visibly shaking. "I'm...so excited to meet them, too!" Inside, I could hear a voice saying, "What are you doing, Ashley? Run! Run now!"
Lola tickled Ashley's cheek. She giggled. "We've got to get you a wrap, little missy! Mommy's arms are probably so tired!" She put a hand on my shoulder. "I have a spare in my car, if you want I can..."
I waved my hands wildly. I couldn't let her see that I have no idea how to use those contraptions. Not even seventeen YouTube videos and a ten-pound bag of flour as a baby stand-in could teach me.
Lola grinned. "Ah, you're one of those 'baby in arms' mommies. Old school. I love it."
I shrugged my shoulders and smiled as if I had any idea what she was talking about.
Lola led me down the hall, past a Tai Chi class for elders and a pottery class for the recently divorced, to a door with a poster of a woman tandem nursing (that means two babies—I learned that last night) her twins. The caption above her head read, I make milk. What's your superpower?
"Apparently, it's lying my way into mom groups," I said under my breath.
"What's that?" asked Lola.
"Oh, nothing! I just can't wait to say hello," I lied.
Lola put one hand on the door handle. "Ready to meet your fans?"
"Fans?" Before I could answer or sprint to my car, she opened the door and pushed me in front of her.
I'd decided to keep a low profile at the meeting. I wouldn't tell anyone what had happened; I'd just make a fresh start based on truth. That plan went out the window the minute Lola spoke.
"Our hero was arrived!" Lola practically yelled and the fifteen-plus women sitting in a semicircle on a large red rug with blankets and pillows broke out into applause. The ones without babies on their breasts even stood up to give me a standing ovation.
I died.
"It's so great to meet you! You are so brave. Can I interview you for my blog about normalizing breastfeeding?" said a bubbly brunette with thick glasses who turned out to be Nina, mom to six-month-old twins, Finch and Aiden.
"I'm, um, thank you, maybe," was my eloquent response.
I sat down with Aubrey, who was practically buzzing at the excitement. Everyone was staring at me, beaming as if I were some kind of lactating Joan of Arc.
Lola took her place among the moms and sat on her knees. "Hi, everyone! I want to formally introduce Ashley Keller, mom to Aubrey! She's the amazing milk warrior I met at the café yesterday. She stood up to ignorance and we're so happy to have her as part of our group."
Everyone clapped again and I did my best to conjure invisibility. This was a mistake, boomed in my head, over and over.
"Ashley, would you like to say a few words?"
I froze. Maybe now was the time for me to speak up and just tell everyone what had happened. Surely they'd understand, I thought. It's such a simple misunderstanding. If I told them now, maybe we could all laugh about it and I could be the Le Lait version of a football waterboy and make sure everyone stays hydrated while they nurse.
But as I looked around the room of smiling faces, hair as disheveled as mine, shirts with mysterious white, filmy, damp stains, eyes with dark bags under them, babies squirming around, I knew that these were my people. I know it sounds crazy, but besides the tiny fact that my diaper bag contains a bottle and powder that I'm pretty sure would leave them recoiling in disgust, we're pretty much the same.
"Thank you so much for having me today," I heard come out of my mouth. "It's time people accepted breastfeeding as normal and natural."
They clapped.
What have I done?
Thursday, February 21, 1 P.M.
Today was everything I dreamed motherhood would be. The La Lait moms and I met up at the park for a lunch potluck. I brought my Lemon Poppyseed Cake (it turned out perfectly and everyone wanted the recipe).
I was finally that mom. The one I always saw laughing and giggling with a group of mommy friends all seated together on a huge blanket surrounded by their babies. Somewhere between eating cubes of cheddar cheese and sipping on Nina's homemade lavender lemonade (which was amazing, by the way), I realized that this is what was missing in my life. I looked down at Aubrey and felt like I was not just a mom; I felt like a whole person. I hadn't felt like that in ages. And for the first time in a long time, I didn't feel completely and utterly alone.
Nina, a seasoned mom of four, and I hit it off especially well. At the first La Lait meeting we spent some time chatting, while she bounced her six-month-old twins, Aiden and Finch, one in each arm.
I almost said, "Wow, you have your hands full," but remembered how much I hate when people say that to me. It's basically code for "Your life looks unmanageable." She dresses just like me: black stretch pants that she woke up in and long-sleeved shirts or hoodies. But our bonding wasn't just over clothing preferences—I love how relaxed she is. Nothing seems to faze her. When Aiden and Finch both started projectile spitting in a stream of white milk, one over each shoulder like some sort of marble water fountain, she just looked at the three-foot-long splat mark on the linoleum and said, "I think that's a new record, boys. Well done." Then she set them down on a mat and wiped the whole thing up with a burp cloth. I would have wanted to sink into the floor. Nina just rolls with the punches. I'd love to be like that one day.
The craziest part about her is that she has FOUR kids, including the twins. Besides Finch and Aiden, there's Everdeen, four, and Lillyanne, six. I have no idea how she does it. She's so cheerful and sarcastic. She told me that the trick to making it through the day is to "always have a glass of wine or piece of chocolate waiting for you at the end of the day...or with lunch, whatever." I love her.
Lola's toddler, Donovan, is her first, but she's hoping for another. When I told her that I'm probably one and done, she said "Just wait," and winked. I got the feeling she's been trying for a second for a while now but didn't want to pry.
I also chitchatted with a mom named Kristen. Her little girl is Alice, who's just three months old. She reminds me of myself when Aubrey was a newborn: quiet, insecure, and trying so hard to find her groove. She was learning how to use a beautiful purple-and-black striped baby carrier on my first day with the group. Three moms were helping: one held the baby while the other two wrapped her up. As I watched her stand there, surrounded by friendship and encouragement, I felt a little pang of sadness. Maybe I wouldn't have had such a hard time getting used to this whole motherhood thing if I'd had a group like this.
Sitting on the grass on overlapping blankets, babies, moms, and containers full of fragrant salads and sandwiches, I felt like I'd finally come home.
Today was an absolute success.
Except for one small incident.
After lunch Aubrey started fussing and I knew she wanted a bottle right away.
Lola knew, too. "Looks like someone wants lunch!"
I froze. Letting Aubrey just starve was out of the question but was I supposed to whip out my plastic container of devil's dust and say, "April fool"?
Aubrey started fussing louder, and within moments was in a full-blown cry. I saw Nina glance at me questioningly and did the only thing I could think of.
I sniffed her bum. "Phew! She's ripe! I'm going to change her in the car before I feed her. Don't want to ruin anyone's appetite." And then I dashed off, diaper bag in hand.
As I sat in the back of my car, feeding Aubrey, I stared down at her face and tried not to cry. What am I doing? I felt like a fugitive. A fake. But I can't lose my friends, I just can't.
I checked into the Motherhood Better Bootcamp portal and nearly everyone has found their way into a playgroup or book club and seems to be having a blast with their new clique. It's too late for me to find a new playgroup and I really, really like these moms.
I know the truth will have to come out eventually, but until then, is it wrong to just enjoy finally having people to talk to?
9 P.M.
Honesty is the foundation for all friendships and it's no different for mommies. Always tell your village what's on your heart. I've found that the soothing, warm water of a sea-salt hot tub makes for a comforting place to get vulnerable.
—Emily Walker, Motherhood Better
I had the best day with Nina today. After the picnic lunch we took the kids to the zoo. Well, I took Aubrey. Nina brought—or should I say "corralled"—her four. I have no idea how she does it. She wore one twin (Finch, I think), used a double stroller for Aiden and Everdeen, and Lillyanne walked.
She makes having one kid look like a walk in the park. It felt almost criminal complaining to her about Aubrey's sleep problems, but she was sympathetic. It was so good to have someone to talk to. Someone who gets it. With David it's like talking to a brick wall. I love him, but trying to get him to understand what motherhood is doing to my brain and body is an exercise in futility.
Nina told me that she remembers what it was like to be a first-time mom and that everything I'm feeling is completely normal. When I'm around her I feel less like a screwup and more like a mom who is just trying to make it through the day, just like them.
Aubrey is starting to really love our outings, too. I don't know if it's because I'm more relaxed, but she was giggling and pointing at all of the animals. She just looked happier. Lillyanne's only six but she was a huge help. When I was changing Aubrey, she reached under the stroller and handed me wipes just when I needed them. Maybe there's something to this whole have-more-than-one-kid thing.
I know I need to come clean about not exactly being a breastfeeding mom sooner than later, but...we're having so much fun together.
* * *
When we got back home, Aubrey was wiped out and slept for two hours. While she dozed, I chopped tomatoes and diced onions for Kristen's homemade pasta sauce. Turns out she's a chef. I told her about my kitchen fiascos and she assured me this one is foolproof. By the time Aubrey woke up it was done, and my house smelled like a basil wonderland. For the first time since I can remember, David went back for seconds at dinner. He's even taking the leftovers to work for lunch.
I wish I could have enjoyed the meal as much as he did. Sure, the sauce was great, but each bite just reminded me how much I need my new friends and that it's all going to end, probably terribly, any day now.
While Aubrey splashed around in the bath, I realized that for the first time in a long time, I actually felt good about myself. I didn't feel like a failure. I felt like a normal mom and was actually enjoying the days, not just getting through them.
As I watched Aubrey's chubby hands slap the water, I made a decision. I had to fight for my friends. I was not going to let them slip away from me. Whatever it took, I was willing to do it. Maybe, just maybe, I could prove that, even though I'm not exactly who they thought I was, I was still a really good person and fun to be around.
David put Aubrey to bed so I had a few minutes to write my wrap-up for the Mama Village Challenge.
Hi everyone. This week was incredible. I'm proud to say that I made a group of great friends! I'm loving getting to know each of them personally and feel like they're really starting to get to know me.
Xo, Ashley
Friday, February 22, 1:30 P.M.
Aubrey just went down for her nap. I had the most incredible morning with the La Lait moms.
I arrived at the meeting at 9:45 a.m., fifteen minutes before it officially began, and helped Lola set up. Aubrey was snug as a bug in a rug in a baby carrier Nina lent me the day before.
"You're really quiet today," Lola said.
"Oh, I'm just thinking," I responded, setting up the coffee and cookies.
"Thinking about what?" Lola had stopped working to breastfeed Donovan on the carpet. She patted the area on the carpet next to her. I took a seat.
"I'm just really happy. I never thought I'd have friends like this again after having Aubrey," I said, stroking the top of Aubrey's head as she lay contentedly against me.
Lola smiled warmly. "You've got a tribe now. No mom should be alone in raising children." I looked at Donovan, who was nursing quietly. His face was hidden in the folds of Lola's multicolored wrap, but his fist was wrapped around one of her long strands of crimson hair.
As we sat there together, in the silence of the community center, I felt something I hadn't felt for a long time. Peace. I realized that it wasn't a lack of crafts, my terrible cooking skills, my crushing sleep deprivation, or even David being gone so much that had made motherhood so hard for me. It was not having this. Real friendship.
Aubrey began fussing.
Lola peered over at her. "Someone wants a snack," she said, eyeing me from the side.
"Oh, yeah," I said, fumbling. I pulled out my phone. "My husband just called me. I'll be right back."
As I ran out of the room to feed Aubrey in my car, I knew I'd have to find a way to make this work.
Sunday, February 24, 3 P.M.
When I was a mom of only one, I designed my home after the Montague residence in Romeo and Juliet. Since then, my design taste has changed, but my commitment to making my home a place of beauty, organization and relaxation has not wavered. You'll never see piles of laundry in my family room or toys strewn about, not because I have live-in help, but because I believe your home should be a place you are proud to call yours.
—Emily Walker, Motherhood Better
Only eighteen hours until the next bootcamp video chat. And I could barely contain my excitement, as it was going to tackle something I have tried, and failed, to get under control: my home.
Before Aubrey was born, David and I lived in a tiny one-bedroom condo that could be cleaned from top to bottom in under an hour, probably because we didn't own that much stuff. We had a set of dishes for four people. There were no baby spoons, baby forks, bottles, baby plates, baby bowls, or sippy cups with lids and weird plastic tubey parts I didn't understand practically bursting out of the kitchen cupboards.
Everything was minimalist, which I loved. There was no item that didn't have a place. Magazines went on the rack beside the couch. Shoes were all lined up in the entryway closet. My bags hung neatly in the bedroom wardrobe.
Now? Aubrey's five pairs of shoes are strewn in a messy pile in front of the door. My diaper bag is lying on its side like a drunken college student in the entryway with a trail of individual infant socks, an empty package of travel wipes and two canisters of sweet-potato-flavored puffs falling out of it. We traded our gorgeous small circular throw rug and slate coffee table for a huge, interlocking, brightly colored foam mat—the kind I said I would NEVER have in my home. All it took was imagining Aubrey hitting her head on a hard edge or the hard floor for all of our beautiful things to go on Craigslist.
When we got married, I said everything in our home would be charcoal and cream. That was our official color scheme. I rubbed a bare foot along the hard plastic of the foam mat. Green, blue, yellow, and red. Primary colors. That's my color scheme now.
Plopping myself on the floor beside Aubrey, I had to admit that our flooring was pretty comfortable. It was like living inside of a children's play center, except with less stomach flu. Aubrey noticed me beside her and took the opportunity to attack my head. In three seconds my hair was damp with drool.
I pried her baby orangutan arms off my head and rolled her onto her tummy. She giggled gleefully as I blew raspberries into her back.
Within a few seconds, Aubrey's laughter dissolved into fussy yelps as she tried to flip onto her back.
"You need tummy time, Aubrey! How are you going to learn to crawl?" I crooned while placing her back on her front.
She screamed at me and waved her arms pathetically, like a beached baby sea lion, before pushing herself onto her back again.
"How can a baby have such a strong will?" I asked her, hoping the self-satisfied glint in her eye was just a figment of my imagination and not a glimpse into her future stubbornness.
Joy posts videos of crawling Ella almost every day now. I'm sure her friends must love the five-minute-long montages of my niece set to classical music.
"Has Aubrey started crawling yet?" she asked me the last time we spoke.
"Not yet, but she sits up and is rocking. She will any day now." I tried to sound confident.
"Don't worry. Some kids are just late bloomers. Maybe if you cleaned up your living room a little you'd have more space for her to move around," was my sister's response.
Double whammy. Note to self: Mail Joy an envelope full of glitter.
She's not all wrong, though. Currently, there are four full baskets of clean(ish) laundry, an exersaucer, a bouncy chair, four throw pillows and a ton of other miscellaneous goods on my living room floor.
I checked my phone's clock.
Only 17.5 more hours until I learn how to finally be someone who is proud of her home.
Monday, February 25, 10:30 A.M.
My interior designer and I worked together to give each room in my home a personality of its own. You spend 85 percent of your life within the walls of your house; you should love every square inch of it.
—Emily Walker, Motherhood Better
The Motherhood Better Bootcamp call had been at 9 a.m., a full hour earlier than normal. Emily wanted us to catch her at home before she left for the studio to film her show.
"Good morning, mommies!" she chirped from the screen. Even in pink sweats and a hat with her pink EW logo on it, she looked fabulous. "I hope you guys had fun with your mama village last week. Now are you ready to tackle the Home Challenge?"
The other moms smiled politely. I wondered if any of them were doubting that they could whip their cluttered, overridden-with-toys houses into shape in just one week.
Emily adjusted her hat and continued, "Your home isn't just a structure, it's your family's safe and sacred space. It's your temple. This week you're going to learn how to treat it as such."
Temple? I looked around my living room where I was sitting barefoot and cross-legged because the laundry baskets left little space to stretch out.
"I've left some instructional guides for you in the portal, but right now, I want to show you around my house! Ready for a tour?"
Emily's camera rose as she stood. She shifted her computer to face out, and a sparkling white room filled the screen. Luxurious eggshell suede couches, a cream rug, glittering chandelier lamps, blue and gold porcelain accent vases...did children really live in this house?
"This is the formal family room. It's where I receive guests. My children love to play in here."
Play what? Sit Still and Try Not to Break Anything?
"Let's move on to the kitchen!"
The camera panned down a long hallway with smooth oak hardwood floors and family photos hanging on the walls, and then opened into a rustic, high-ceilinged kitchen. Pots and pans hung from the beams over the chef's kitchen. Stainless steel appliances with not a trace of fingerprints twinkled as they caught the sunlight.
"The kitchen is where my family gathers several times a day not just to feed their bodies, but their souls."
Over the next half hour, we saw every immaculate room in Emily's house, including her children's themed bedrooms (Unicorn Wonderland, Horses Galore, Nighttime Whimsy, Forest Magic and Beyond Space and Time), her bedroom—it looked straight out of Arabian Nights—the den, her many bathrooms, her meditation room, her dining room, her craft room, her office, her garage and the backyard.
At the end of the tour, there was just jealous silence.
"I hope you got inspired to create a truly beautiful living space of your own. As always, if you need any direction, consult your copy of Motherhood Better, chitchat in the portal, or send me a message. Love you guys!"
Consult the portal? Are there a few hundred thousand dollars in there for me to make my home look like a magazine spread?
Ugh. I clicked through to the message boards and opened the Home Challenge Guide Emily had written for us.
"Ready to start? First I'm going to teach you how to clean up your space, naturally. Check out these recipes for homemade cleaning products!"
I snapped my computer shut. As I looked at Aubrey, who had fallen asleep in a pile of mismatched socks, I knew it: this challenge was going to end me.
5 P.M.
Keeping your home clutter-free should be a priority for all mothers. When a home is tidy and organized children are far more relaxed and better behaved. If you don't have live-in help, spend 40 minutes a day picking up and keep all toys out of sight.
—Emily Walker, Motherhood Better
David should have already come home. Balancing a still-pajamaed Aubrey on my hip, I stood in front of the stove and stirred the rice, soy sauce, cubed chicken and broccoli concoction I'd thrown together half an hour earlier. If only the recipe website I'd used had been more specific about cooking the rice before mixing it with the other ingredients. I hoped David didn't mind it a little al dente.
Other than my blasphemous attempt at stir fry, I felt more put together than normal. Aubrey'd had a great nap and I'd already done the obligatory pre-husband-coming-home speed clean. David and I had an unspoken rule that he wasn't allowed to see the state of our home before I could take it from Dumpster Rat Wedding to Somewhat Livable. It wasn't about my feeling like I had to show off for him, it was about my dignity as a person. I couldn't let him see how I lived during the day.
My phone buzzed on the counter. It was David. Be home in 20 min.
Put all the toys back in their bins.
Clear the dining room table of breakfast plates, milk splotches, dirty bibs, baby socks, empty bowls with dried-up baby-food goo and junk mail.
Sweep the Funny O's off the floor.
Wipe my hair off the bathroom floor (seriously, it looked like an infestation of seaweed on a dried up beach).
Pick up the clothes that I'd left all over the house during the day.
Hastily make our bed.
Wipe down the kitchen counters.
Spray some all-purpose cleaner into the air to give the impression that someone who lives here cares.
This is the type of cleaning that affects the top layer of the house only. If you were to open a closet door, an avalanche of random goods would come bursting out, revealing me as the fraud I am. To move any appliance half an inch to the left or right would expose a grime outline like some sort of waiting-to-be-filled-in coloring sheet. Peek into a linen closet and you'd find bunched up fitted sheets, towels strewn about and random panties.
A quick once-over of the interior of my home would fool you into thinking that someone conscientious and domestically proficient resides within these walls, but no. Anyone with an eye for detail, i.e., my mother-in-law, would know better in a matter of moments.
I've gotten really good at the speed clean over the past few months but the Motherhood Better Home Challenge is all about making real change. I don't want Aubrey to grow up in a pigsty, embarrassed to bring her friends over to the house.
* * *
Flash-forward to ten years from now...
Me: Aubrey, why don't you have a sleepover this weekend?
Aubrey: (taking my hand) I'd love to, Mom, but the other parents won't let their children spend the night here on account of the... (She gestures around the room at the laundry pile that is now to the ceiling.)
* * *
No. I needed to get this under control now. Tomorrow I tackle the clothing situation that is haunting me like some kind of 100-percent-cotton phantom of the opera.
I shifted Aubrey onto my other hip and mixed our sorry dinner some more.
"All it needs is a little love," I sang to Aubrey as I brought a mouthful of the now-congealing goo to my lips, blowing before tasting it. The gummy rice was somehow still hard in the middle. I felt the grains crack under my molars.
Aubrey winced, "Yucky."
She wasn't wrong.
Tuesday, February 26, 10:30 A.M.
"What have I gotten myself into?" I whispered. There I sat, smack dab in the middle of my bedroom, surrounded by no less than eighteen loads of laundry that represented every item of clothing my family owned. The oppressive cotton and poly-spandex blends formed valleys and peaks, they mingled, socks with ties, panty hose with infant tutus, conspiring against my sanity like rebel forces. The dark wood was completely hidden under the sea of multicolored, wrinkled fabric.
At 9:30 that morning I decided to jump into the Home Challenge headfirst and tackle the first of three of Emily's sub-challenges.
Motherhood Better Mail
From: Emily Walker
To: My Mommies
Good morning from Manhattan! I'm meeting with buyers from Neiman Marcus (hush-hush!) this morning and will have a big surprise for you in a couple of days. But first, as you know, I've divided the Home Challenge into three bite-sized goals that I just know you ladies are going to rock.
Declutter
Deep Clean
Design
Today we're tackling a hot topic: laundry. Are you REALLY wearing all of those clothes? Lay everything out in front of you and get rid of what you haven't worn in the past ten days. Only store pieces that 1) you truly cherish, such as your wedding dress or a piece from the Emily Walker MAMA collection coming out this fall, or 2) you can say with 99% certainty you'll wear again one day—like how the MAMA collection can follow you through all of the stages of motherhood. Do the same for your kids. This challenge is all about making your life and homes LIGHTER! Can you feel it? You're a cloud.
Love you!
Xox Emily
I'd tried earlier that morning to organize Aubrey's closet and was doing pretty well until the crushing nervous breakdown complete with heaving sobs. It didn't happen all at once. In fact, everything was going fine up until I found her newborn socks. Newborn socks that she'll never wear again, to be more specific.
I'd been sorting her clothes into two storage containers: one massive gray one for donating and one medium-sized blue one for keepsake items to reminisce over when I'm seventy or to give to my grandchildren. After twenty minutes, the donation container was next to empty, other than an over-the-top stark white, frilly newborn dress, complete with a scratchy tulle liner and headband that Gloria tried to insist I bring Aubrey home in.
I declined, of course. It seemed cruel to make an infant go from floating within the soft, warm walls of the embryonic sac to scratchy tulle in a matter of hours. The only solution had been to misplace the hideous dress until Aubrey grew out of it.
I'd just thrown the garment into the donation container and was scraping around the back of her closet when I found the socks. Two little yellow fuzzy socks that never seemed to stay on her plucky newborn feet. They were like chicken legs; I remembered how her toes would fray when she cried.
And, oh, how she cried. I'd heard babies cry before and it had never affected me, but her screechy wails sent pangs to my heart in a way that was so unexpected and all-consuming. Sitting on Aubrey's pale pink carpet, I thought about how it seemed like yesterday that I would swaddle her in a white muslin blanket (my wrapping style was rather sloppy and she often looked like a messy burrito) and tug those socks onto her feet. Three seconds later they were off again.
I know they say newborns can't smile and it's just gas, but I swear, every time I, exasperated, put those socks back on her, the edges of her mouth would turn up as if to say, "I don't think so, lady."
As I held the socks, sitting on the floor of her bedroom, watching my now nine-month-old play with her toes that were so much bigger and less chicken-like and more toddler-like, I started to cry. Almost a year had gone by. It was all happening too fast. I can't even remember what it felt like to hold Aubrey as a newborn. All I had left were her socks, and I was supposed to just give them away?
I began to pull out all of her newborn sleepers, blankets and bitty hats. These were not just clothes, they were memories from my first few months of being a mom. I couldn't throw them in a black garbage bag and leave them outside of a donation center on the sidewalk like trash. It's easier for Emily, she has five kids and gets to see the same socks worn over and over. I only have Aubrey and frankly, my plate feels full, overflowing, really.
I added the socks to the Keep pile. And then the sleepers. Then the hats. Then the burp rags, so soft from multiple washings. In half an hour, I'd gone through every item Aubrey had ever owned and not only had I failed to part with anything, I also had a headache from crying.
#Success.
Then I remembered a DIY quilt tutorial I'd seen on Pinterest. Who knew—maybe one day I'd turn all of this into a fabulous, handmade blanket. The chances of that are about as high as me taking up competitive deep-sea diving, but it was the only excuse I needed to put all of Aubrey's outgrown clothes right back in the closet where I found them. At least they were folded now. That had to count for something.
Things went a little better with my own clothes. As I already knew, I owned a separate wardrobe for each of the different versions of myself.
Pre-Pregnancy Me
This person was always trying to improve her body despite being quite hot. She owned pantsuits, fitted sports jackets (that I can no longer button over a wobbly muffin top), skinny jeans for spending the day shopping or reading in a bookstore, matching exercise outfits, bras that wouldn't come close to containing the gals today and cute, teeny-tiny panties that would maybe cover one of my butt cheeks.
Pregnant Me
This person started off cute enough: fashionable, boot-cut maternity jeans and silky tops that were professional but showed off my teeny-tiny bump. Dressing for the beginning of my second trimester was a blast. I had a perfectly round bump that was downright adorable under baby-doll dresses and clingy tops.
Somewhere between the end of the twenty-eighth week and the beginning of the thirtieth, I exploded into a sea creature and grew so large that strangers winced as I waddled past them. Bye-bye stretchy denim, hello yoga pants. Dressing for comfort meant breathable fabrics, dark colors (to hide the food stains) and whatever shirts would cover my rapidly expanding bump.
Postpartum Me
Even if I could fit back into my pre-pregnancy clothes, I wouldn't wear them. My days are spent collapsing strollers, rolling around the living room floor, running errands and foraging for coffee. Pantsuits? Yeah, right. I wear absorbent fabrics because they double as a paper towel. If it looks and feels like pajamas, sign me up. A fashion designer might call my look Sleepwear Chic or Bedroom Casual.
All I could do was stare at my entire adult life represented in skirts, bras and tops. Where to even begin?
Aubrey let out a muffled squeal from under a maternity shirt. I pulled it off her and she beamed. Silly girl. I rubbed the pale blue stretchy cotton between my fingers. This was the shirt I was wearing when I first felt her kick.
"That's enough, little missy," I said, plopping her into her jumparoo hanging in the doorway. She began pushing off the floor with her footie-pajamaed legs, launching herself into the air and then bouncing back again. They really should make those for adults.
I dragged four large storage containers into the room from the hallway. Time to organize.
An hour later, Aubrey was asleep in her playpen and I snapped the last storage container shut. On my bed were six pairs of black stretch pants, eight tank tops, two dresses and four sweatshirts. That's it. That's all I wear. I basically had the wardrobe (but not the body!) of a yoga instructor.
Now the big question: What to do with the two humongous storage containers of clothes that either a) not even a 10-day juice cleanse would get me into or b) are impractical for my life as a stay-at-home mom? Giving them away seems hasty. What if I go back to work?
And my maternity wardrobe cost a small fortune. I bought it before I knew how much formula cost. Even if I didn't intend to get pregnant again, I should at least try to sell it. Yes, that's what I'd do, I decided. Not today, obviously. I'd already overextended myself. If anyone had earned a break, it was me.
I quietly pushed the storage containers into the hall, knowing that David would move them to the garage as soon as he got tired of tripping over them.
All in all, I felt like I'd aced the day. Maybe I didn't get rid of anything, but I did move it all around, which counts for something.
8 P.M.
David was working late again, so with Aubrey sleeping soundly, tuckered out from another splashy bath, I took the opportunity to learn a little more about my Motherhood Better Bootcamp competitors. While we're buddy-buddy on the conference calls, at the end of the day, we all want to take home the $100,000 grand prize.
Based on their Motherhood Better community posts and profiles, I think I know who'll be the biggest competition.
Fiona Martin: mom of three. Despite probably being up to her armpits in diapers, during the craft challenge she learned how to jar fresh tomatoes from her garden and crocheted hats for an entire neonatal intensive care unit.
Janice Paulsen: mom of three girls ages three months, four, and six. She took the body challenge and ran with it. Literally. She completed her first marathon last week and is launching her own line of weightlifting DVDs for postpartum moms.
And last, but not least, Samantha Davidson: mom of two-year-old Henry. I knew her face looked familiar. Samantha's a hugely popular mom blogger. Her website, Homestead Mama, is full of gorgeous photos of her ranch and horses, and her down-home country recipes.
I can't even look at her dishes after 9 p.m. They say her macaroni and cheese changes lives. What is she doing in this competition? Every other pic on her blog is of her beautiful son running through wheat fields in overalls with a red bandana around his neck and a cowboy hat sitting atop his golden ringlets. I read all of her Motherhood Better journal entries and she's completing them perfectly. For the marriage challenge she took it a step further by organizing a massive in-hospital date night for pregnant moms on bed rest. It was catered by a Mexican restaurant and she even hired a mariachi band.
I know I said I wasn't only in it for the grand prize, but I've been thinking of what I could do with $100,000...anyway, it's out of the question for me unless I can figure out a way to make myself stand out—and fast.
Wednesday, February 27, Middle of the Night Sometime / Too Tired to Care
Establishing a sleep schedule is vital, not only for your child, but for your own well-being. Thanks to the Family Bed, all five of my children slept through the night by three days old.
—Emily Walker, Motherhood Better
Aubrey woke up again. That's four times in one night, not that I'm counting. I refuse to look at the clock right now. I don't even want to know what time it is.
I've tried everything to help her teething: an amber tree sap necklace that the woman with henna tattoos on her arms at the health store promised would work like a miracle, aspirin and mouth-numbing cream. I even tried homeopathic remedies, although David said they're practically water. At this point I'll give anything a shot.
Nothing is working. I'm starting to wonder if something more serious is wrong with her. I'm researching online now. Maybe something terrible is wrong in her body. Like a tumor. Here I am, worried about my sleep, when my baby's kidneys are being squished by tumors.
To: Dr. Ross
From: Ashley Keller
Subject: Emergency Appointment
Dear Dr. Ross,
I know it's late, but I couldn't find your home or cell phone online anywhere. I'd like to set up an emergency full-body scan for Aubrey first thing in the morning. She's been screaming all night and something is seriously wrong. Attached are 47 pages of my findings.
Thank you.
Ashley
To: Ashley Keller
From. Dr. Cynthia Ross, Pediatrics
Subject: Re: Emergency Appointment
Hello Ashley,
I'm sorry to hear that Aubrey isn't feeling well. She seemed fine at her last appointment. It sounds like she's teething and possibly going through a growth spurt. I went over your "findings" (which seemed to be links to various blogs and obscure pseudo-scientific medical websites) and would like you to stop Googling her symptoms.
Full body scans are not done on children Aubrey's age, nor does she need one.
I suggest Tylenol and something cold to chew on, like a frozen washcloth.
As for my home and cell phone numbers, I don't give those out to patients. You are free to leave a message at the office or email me anytime. As always, in a (true) emergency, don't hesitate to call 911.
Take care,
Dr. Cynthia Ross
To: Dr. Ross
From: Ashley Keller
Subject: Re: Re: Emergency Appointment
Thank you so much for the advice. Did you happen to check out any of those links? I'm wondering if the connection between dust mites and molar pain have any substance to them? I already purchased the dust mite elimination ray advertised and plan to sweep the whole house with it. They're on sale for $399 if you're interested in one for the office.
If I had your cell phone number it would much easier to just text you the direct link. I would only use it in emergencies like this, and wouldn't give your number to anyone else.
Aubrey's settled down a bit. Most of her crying is done at night. Do you make night appointments? House calls? Like in old movies?
Ashley
To: Ashley Keller
From: Dr. Cynthia Ross
Subject: Re: Re: Re: Emergency Appointment
I don't make house calls or book "night appointments." The article about dust mites was complete lunacy and I hope the dust mite ray comes gold-plated at that price.
Feel free to call the office and make an appointment anytime. I only ask that you not bring your binder of printouts from the internet as they tend to make our visits last much longer than they need to.
Take care,
Dr. Ross
10 A.M.
I credit fresh air, good food and exercise for my children never having so much as a sniffle. Mother Nature is their pediatrician.
—Emily Walker, Motherhood Better
There must be a way to let someone know that their baby doesn't have a dust mite-induced infection without laughing in their face, right? If there is, Dr. Ross hasn't heard of it.
If I wasn't so tired I would have said something like, Excuse me if I don't have more experience with teething, but if you'd heard my child crying you would have thought her internal organs were being disintegrated by the toxic feces of microscopic pests, too.
But I didn't.
We were in the driveway. Aubrey was sleeping in her stroller. There was no way I was moving her. Maybe I could catch some Z's, too. So tired.
11:45 P.M.
For teething pain I highly recommend using aromatherapy. My babies love the smell of lavender and jasmine diffused through Baltic sea water. Who needs big pharma when we have precious oils?
—Emily Walker, Motherhood Better
Aubrey woke up again. I brought her into our room even though Joy's #1 rule of parenting is "Never let them into your bed." Aubrey was sleeping at my side now, and I had about six inches of space so I figured I'd just stay awake until morning.
I couldn't go back to sleep if I tried. The type of shrill yell she woke me up with sent about fourteen gallons of adrenaline into my bloodstream. David, of course, slept peacefully through the whole thing. Would it be wrong to heat a fork and poke him with it? Kidding.
Thursday, February 28, 5 A.M.
I was beyond exhausted. Over the last few days I'd probably gotten eight hours of sleep total. Aubrey would only doze when I was holding her. I'd tried every over-the-counter remedy, every hippie remedy and everything in between. I even burned sage in the corners of her bedroom to ward off bad energy. That was Joy's idea.
"Have you considered taking her to a channel to see if there's something in a past life upsetting her?" was another bit of Joy's brilliant advice.
"No, but thanks for the tip."
"It's all so strange. Ella sleeps soundly. So does George."
The worst thing a mom can do is brag when you're complaining.
"Oh, you're struggling to lose ten pounds? I can't seem to gain weight!"
"Oh, you're having financial problems? We can't figure out whether to buy a yacht or another summer home!"
So there we were, at 5 a.m., once again standing in the kitchen, Aubrey in her pink-and-white footie pajamas and me in one of David's old college T-shirts and sweatpants. The sad fact was that I was dressed for the day. One great thing about being exhausted is that you don't care what anyone thinks of your outfit choices.
Aubrey leaned into my chest and I pushed the black start button on the coffeemaker while I hugged her to my body with my free arm. She nuzzled. She was obviously tired—why wouldn't she sleep? Was this normal?
Facebook Status: I remember when I thought eight o'clock classes were too early. Zzzzzzzz.
The coffee machine sizzled as it finished pouring the steaming black liquid into my Best Mommy Ever mug. David had surprised me with it in the birthing center. Wishful thinking, I suppose.
I dumped in all the vanilla creamer that would fit into the cup without splashing out and stirred it quickly with my finger.
Toting my coffee and daughter, I shuffled over to the couch and flipped the TV on to some home makeover show. It was always entertaining, seeing a dilapidated basement go from unfinished baseboards and exposed wires to an impressive, impeccably designed playroom.
I took a greedy sip of my coffee. Sweet and delicious. What would I do without this comforting blend of caffeine and sugar? Motherhood would be absolutely impossible without it. Suddenly, I realized that with all of Aubrey's sleep issues I hadn't checked in to the portal for over forty-eight hours. I wonder what I'd missed. Probably Samantha Davidson sharing photos of a baby calf she delivered with her own hands or Serena Hossfield posting a recipe for homemade toothpaste.
There was a message from two days ago, but it was from Emily herself! What did I miss? I shifted Aubrey, who was now sleeping, in my arms, and moved as close as I could to the screen. What had she said?
Motherhood Better Message:
From: Emily Walker
To: <<Entire Group>>
Hello ladies! I'm loving your posts about the Home Challenge. Samantha, your hand-reupholstered dining room set looks fantastic! Bravo! And Heather, the canary yellow paint is just what your kitchen needed. It looks full of sunlight!
I have a surprise for all of you. As I hinted during our last web call, I'm launching a new line called Emily at Home that will feature beautiful and practical items from furniture to hand towels. To make this challenge a little more exciting, I'm sending my right-hand man and chief designer, François De La Rose, to each of your homes for a one-on-one consultation! He'll help you use what you have, along with a few complimentary pieces from my line, to finish out this challenge with a bang!
I've posted appointment assignments below. If you need to reschedule, let me know ASAP, otherwise I'll assume we're good to go.
Happy designing!
Love and Hugs,
Emily
I scanned the bottom of the email with all of the ladies' names, cities and dates until I found mine.
Ashley Keller....what? That date can't be right. I opened my computer's calendar and sure enough...today. François De La Rose was coming to my house today. In three hours, to be exact.
I looked down at Aubrey, who was snoring contentedly in my arms, and then up at the pile of underwear and socks in the middle of my living room, three days' worth of mail, one day's worth of breakfast and a week's worth of snack remnants on the dining room table. A trail of granola bar littered the entire floor. The kitchen sink was overflowing with dishes. My bedroom was a mess. Aubrey's bedroom had toys everywhere and this famous French interior designer, who reports directly to Emily and influences who wins the Motherhood Better Bootcamp, would be here in three, no, two hours and forty-five minutes.
Well, shoot.
I crept up the stairs and gently laid Aubrey down in her crib. She gave me two seconds before she stirred awake and began to cry softly. I picked her back up knowing that she'd be in a full-blown howl in minutes. The only thing left to do was to speed clean. With one hand, naturally.
With Aubrey in one arm and a garbage bag in the other, I began throwing things into the bag. It made no difference whether it was clothing, a paper plate, socks or a checkbook, it went in the bag. I could sort it out later. For now, I had to convince François De La Rose that I was not the maternal version of Oscar the Grouch.
An hour and six bags hidden in my closet under a comforter later, the house looked deceivingly put together. Aubrey still lay comfortably in my arms, even though I'd had to switch her from side to side numerous times as my cut-off circulation turned all sensation in my arms to pins and needles. I rushed over to the sink. The dishes. The dishwasher was full so I rinsed the cups and plates before stacking them in the oven.
The house looked cleaner than it had in months and I still had a full hour to get dressed.
I was halfway up the stairs when the doorbell rang.
"Please be the mail, please be the mail," I murmured to myself, running toward the door.
I swung it open and standing before me was not the mailman, unless the mailman was a four-foot-three, tanned and Botoxed Frenchman wearing an all-white satin suit and crimson crocodile shoes with a matching red bow tie, who traveled with a full camera crew.
"Allo, mama!" the man said, waving his hands with flourish. A camera flashed and the light blinded me and caused Aubrey to stir. "Je m'appelle François De La Rose!" he said, entering the house while looking madly around.
The crew of three burly men dressed in black work pants and black short-sleeved shirts, and one mousy-looking intern in a wool skirt and collared T-shirt covered with a dark vest, followed.
I followed François as he made his way into the living room. He looked around with a troubled expression on his face, as if the place were on fire or crawling with poisonous snakes.
He remembered I was there and turned to face me.
"Chérie. You must be Ashley," he said sweetly before kissing me on either cheek. He inhaled sharply, "And this precious bébé, elle s'appelle comment?"
He gently tapped Aubrey, who was fully awake now and staring at the men with lights and cameras, on the head.
"She's Aubrey. It is so nice to meet you! Thank you for coming! Can I get you anything? Coffee? Tea? Wine? I would have had something prepared but..." I rambled on.
The camera crew stayed close, focusing the lights and microphones on us. Their lights felt like a laser beam. I had no idea this would be videotaped. Could I be any less prepared? I smoothed the front of my T-shirt and sucked in while trying to remember the last time I had washed my hair.
"I'm so sorry, I was just about to get in the shower—" I blubbered, wishing they would turn the damn cameras off for a minute.
François held one hand up. "No, sorry. You are a busy mama of..." He looked around the room as if something was missing. "How many kids zoo you have?"
I felt my face get hot and coughed self-consciously into my hand. "Just the one. I have one child."
François's eyes grew large and he laughed loudly. "One? Mais non, surely there are three or four children who live in zee home. Whose things are zese?" he asked, gesturing at the overflowing toy bin, walker, bouncy chair, exersaucer, sippy cups and piles of baby clothes. "Zoo you run a daycare?"
I shifted from foot to foot. "No daycare, just the one."
François gestured around the room, unable to comprehend what I was saying. "Mais surely, you are hiding some extra children somewhere?" He lifted a couch cushion, perhaps hoping to find triplet three-year-olds, but all he discovered were three stale French fries and a heavy dusting of crumbs.
He jumped as if the furniture food had startled him. "OH, MY!"
Forcing a smile, I lowered the couch cushion and gestured for him to sit directly on top of it.
François sat next to me, shifting as if he could feel every hard morsel under the cushion a la Princess and the Pea, and took my hand, "I see now why you have joined zee challenge. But do not worry, chérie. François is here to clean up your space."
One hour and frantic half-French, half-English phone calls to an interior designer, professional organizer and commercial cleaner (François thought a domestic cleaner might get overwhelmed by my home) later, everything was in motion for my home to go from raccoon Dumpster party to gorgeous family home. The cleaner was coming tomorrow morning, followed by the designer, then the organizer. They weren't doing anything drastic, but "optimizing my space."
I was overwhelmed with excitement.
"Thank you so much, François," I gushed.
Without answering he bent down and pulled a black binder out of his satchel. "Wait, mademoiselle, zere is more." He smiled devilishly.
Tickets to Jamaica? Free babysitting for life? A sister wife?
He opened the binder. The first page was a glossy insert with Emily Walker Home printed in white calligraphy.
"Emily Walker has arranged for all of zee women to preview the Emily Walker Home line," he said in a hushed tone as if the CIA were listening in.
My heart skipped a beat. I'd get to have the Emily Walker line before anyone else? Imagine the Facebook posts. Joy would perish from jealousy.
He handed me the binder and I began to flip through page after page of stunningly beautiful furniture.
François leaned over and turned to a spread. "Allow me. Zis one would look beautiful in your family room."
Before me was a beige leather couch, loveseat and recliner, a coffee table and an entertainment center with loads of hidden storage called the Verdanza Package. It was amazing. I felt tears spring into my eyes. So this is how celebrities feel.
"Yes. I love it. I'll take it," I whispered.
François clapped his hands. "Perfect! How would you like to pay?"
I blinked. "Pay?"
"Ah, chérie, oui. Your designers and organizers, and a few pieces are free, but zee entire Emily Walker Home line is being offered to you before the general public at wholesale price because you are in zee...bootcamp."
"Which pieces are free?"
François flipped through the catalog and pointed to a set of three throw pillows. "Zere."
I held my breath. There was no way, even at wholesale prices, I could afford a new living room set.
"How much is it?"
François flipped to the next page.
Verdanza Package: $1,025
That's it? I thought. You can't even buy a couch in some stores for that. This is brand-new designer furniture at prices that will be gone in three months. The pieces themselves will probably sell out. Yes, David is worried about money, but he's always worried about money. That's never going to change. Anyway, he's probably securing the DentaFresh account right now. If I don't buy this set I'll be wasting money, throwing it down the drain.
Furniture is also a great investment. It's so well-made it will last forever. The holidays are coming up. I'd love to host everyone and see the looks on their faces when they see such a chic collection in our home.
François cleared his throat. "Would you like to call your husband?"
I exhaled sharply. A year ago I was managing million-dollar client accounts and now I'm some stay-at-home mom who has to call her husband before making a purchase? Absolutely not. I'm a modern woman. Just because I'm not making the money doesn't mean it doesn't belong to both of us. We're both contributing. If I didn't take care of Aubrey, he wouldn't be able to work. I don't need his permission to spend our money. I'll just use the credit card he doesn't know about.
"Is Visa okay?" I heard myself ask.
"Absolutely."
François copied my card information and promised to send me a receipt by email. The furniture is set to be delivered a week from tomorrow.
Before leaving he looked around again, perhaps expecting a busload of children to come running down the stairs. I really do need to pick up more. The new living room set is really going to inspire me.
11 P.M.
I just checked my email for the receipt from François.
6-piece Verdanza Package: Emily Walker Home
Ashley Keller
Visa 4875-****-****-****
Total: $8,025
My entire body morphed into an ice cube. Eight thousand and twenty-five dollars. There had to be some mistake. This was someone else's order. I scanned the itemized bill.
3-section couch: $2,500
Loveseat: $1,025
Recliner: $1,025
As I kept reading, no, no, no, no, echoed in my head. The price François had shown me was for just one piece, not for the set. How could I have been so dense? I didn't even know if I had that much credit available. I immediately hit Reply to tell François to cancel the order, but something stopped me. If I did, Emily would find out, which would mean not only would I be humiliated in front of my idol, I'd lose any chance of winning the grand prize. I closed the email window.
What was I going to tell David?
Nothing. I was going to tell him absolutely nothing. He was already worried about money; this would send him over the edge and he'd demand everything go back immediately, which would make all the hard work I'd done in the Motherhood Better Bootcamp a complete waste.
I had to deal with this myself. Either I'd win the prize money or I'd pay it off without him knowing. All I needed was a little side money. How much was $8,025 anyway?
A lot. It was a lot.
Oh, crap.
Friday, March 1, 4:45 P.M.
I spent the entire day trying not to think about the fact that I spent almost $10,000 on furniture behind my husband's back. That's the price of a car. Not a brand-new car, but a good one. That money could have gone toward our mortgage. I remembered David's reaction to the dress I bought for our date that never was and tried to picture his face if he found out about the furniture. He'd blow a fuse. What if he walked out of the house and just drove away? He'd never do that to us...to Aubrey. As I popped a frozen lasagna in the oven, I tried to snap myself out of the fear cycle. "It's only money," I said over and over.
"Ma-nee. Ma-nee," Aubrey repeated from her high chair. She was starting to talk a lot more lately. Note to self: Be careful what I say around her.
I heard my phone vibrate against the countertop.
David. Going to be late. Also, I'm taking my car to the shop tomorrow. Transmission. Oil change. I'll need yours for work.
Well thanks for the notice, I thought. Just because I'm a stay-at-home mom doesn't mean I actually stay at home all day. Use of a vehicle would be nice. Also, François and his team are coming over to give the house the grand makeover I can't afford. I'd planned to be out all day. Without a car what was I supposed to do? Hang out in the backyard with Aubrey? Set up a tent at the mall?
I quickly fired off a text to David explaining my predicament (minus the furniture we couldn't afford part).
He responded five minutes later with a simple, Problem solved! My mom will pick you up at 9 o'clock and take you to her house.
WHAT? Yes, she may have come through for me with dinner before, and I may have said a few times that I wanted to get to know Gloria better outside of the context where she tells me things like "Your house sure is full of stuff," and "Any thought on when you'll be getting the baby some proper shoes instead of those overpriced granny slippers?" But an entire day?
I was just about to call David when he texted he was going into the DentaFresh pitch. I wished him luck. Now wasn't the time to stress him out. I slammed my phone down on the counter.
"Crap." An entire day with Gloria.
"Cwap. Cwap. Cwap!" Aubrey yelled, hitting her high chair tray to punctuate each word.
I really needed to watch my language.
What was I going to do? There was only one thing I could do. Eat my feelings; tuck them safely into my stomach and thighs. I popped a corn chip into my mouth and washed it down with a generous splash of pinot noir out of a lidless sippy cup.
Aubrey giggled at me from her high chair.
"Tomorrow, we're going to grandma's house." She clapped her hands gleefully.
Saturday, March 2, 8:30 A.M.
I'd spent the last three hours cleaning the house from top to bottom. No more French fries in the couch. I even cleaned out the high chair and discovered that Aubrey has never eaten anything, ever. She's been tucking food away like a rodent under the plastic cushion of her chair. I swear I found enough food to feed a small nation for weeks. But that's all gone now.
Joy called me while I was a tornado of all-purpose cleaner and rags.
"You actually cleaned?" she asked in an irritated tone. As I predicted, she was teeming with jealousy once she found out (via my dramatic Facebook post—the one I'd made before knowing what I'd actually spent) that I'd ordered the Emily Walker Home line and was getting my home redone. Since I'd been accepted into the Motherhood Better Bootcamp, Joy had been downplaying it as my "little support group." It felt good to finally have something over her.
"Yes, I cleaned. I do it all the time," I answered, out of breath from trying to remove a month's worth of grime from inside the microwave.
"So, what time is Gloria picking you up?" Joy knew how to take the buzz out of any situation.
Gloria. I'd been trying not to think about the fact that I'd be spending the entire day with my mother-in-law.
"Hopefully never o'clock. Are you sure you can't come get me?" I really must have been desperate if I was begging my sister to let me spend the day in her Stepford-land.
"Like I said, I'm making the drive up to see Mom with Ella. We're going to see Veggie Friends on Ice."
I already knew that. I'd tried, and failed, to get tickets to the show even though the televised version makes my ears bleed and the three-hour drive to the arena and back with Ella sounded like pure hell. Anything to avoid the awkward afternoon that lay ahead of me. But they were all sold out.
"Fine. Abandon your sister in her time of need."
Joy huffed. "Oh, stop being so dramatic. Maybe you'll learn something."
I started to say, "What's that supposed to mean?" but Joy cut me off.
"Ella needs a change. Talk to you later!"
As I clicked off, the doorbell rang. Of course Gloria would be early.
I picked up Aubrey from her playpen and held her in front of me like a bulletproof vest. I swung open the door and was surprised to see a team of five women in crisp pink cotton dress uniforms with white aprons holding buckets full of cleaning supplies.
"Happy Maids to the rescue!" one sang.
Another chimed in, "We're happy maids, we love to dust. Get a sparkling house without the fuss!" she belted out.
Aubrey shrieked with happiness at the impromptu musical.
"Wow! That's...something," I said. "Come in, come in." I invited the barbershop quintet inside and they immediately spread out in all directions with mops, buckets and spray bottles filled with a rainbow of colors. I heard water running in the bathroom.
"Okay then, let me know if you need anything..." I'm not sure if any of them heard me as the only two in sight were already sweeping underneath the couches and vacuuming the drapes in the living room.
Suddenly I felt a tap on my shoulder. I turned around and a cheery-looking Happy Maid was standing there, holding a business card.
"I'm Mary! I love being a Happy Maid! We'll be in and out in an hour, Mrs. Keller," she practically sang before running off into the kitchen.
The doorbell rang again. This time when I opened it, standing in front of me was an impossibly tall, slender woman in brown slacks and a T-shirt from the concert of a band I'm probably not cool enough to know. Over the T-shirt she wore an expensive-looking caramel leather jacket with brass buttons. Her hair was in tiny black braids all the way down her back. She looked oddly familiar.
"Hi, I'm Ashley Keller." I stretched out my hand. Aubrey babbled on my hip.
"Hi, Ashley, I'm Shelly Harbor," she said, studying my porch.
Shelly Harbor! The interior designer to the stars! The brains behind every celebrity baby nursery was about to enter the aesthetic disaster I call my home. I gulped.
"Oh, my goodness, Shelly! I'm a big fan. I love your work!" I couldn't believe she was here. In the flesh. A TV person who rubs elbows with famous actors every day. I bet she just came from a mansion with twenty-foot ceilings. My home was going to look like a campground compared to what she normally deals with.
"It's nice to meet you," she said sweetly, entering the house. She carried a white suede clutch with gold accents that somehow paired perfectly with her slacks and T-shirt. Even in white ballet flats she was so glamorous.
"Can I get you anything to drink or eat? Breakfast?" I asked. Yeah, Ashley, she wants some eggs and orange juice. Get it together. Pretend like you interact with people on a daily basis, I thought.
She smiled. "I'm fine. It's so great to meet you. Emily sent me the photos from your home and I think there's a lot we can do here."
It was only then that I remembered that I'd sent in photos of every room as part of the bootcamp contest entry form. There was a slight possibility that I'd edited out a little bit of the clutter. If Joy can Photoshop her kid's lashes, is it so wrong to make a little laundry disappear?
Shelly sat down at the kitchen table and opened up a sketchbook with all kinds of collages from magazines. Two feet away from us a Happy Maid was spraying and wiping down the cabinets. We're supposed to clean the cabinets?
Shelly barely seemed to notice, but I found it tough to stay focused with all of the excitement.
"Your home is already beautiful, and the paint looks recent. All that's missing are livable storage spaces for things. I'm thinking a modern country look updated to suit a growing family. How many kids do you have?"
Not again. I shifted Aubrey from one knee to the other. "Just the one."
Shelly touched her face. "Oh... I thought from the photos..."
Apparently I hadn't edited ALL of the clutter out.
"She has a lot of toys."
Shelly smiled kindly. "I'm sure it's normal. You should have seen Emily's house before I redesigned it." She laughed.
Before she redesigned it? I thought Emily did all of her own interior design.
I cleared my throat. "Doesn't Emily—" But I was interrupted by the beeping of a truck backing up.
Shelly stood up. "We have a surprise for you, Ashley! Your Emily Walker Home furniture is coming in today and we threw in a few extras. You're going to love it."
I felt a bubble of excitement begin to rise into my throat. It was followed by a bubble of dread. Who knows, maybe I'll win the lottery...
The doorbell rang again.
Shelly stood up. "It's showtime!"
I swung the door open again and there was François. I was relieved to see that there was no camera crew this time.
"François!"
"Allo! I just wanted to pop by and help out any way zat I can!" He pushed past me and hugged Shelly. Of course they'd know each other.
"Did she tell you zee good news?" François said while pulling a little black-and-white striped handkerchief out of his lapel to dab at his brow.
"Yes, the furniture is here! I'm so excited!"
It was then that I noticed François had brought a guest who was still in the doorway. He was tall, in his fifties and was wearing a gray suit and tie. His formal appearance was in stark contrast to Shelly's rockstar glam and François's French chic looks.
"Hello, I'm Ashley." I reached out my hand and he shook it curtly.
François cut in. "Ah, yes. Ashley, I want you to meet Dr. Simpson."
Dr. Simpson stared at me as if he was trying to figure something out. He noted the flurry of cleaning ladies running around in dresses and nodded.
"How brave of you to let them into your space," Dr. Simpson said, nodding toward the Happy Maids. "How are you feeling about this?" He removed a notepad and pen from his jacket pocket.
"Excuse me?" I asked, puzzled.
François touched my elbow. "Is zere somewhere we can sit down?"
"Sure."
Shelly coughed nervously and then excused herself. "I'm going to help the delivery men...good luck."
I led Dr. Simpson and François to the couch where a Happy Maid was using a broom to hit toys out from under the recliner. A sippy cup filled with what had probably been milk at some point came shooting out and hit the wall, causing the top to fall off and a cottage-cheese-like substance to come spraying out. I was mortified.
I stood to help. "I'll get that." But the Happy Maid just waved me away and began cleaning it up with gloved hands.
At the sight of her forgotten cup, Aubrey tried to leap out of my lap and slurp down its rotten contents.
"No, Aubrey, yucky." I distracted her with a stuffed octopus with mirrors on each tentacle.
I looked up to see Dr. Simpson and François staring at me. François had a look of abject horror on his face. It's probably not every day he sees homemade cheese spray all over a wall.
Dr. Simpson and François sat on either side of me.
François shifted nervously. "Ashley. I brought zee doctor here after seeing your condition yesterday," he spoke calmly, as if talking down a toddler holding a Sharpie.
"What condition?" I asked, while Aubrey pulled my hair.
I looked at Dr. Simpson whose presence was starting to feel more and more looming, especially with him studying my face as if I were a specimen under a microscope.
The doctor cleared his throat. "Ashley, being a hoarder is nothing to be ashamed of. I'm here to see if we can make some breakthroughs today."
I choked on the air and burst out laughing. "A hoarder? I'm not a hoarder! Would a hoarder's house look like this?" I gestured around the room and quickly figured out that while it looked clean to me, three laundry baskets of clothes, an entire wall of toys, and the recent cup o'curds weren't helping my argument.
"No one eez judging you. We only want you to not live in your own filth." François nodded patronizingly.
I sputtered, feeling insulted. "Okay, look. I buy my daughter a lot of toys but I'm not a hoarder. Dr. Simpson, feel free to tour my home and see for yourself."
Dr. Simpson nodded without saying a word as if he were witnessing massive denial.
Suddenly a Happy Maid holding a large garbage bag was standing in front of us.
"Mrs. Keller, what would you like to do with this?" Oh, no. It was one of the "hurry up people are coming" bags from my bedroom. To my absolute shock she emptied the bag right there on the living room floor. Dr. Simpson, François and I stared at the foot-high pile of underwear, solo socks, candy wrappers, a wine bottle or two, stuffed animals and other random goods.
I set Aubrey on the floor and began hurriedly tossing items back into the bag.
I looked up at Dr. Simpson. "I was in a rush to clean." I swiveled my head to the Happy Maid whose ever-present smile had slightly faded. "I'll take care of this."
It took half an hour and a tour of my home, but I finally convinced Dr. Simpson and François that I wasn't a hoarder, just very bad at home management.
"Ah, so you are just very messy, zen!" François declared happily.
"Exactly!" I agreed.
François took my hand "I'm so, so sorry, Ashley. I was simply worried," he explained.
"It's quite alright," I said, feeling both embarrassed and relieved. At least now when David complains about the house I can say that a psychiatrist signed off on it.
"If you ever want to get to the root of your issues, feel free to get in touch," Dr. Simpson said before handing me his card.
François and I bid Dr. Simpson adieu. When we closed the door I gave him a look.
"I am so sorry, Ashley. I just had to be sure," he sputtered.
"It's alright," I assured him. He probably just hadn't seen many homes cared for by first-time moms with an Amazon Prime account. Which led me to wonder. What did the other moms' houses look like?
"Am I the first bootcamp mom you're visiting?" I inquired.
"Mais no, I have already completed five home transformations!" I gulped. That means he had seen other houses and mine was the worst.
"And my house was the messiest so far?" I squeaked.
François tapped my shoulder the way someone would try to comfort a potentially volatile person.
"Zere, zere, Ashley. It's not a competition."
Actually, it was. And $100,000 plus my pride was on the line.
François puttered off to consult with Shelly about the placement of the new furniture. I couldn't bring myself to look at it quite yet. Not when it symbolized the potential destruction of my husband's trust in me. As I walked upstairs to change Aubrey, I passed a Happy Maid pushing my bed away from the wall to vacuum. We're supposed to do that? Move furniture to clean?
Once Aubrey was changed, I packed her diaper bag and sat on the front porch with her while she devoured a bag of crackers. It felt so weird to have people in my home. François assured me that he would stay until the last person left and lock up. "You are going to be dazzled when you return." I had to admit that I was excited.
Aubrey shoved another cracker into her mouth and greedily gummed it until it dissolved.
"She might eat more at meals if she didn't snack so much," a voice said. I didn't have to look up to know who it was.
"Hello, Gloria." I picked up Aubrey and handed her to Grandma.
Gloria was dressed resort casual in white capris and a brightly colored, flowing button-up top decorated with a tropical jungle print complete with several toucans. Her large white sun hat was tied under her chin.
Aubrey screamed happily as Gloria nuzzled her.
"My sweet girl! What are you eating? Oh, you're so hungry! Did you have breakfast? You feel lighter. Does she feel lighter to you?"
She bounced Aubrey up and down like a melon.
"She is a little bit lighter but only because I'm starving her," I joked dryly.
Gloria pursed her lips. She never did appreciate my sarcasm. "Are we ready to go? I can't wait to spend the day with you!" she squealed, looking at Aubrey.
"It's going to be fun!" I tried to convince myself, grabbing my diaper bag.
Gloria began walking Aubrey to the car. Thankfully David had installed the car seat the night before. She turned back to me. "Did you remember the diapers? I'd hate for my grandbaby to have to suffer through another panty debacle."
My face went hot. "Diapers are all here."
Five minutes later we were rushing down the highway, Gloria in the driver's seat, me in my own personal Hades.
To Grandmother's house we go.
When we arrived at Gloria's house I was prepared to hear Terry yapping away as we walked up to the door, but it was quiet.
She guessed what I was thinking, "He's at the vet today. Gall bladder surgery. A doggy mommy's work is never done."
Gloria opened the front door and Aubrey and I followed her inside David's childhood home.
The décor was tropical island chic, her favorite. Crystal palm trees from every vacation spot she'd ever been to, paintings of beaches with white sand and little dancing figurines that shook their hips when touched could be seen in every corner. It looked more like a hotel gift shop than a home. It had been many years since Mr. Keller had passed away, but Gloria had kept the massive three-story house rather than moving into a condo like David begged her to, and no wonder—half of her things would have to go into storage.
I set the diaper bag on the floor near the stairs. Aubrey put her hands in the air toward her grandmother, begging her to come get her.
"I have a treat for my little princess!" Gloria sang, as she whisked Aubrey into her arms and took her into the family room.
I followed them and heard Aubrey scream in delight. When I rounded the corner, before me was a three-foot by three-foot by three-foot plastic multicolored cube of flashing lights, whirring parts and spinning tops.
"It's the BabyBox!" declared Gloria. "Have you heard of it?"
My mouth hung agape. Yes, I'd heard of it. It was listed on VillageofMommies as the most obnoxious toy of the year. It was twenty-seven cubic feet of migraine-inducing noise and seizure-inspiring lights, had only one volume level and was known to turn on spontaneously in the dead of night. It was designed as an interactive toy for toddlers—there were buttons to push and levers to pull all around the cube—but I'd made a mental note to never own one because it broke my number-one toy rule: never own a toy louder than your child. It was also HUGE.
"Wow, Gloria..." I struggled to find the words. "This is so neat!"
I bent down to sit on the floor next to Aubrey. She poked a bright blue button and a song erupted like an outbreak of herpes. "WE LOVE SHAPES! SHAPES LOVE US! SHAPES ARE FUN SO FUN SO FUN!"
This was the kind of music that, when played backward, said things like, "Get a knife. Kill kill kill." There was no way this was coming home with us.
Gloria clapped her hands, "This one is for my house."
I breathed a sigh of relief. "I bought one for yours, too. You still have to put it together, though."
She pointed to an enormous box in the corner that looked like it contained several thousand individual parts.
Why me? Why?
"Thanks, Gloria. Aubrey seems to really love it."
"I'll go check on lunch. I have minestrone soup in the slow cooker. Slow-cooker meals are really easy, Ashley. Even for people with not a lot of experience in the kitchen. I'll give you the recipe," she said, walking into the kitchen.
I gritted my teeth. Aubrey pushed another button. "SQUARE! RED SQUARE! YOU DID IT! HOORAY!"
At home Aubrey's attention span lasts ten seconds and she floats from toy to me to another toy to me so quickly I get dizzy. But when it came to the Hell Cube, she played with it for a solid hour and a half until it was time for lunch. Maybe it wouldn't be so bad. I'd just have to figure out a way to disable the sound. I could already feel a headache coming on from the incessant noise.
I rooted around my purse for an aspirin. I'd never been so happy to hear someone say, "Lunchtime!"
Gloria insisted that we eat in the formal dining room and had set three places.
"Are you expecting someone?" I said, looking at the third plate and flatware.
Gloria picked up Aubrey and placed her on the chair in front of an adult bowl, plate, fork, knife and glass. An actual glass.
"If you train children to sit at the table, it encourages good eating habits," she said, in a kindergarten teacher tone.
I said nothing and sat down, placing the beige linen napkin on my lap. I decided to let the natural consequences play out. Of course, I'd make sure Aubrey didn't hurt herself with the table knife or the broken glass when she inevitably threw it against the wall like she does with her sippy cup for every meal, but I wasn't going to save the day.
Gloria fit a little white bib around Aubrey's neck. It was the size of a dollar bill. For meals at home, I've resorted to stripping Aubrey naked. For a while I used those full-frontal plastic bibs intended for toddlers when fingerpainting to keep her clean, but even that didn't stop her from mashing a handful of potatoes into her back.
"That's a very cute bib," I said pleasantly.
"Now say ahhh," Gloria instructed, bringing a spoonful of room-temperature soup to Aubrey's mouth. The spoon contained beans, pasta and green peas swimming in a red broth. The last time I tried to put a mix of foods in Aubrey's mouth, she spat it directly in my face. This should be interesting. I looked down so that my smile would be concealed.
"Ahhh!" I heard my daughter's voice say.
My eyes darted upward just in time to see her eat the entire bite, chew it with her gums, then open her mouth for another.
What kind of witchcraft was this? I watched in disgust and amazement as the process was repeated until Aubrey finished the entire bowl of soup.
"You were a hungry girl, weren't you!" exclaimed Gloria, placing the bowl and spoon in the sink. "Ashley, you really must attempt this recipe."
Attempt?
When lunch was all cleaned up, I watched while the two played with the Torture Cube for a few minutes before Gloria announced that she was putting Aubrey down for a nap. I relaxed into the couch. Finally, I'd have some time to myself. Nap time meant twenty minutes of rocking Aubrey before she finally settled down. If Gloria wanted to take that on, she was more than welcome.
I kissed Aubrey on the cheek and handed her to Grandma. "Good luck!"
When I heard Gloria walking back down the steps after two minutes, I stood with a start.
"Do you need some help?" I offered, a smug smile playing across my lips.
"No." Gloria took a seat on the recliner. "She went right down. She always does when she's here. It's all about having a routine."
"We have a routine," I muttered, sitting back down.
Now what were we going to talk about? Being alone with Gloria isn't something I look forward to.
"So, Ashley. How is my David?" she asked innocently.
Why did she always call him "my David"? Of course, he'd always be her son, but the phrase sounded so unnecessarily possessive.
"Your David is fine. He's a little stressed about the business, but they've all but landed a huge account."
"The DentaFresh account?"
I sat up, startled. How did she know? "Yes, actually."
Gloria took a sip of her tea. "No, that client went to another company. David called me yesterday. He was really upset. He didn't tell you?"
My body stiffened. It took everything not to run out of the room and call David immediately. What did she mean he didn't get the account? And he told his mom, but not me?
"Oh, I must have confused them for another company. My mind is so jumbled these days." I slowly pulled my phone out of my pocket. "Excuse me. I'm just going to check on how the home makeover is going."
I ducked into the kitchen and fired off a quick text to David. Did you lose the DentaFresh pitch and not tell me but tell YOUR MOM?
I slid my phone back into my pocket. I walked calmly back into the living room and sat back down.
Gloria cleared her throat. "How is that...bootcamp going? Is it helping much?"
Why didn't she just say "Is it helping you be less of a screwup?" That's what she meant, I was sure.
"I'm actually learning a lot," I said flatly. I'd hoped not offering any other details would mean the end of the conversation. I was more than happy to sit in silence on my phone, like I do at home while Aubrey slept.
"You could have just come to me, of course. I can teach you everything you need to know about raising kids."
"Yes, you're very knowledgeable." I smiled tightly. In my pocket, my phone buzzed.
I discreetly pulled it out. On the screen was a text from David.
I was going to talk to you about it tonight. I didn't think she'd say anything. Sorry.
That's all he had to say for himself?
Is everything going to be ok? I texted.
"Tell David I say hi," sang Gloria.
I looked up and smiled.
We'll talk about it later, he texted back.
I tucked my phone away again.
"I think I heard Aubrey. I'd better check on her," I lied, standing up.
"Feel free to lie down in the guest bedroom if you'd like. You should always sleep when the baby sleeps."
I took her up on the offer and, after peeking in on a peacefully sleeping Aubrey, fell into an exhausted sleep in the Caribbean-themed guest bedroom.
I woke up to Gloria gently whispering my name. "Ashley. Ashley. David is here to pick you up."
My head swam. What day was it? What time? Where was I?
Gloria read my mind. "It's 4 o'clock in the afternoon. Aubrey woke up an hour ago and we've been playing. I didn't want to wake you."
Bless her for that. I must have been exhausted. I rubbed my eyes and reluctantly lifted my head from the soft palm-tree-printed pillow.
"Thanks, Gloria," I said, putting on my shoes. "I really appreciate it."
Gloria sat next to me on the bed. "Don't be mad at David for not telling you. He probably just didn't want you to worry."
This wasn't a conversation I felt comfortable having. "I know."
"Maybe he'd feel more comfortable talking to you if you didn't seem so angry all the time..."
I felt my heart skip a beat.
"Angry?"
"Yes, he says you're always upset and stressed."
I turned to face her. "He talks about me?" My blood began boiling.
"Just a little. I am his mother."
And he's still your baby boy, apparently.
I couldn't hold back my emotions, they were coming at me faster than I could screen them. "I appreciate you letting me sleep, but please stay out of my marriage."
Gloria sputtered. "I didn't get into your marriage. David brought me in when he couldn't talk to you..."
"Well," was all I managed to say. With that I stood up and began walking toward the door. I didn't want to be rude but angry tears had already sprung into my eyes and I wanted to hang on to the few shreds of dignity I had left.
My legs were still struggling to wake up as I made my way down the stairs, and I tripped a little on the bottom step. David's arm reached out to steady me.
"Hi, Ashley! Did you sleep well?" He was grinning and holding a contented Aubrey.
I shot daggers at him with my eyes. "So you think I'm always angry?"
David shot a pleading glance up the stairs to where his mom was standing.
"She can't save you now." I picked up Aubrey's bag and walked out the door to wait in the car.
When David finished buckling Aubrey into her seat, he turned to me. "Ashley, I just—"
I put up a hand. "Don't. I'm not talking to you with your mom watching from the window." I turned toward the house, and sure enough a drape fell where Gloria had been watching.
"Okay, fine." David turned over the ignition.
When we were a block away, I unleashed.
"How dare you discuss our marriage with your mom? And tell her about the DentaFresh account before me, knowing I was spending the day here? You made me look like an idiot. An angry idiot."
David kept his eyes on the road and struggled to find the words. "I was just stressed and needed someone to talk to, Ashley..."
"The person you talk to is me. Not your mom."
"I'd love to talk to you but you're either complaining, frustrated, angry at me or exhausted from Aubrey," he spit out.
"And you're not preoccupied at all? You're at work almost all the time and when you're home, you're relaxing from work. Do you see me ever relaxing? That nap I had was the best rest I've gotten in months."
David erupted. "Yes, I know! You hate your life. I'm failing at work and I'm failing to make you happy. I get it, Ashley! Okay?"
He was practically shaking. I sat, shocked, staring at him.
"I don't..." I put a hand on his on the steering wheel. "I don't hate my life... I'm just stressed. And you're not failing..."
David was quiet for a moment. "Yes, I am, Ashley. We lost the DentaFresh account. It's over. We're going to have to sell the house."
I felt the wind get knocked out of me. I knew things were hard but I didn't know they were that bad. Sell the house? Where would we live? My blood ran cold. The furniture bill. I still hadn't told him about the $8,000.
I took a deep breath. "David, I have something to tell you."
He turned to glance at me. "What is it?"
"The home makeover... I thought I spent a grand on the furniture..."
David clenched his teeth. "Ashley, we don't have an extra thousand!"
I kept going, determined. "But I really spent $8,000. I put it on my credit card. It's nonrefundable." It was true. It was in the fine print.
David slammed the steering wheel with his hand. "Dammit, Ashley! That's our entire savings. It was going to help us find a rental if we move."
I felt a tear slide down my cheek. "I'm so sorry."
David's shoulders hunched over in utter defeat. "If I don't get another account, we won't be able to afford a rental. We'll probably have to stay with my mom for a while."
My stomach flip-flopped. "With your mom? For how long?"
"A few months. Hopefully."
We didn't speak for the rest of the ride home.
When we arrived at the house, everything was locked up, just as François had promised. The door swung open and all was dark. It wasn't until David flipped on the light that I saw it. I gasped. It was a whole new house. Everything sparkled and shone.
Even David said "Wow" under his breath. "I'm going to put Aubrey down," he said gently, before heading upstairs. I could barely reply as I looked around.
It was like walking into one of those home-and-garden magazines. The wooden floors were brighter than I'd ever seen them. I floated into the kitchen and, as the light flooded it, I was dazzled. Nothing was out of place and everything looked so fresh, like it was right off the assembly line. I couldn't find a speck of grime or a crumb anywhere. I opened a cabinet, and instead of almost being buried in plastic containers falling out, found everything stacked neatly.
I wandered into the living room. The furniture. It was even more beautiful than the catalog had promised. The living room set was perfectly placed and screamed "luxury." Aubrey's toys were nowhere to be seen—I lifted up the soft leather ottoman and found them tucked out of sight. They'd even thrown in a large chestnut area rug and several beautiful wooden spheres for the mantel. Was this really my house? I collapsed onto the couch and it supported and hugged my body at the same time. It all certainly looked like $8,000. Or more. I felt like I was in an episode of Lifestyles of the Rich and Famous, only in a parallel universe where I'd only get to enjoy these things for less than a month before we had to sell them online to afford utilities.
I wrung my hands together. I looked at the corner where Aubrey had rolled over for the first time on the colored mats that were nowhere to be found. I guess Shelly thought they didn't fit in with the décor. I stared at the middle of the floor, where I'd spent more afternoons than I could count folding laundry while Aubrey lay on her back and tried to bite her toes. The laundry was gone; finally put away. Everything was how I'd always wanted it, but not at all right. For the past ten months I'd felt trapped in this house, and now it was all going away.
I curled up on the oversized couch, tucked my knees into my chest and cried.
Sunday, March 3, 9:30 A.M.
David barely spoke this morning, other than to tell me that a Realtor was coming to look at the house sometime this week. I couldn't believe this was really happening. He said if we couldn't find a place to rent for the right price, he'd have to ask his mom if we could stay with her for a few months.
He'd already put in résumés with marketing firms, but in the meantime, he said we were in what he called "money-saving mode." I think that was code for "don't spend another $8K on furniture, please." What he didn't seem to understand was that I was the one who would be staying home with Aubrey and his mom all day. He asked me if I wanted to go back to work and have Gloria watch the baby, and suddenly all I wanted to be was a stay-at-home mom.
For the past ten months I'd been complaining about how hard life was and not realizing how hard it could get.
I looked over to where Aubrey was sleeping peacefully on her back in her playpen. The last Motherhood Better Bootcamp call was tomorrow. I'd submitted my Home Challenge diary entry already.
Hi everyone,
I'd like to thank Emily for the amazing work her team did on my home. It's cleaner and more organized that I've ever seen it. It's how I always dreamed my house would look. The new Verdanza living room set is an absolute dream. My home looks incredible. The only thing I could ask for now is for great memories to be had in it.
Ashley Keller
I included Before and After photos, and everyone oohed and aahed in the comments. The difference really was striking, but it all felt so hollow. It was such a cruel twist of fate for me to finally have the house I wanted but to have to give it away in two weeks.
The one piece of good news was that I'd be flying out to Napa this week for the Motherhood Better Bootcamp Finale. Did I mention that I was going to be on TV? No? That's because I only just found out. Emily posted in the portal early this morning that we'd be spending Thursday relaxing in outdoor hot tubs, being treated to massages, and getting a personalized makeover. But on Friday we'd be broadcasting live on The Emily Walker Show to announce the winner.
At this point, I'm not holding my breath. While I was conning my way into mom groups and working for phone sex companies, Janice Paulsen from Minnesota lost twenty-five pounds and raised $20,000 for a charity that matches foster children up with available families. Heather Logan has pumped over 300 ounces of breast milk for preemies, and Naomi Price knitted 150 quilts for moms on bed rest in her local maternity ward.
Tomorrow is my last La Lait meeting before my trip and I've decided to come clean. Before the general announcements, I'm going to stand up and apologize to everyone for misleading them and beg them to let me stay. I owe them the truth.
Having to give up the house is putting everything into perspective. I can't live any more lies.
Monday, March 4, 10:30 A.M.
The last Motherhood Better Bootcamp video chat was this morning. Emily looked as chipper as ever wearing her new line of athletic gear: EW Move. She had on a white crushed-velvet tracksuit with her initials monogrammed over the chest.
"Is everyone ready for our Napa getaway tomorrow? I've been reading your wrap-up posts and can't think of a group of moms more deserving."
The wrap-up posts she was referring to were the 200-word personal reflection essays, due by tonight at midnight, that summarized what we'd learned from the bootcamp. I hadn't submitted mine yet.
"Don't forget to send yours in by tonight. No matter what happens on Friday, you're all winners in my book," Emily said, her hand dramatically placed over her heart.
Winners, right, I thought, bouncing a squirmy Aubrey on my lap. I tried to focus on the call but couldn't stop thinking about the La Lait meeting in an hour.
What were they going to say? I pictured myself standing in the middle of the room being squirted aggressively with milk from all directions, straight from the nipples of the moms I'd offended. "Please, stop. I'm sorry!" I'd yell, trying to shield Aubrey from the sprays of milky anger.
Emily's voice cut through my nightmare. "This week, I want you to reflect on everything you've learned because you'll be sharing a few words live on my show. I can't wait to see all of you on Wednesday night. My personal chef will be preparing all of our meals, and for Thursday I've also booked you head-to-toe makeovers!"
Everyone oohed giddily and clapped their hands. I managed a halfhearted smile. A month ago, the thought of a few days away, a haircut and a soak in a hot tub would have left me dizzy with glee, but between our impending move and the inevitable loss of my only friends, I couldn't get excited.
"I'm just so proud of all of you. Hugs and kisses, ladies!" Emily said, blowing a kiss to her webcam.
When the chat screen closed, I shut my computer and carried Aubrey into her bedroom. I changed her diaper and put her into a pair of gray sweatpants and a matching hoodie. I looked down and realized we were wearing almost exactly the same outfit.
Half an hour later we were walking through the front doors of the community center. I held my breath as I pushed the La Lait meeting doors open. This was it. There was no turning back.
I inhaled deeply and walked through, trying to steady my nerves against the weight of the moment.
"Hi, every..." My voice trailed off as I froze against the sight in front of me.
All twenty moms, including Lola, Kristen and Nina, were standing under an enormous white construction-paper banner that read "Good luck, Ashley!"
Lola threw a handful of confetti in the air. "Surprise!"
Nina pulled a cord, sending a cascade of balloons from a net affixed to the ceiling. Aubrey squealed with delight.
Lola's booming voice filled the room. "Ashley, we just wanted to send you off to the Motherhood Better Bootcamp knowing that we're behind you one hundred percent. We love you!"
With that, all of the moms rushed forward and surrounded me, hugging me from all sides. I felt a warm bubble of emotion rise from the pit of my stomach and get lodged in my throat. My eyes filled with tears, and as they streamed down my face, I actually, genuinely, wholeheartedly laughed.
"I can't... I can't believe this!" I sputtered. Nina wrapped me in a bear hug, the twins strapped to her chest. "No matter what happens in Napa, remember that you're already a great mom." A fresh batch of tears ran down my cheeks.
I turned every which way, hugging the women around me. I'd never felt so supported in my entire life. Every mom had different words of encouragement for me, but they all were in the same thread: "You're amazing just the way you are." That's all I've ever wanted to hear.
After ten or so minutes everything settled down and we were sitting and lying on the giant rug surrounded by pillows and toddling, squirming babies. Every few minutes a different mom would pop up and hug me, wishing me well on my trip.
The meeting flew by. I looked at my phone. I'd almost forgotten that I hadn't done the only thing I'd intended to do. There were only ten minutes left. I wrung my hands together and watched Aubrey crawl her way over to Donovan and tap him gently on the head as if to say, "Hello friend!" They both dissolved into delicious baby giggles.
It wasn't the right time. I couldn't. My confession would have to wait until I returned from the bootcamp finale.
Wednesday, March 6, 6 A.M.
The morning hadn't been an easy one. Since Aubrey was born I'd dreamt of taking even just one night off, but putting her down last night was next to impossible, as I couldn't stop hugging her. I knew I'd only be gone two and a half days, but if you were to peek in on me, both arms tight around her pajamaed body, rocking her in the glider in the dark room, tears rolling down my cheeks, you would have thought I was leaving for war. Tonight was going to be my first night away from her, ever.
I'd hardly been able to sleep, either. Even though I'd set multiple alarms on my phone and David's phone, I woke up every half hour.
"You're going to be great," David said, cupping my face in his hands as the Town Car driver pushed my suitcase into the trunk. "And don't forget to relax. Have some fun."
He kissed my cheek and I turned toward the waiting car. Leave it to Emily Walker to arrange a fancy black car for a pickup. As I slipped inside and glided across the black leather interior, I felt like a movie star. I watched David disappear into the house.
People always complain about travel, but I found navigating through the bustling airport and a particularly grumpy TSA agent easier than grocery shopping with a tired baby. For the first time in forever, I only had myself to worry about. By the time I was seated in 4A, a window seat in first class, I felt like I'd spent the day at a spa.
I'd never flown first class before and was slightly embarrassed to board before everyone else. The main cabin was still empty as I, along with a few business people, made myself comfortable in a large, plush seat in the luxury section of the plane.
"Can I interest you in a beverage? Tea? Coffee? Wine?" the perky brunette flight attendant asked me.
"Coffee would be wonderful, thank you," I said, trying to sound as gracious and unspoiled as possible.
"How do you take it?"
It took everything inside me not to say "Cold, and with a baby on my hip."
"Sugar and cream would be fantastic. Thank you very much."
A few minutes later, a piping-hot mug of caramel-colored coffee was placed on my tray, alongside a glass plate with a warm blueberry muffin.
"They're freshly baked," the flight attendant said, winking at me.
I was speechless. Coffee and a muffin? And I didn't have to share it with anyone? I was on cloud nine.
The main cabin began filling up as passengers shuffled past first class and into the main section. Suddenly, I felt self-conscious of not only my priority seating but the continental breakfast in front of me. I noticed a few people struggling to make their way through the narrow aisle steal judge-y glances at me, and I wanted to say, "I'm not rich! I usually eat stale cereal off my daughter's high chair for breakfast in stained yoga pants and an oversized sweatshirt!"
The familiar sound of a fussing baby caught my ear and I saw a young woman juggling an infant car seat, diaper bag and carry-on bag, while wearing a baby who could be no more than six months old in a wrap.
A pang of sympathy shot through my chest. The look in her eyes was a familiar one: a mix of defeat, frustration and determination. Our eyes met and I smiled empathetically. I'd been there. The diaper bag strap slid down her arm into the crook of her elbow.
"Let me help you with that," I said, standing. I slid the strap back to its rightful location. "I have a baby, too. Hang in there."
She smiled appreciatively at me. "Thank you. It's been one of those mornings."
She continued making her way back, stopping in the first row of economy seats, just behind me. I watched in awe as she pushed her carry-on into the overhead compartment and placed her belongings in her seats, all while bouncing her increasingly upset baby in the wrap. As she took care of business, I noticed an older man behind her get fussy over the hold-up in the line. My blood began to boil. What happened to common courtesy? Instead of tapping his foot, he could be helping her!
I stood up in my seat again. "Can I help you with anything?"
She blew a strand of hair out of her face and tilted her head gratefully in my direction. "I'm okay. But thank you. Again. You're very kind," she said, shooting a glare at the gentleman who was now twitching with impatience.
Finally, she slid into her seat and unwrapped her baby from her chest. The pajama-clad infant let out a shriek of discomfort over being removed from his cozy cocoon.
"Shhh, shhhh...you're okay," she cooed.
Ten minutes later, everyone was in their seats and the emergency landing routine had just wrapped up.
A voice over the intercom said, "Hello, everyone, I'm your captain, Jack Ross. Thank you for flying Air United today. Our flight time is approximately three hours and twenty minutes."
I'm not sure when I dozed off, but the next thing I heard were the sounds of a baby in full meltdown mode. I awoke with a start, and for a moment, I forgot I was on a plane and had the urge to run upstairs and collect Aubrey from her nap.
The sound was coming from behind me and was slightly muffled by the closed First Class curtain. I pulled it to the side and peeked through. The young mom was frantically trying to comfort her baby, who was strapped into his car seat in the seat beside her.
"Oh, great!" I heard a woman's voice from the middle of the plane exclaim.
The mother's face said it all. She was mortified.
"Can I help you with anything?" I whispered to her.
"No... I'm so sorry about the noise. He's just tired."
"No need to be sorry," I said softly. "Babies cry."
A female flight attendant with a tight bun crouched beside the mother. "Ma'am, we're getting some complaints from other passengers. Is there anything you can do to calm your little one down?"
It was like someone slapped me in the face. Was she serious?
"I'm doing my best..." I heard the mother's voice crack. "I'll feed him."
I slid back into my seat, feeling utterly devastated for her.
The next thing I knew, the same older gentleman from before who was sitting in the aisle across from the young mother was roaring, "You've got to be kidding me! Now you're going to flash us?"
I heard the mom's feeble voice, "I'm feeding my baby..."
I peeked through the curtain again to see the baby happily nursing, the mother's tank top slightly lifted to make room for his head. Her eyes were full of tears.
It was like someone lit a match under me. I stood up and whipped the curtain open. I leaned over my seat.
"HEY, YOU!" I heard myself say. "SHUT UP! She's a mother trying to take care of her baby. News flash: they cry. They need to eat. Moms need to take them places. We can't stay home twenty-four hours a day to save your precious little ears and eyes from our HARD work raising the next generation. If you can't handle it, maybe you should be the one to stay home."
The man's face turned red and he fumbled the newspaper in his hand. "I'm just asking for common decency!"
I stood and walked right up to the man who was now almost trembling. I pointed in his face. Something inside me had snapped.
"Why don't you have the DECENCY to let this mother tend to her baby in peace! She's doing an excellent job and shouldn't have to put up with jackholes like you!"
I gestured to the rest of the plane. "Do any of you know how hard it is to be a mom? You're supposed to be perfect and invisible at the same time! This mom is just trying to do her best and you're making her feel like crap! Moms can't win!"
I felt a tap on my shoulder. It was the female flight attendant. "Ma'am, I'm going to have to ask you to take your seat."
"I'll sit down when I'm done!" I was on fire now. "Moms can't win with any of you. If we work, we're neglecting our children. If we stay home, we're wasting our lives. If we don't breastfeed, we're failures. If we do, we need to do it in the dark, under a blanket, on a different planet so we don't offend your fragile, weak sensitivities! Give a mother a freaking break!"
I felt a tap on my shoulder again. I turned around. "WHAT?" And was face to chest with what I had to assume was a human giant. He had to be seven feet tall. His voice was a deep baritone and he was cut, like, bodybuilder cut.
"Can I help you?" I said, indignantly.
"Yes, ma'am, I'm going to have to ask you to take your seat."
I flipped my hair. "And just who are you, exactly?"
He pulled a badge out of his jacket pocket. "I'm a flight marshal."
My body ran warm. "Oh. In that case, okay."
I started to make my way back to my seat, but turned around and faced the plane one more time. "And the next person that bothers this woman is going to have to deal with me!"
The flight marshal gave me a look.
"I'm sitting down, sir."
I took my seat and inhaled sharply, trying to steady my nerves. I looked at the mother whose mouth was hanging open. Tears were now streaming down her face. To my surprise, they were falling from mine, too.
"Thank you," she squeaked.
I was afraid that if I answered I'd start sobbing, so I mouthed, "You're welcome," before leaning back into my seat.
The rest of the flight was a quiet one. After we landed and people began collecting their things, I noticed that the older man sheepishly allowed the mom to collect her belongings without a hint of impatience. Our eyes met again before I exited the plane, and her beaming face said it all.
11 A.M.
There I stood, in the foyer of Emily Walker's beautiful wine-country home (yes, wine-country home). I closed my eyes and took a deep breath. Was this really happening? We were surrounded by row after row of gorgeous vineyards, heavy with the small purple grapes that made my evenings so delicious.
Was I really standing in one of Emily Walker's mansions? I could barely take it all in. The white and gray tiled floor sparkled in the California sunlight that poured in through the long vertical windows. Ahead of me were two staircases that met halfway from the top to become one—it looked like the kind of staircase a princess walks down to enter a ball. One of Emily's assistants, Anna, a short brunette with a classic bob and enormous glasses, had already had one of the many men and women I'd seen scurrying about in white sport jackets and black pants take my bags to my room. A room that I'd yet to see.
"Someone will escort you to your room in just a minute! First, you must be hungry from your long journey," Anna said, before disappearing down a long hallway. Ten minutes later she reappeared holding a clipboard and with a Bluetooth device in her ear, and led me down the same hallway and through three doors. I tried to remember which way we turned and what the rooms we passed through looked like, as if I were some kind of blindfolded hostage being taken away by car. I'd practically need GPS in this house!
Finally, she flung a set of double doors open to reveal a party in progress. I stared, gawking at round tables set with full flatware and centerpieces as if it were a wedding. Glittery lights twinkled in the multiple chandeliers. Women crowded the room—the women! I instantly recognized many of them from the bootcamp video conferences. Only one thing was wrong: they were all dressed to the nines. Every last woman had donned cute skirt and sweater combinations, pastel pumps, A-line dresses and dangly earrings. I stood, self-conscious, at the entrance next to Anna.
I leaned over, "Anna, is there any way I can change—" I gestured down at my black saggy leggings and university sweatshirt.
"Don't worry, this is just the reception brunch. It was on your itinerary. It's very casual."
I remembered the reception brunch, but I was thinking it'd be more scrambled eggs, croissants and mimosas over giggles in sweatpants, not what looked like Easter Sunday at the Vatican.
I took off my backpack and placed it by the door. David had insisted I take his hiking backpack as my carry-on "because of all the pockets."
Walking slowly toward the buffet, I redid my ponytail.
"Ashley? Ashley Keller, is that you?" A high-pitched voice cut through me right as I was reaching for what looked like a grapefruit champagne cocktail.
I turned around to see a six-foot leggy blonde in a pale pink, knee-length taffeta dress and matching heels running toward me. It was Heather Logan, mom of three-month-old twins from New Jersey. I recognized her from her posts featuring chalkboard paint tutorials, making door wreaths for every season and basically any craft you can think of. She was a star on the Motherhood Better Bootcamp portal.
She gathered me in a tight hug for several seconds before pushing me playfully away. I tried not to lose my balance.
"Hi, Heather! You look fantastic!" She really did. I wish I'd gotten the memo about dresses.
"Thank you, doll! And you look...no way, did you already find the gym? You are such an overachiever!" she practically yelled. She motioned toward several ladies who were gathered in a small circle near us.
"You guys, Ashley already worked out!" she boomed, pointing at me.
A woman in a black pencil skirt, red fitted blazer and red pumps turned toward us. "No way. I've been dying to get on the treadmill. Only two days until six million people are staring at us on TV." She flipped her hair and looked me up and down. "Where is it?"
I laughed nervously. "Where's what?"
A small crowd was forming now. They were eyeing me carefully, as if I were a threat, while simultaneously circling me like easy prey.
"There's a gym?" I heard someone mutter.
"Yeah, she already went," said someone else.
Heather waved her hands as if to clear the air. "Okay, calm down, ladies! You'll all have a chance to kill yourselves on the elliptical later!" The crowd dissipated.
I exhaled, relieved.
"So," Heather went on. "Have you met Emily yet?" She said Emily's name as if she were a third grader teasing her schoolyard friend about her crush.
I grabbed the fruity cocktail and took a big sip. "I just got here, no. Have—" Before I had a chance to finish the sentence, Heather was dragging me across the floor by my hand.
We stopped in front of a woman who was in conversation with one of the waitstaff, but even with her back turned to us, I could tell it was Emily. I felt myself get hot and then cold all over. No, no, no! I couldn't meet Emily Walker dressed like someone on laundry day!
But it was too late. Heather tapped Emily on the shoulder. As she turned toward me, I'm positive I saw a beam of light encircle her face. Her makeup was flawless, her hair perfectly done up in a stylish ponytail, not a raggedy slept-on one like mine. A short jade dress accentuated her lean, curvy figure.
I was speechless. For once I was grateful to have Heather's mouth do the talking for me. "Emily, have you met Ashley?"
Emily's eyes lit up. "Ashley Keller!" She took the sides of my arms gently and gave me a kiss on each cheek. I moved, stiffly, unsure of how this greeting was supposed to happen. I'd only ever seen it on a few travel shows.
"It's so wonderful to finally meet you! I feel like I've known you forever. This is Sage." She looked down and for the first time I noticed the toddler peeking through her legs. "He's a little shy." She bent down gracefully and scooped up the child whose curly brown hair framed his long black eyelashes. He looked like a child model in his white shorts and a white sweater with a little navy anchor on the chest.
"He's getting tired," Emily purred into Sage's ear and he laid his head against her chest.
I gawked, awestruck. If Aubrey were here, she'd be pulling at my earrings, screaming for a scone and generally raising hell, but here was Emily, being an amazing mom, hosting a party and looking fabulous while doing it. She was absolutely perfect.
"Ashley, I can't wait to talk to you more, but I'm going to give a little speech before everyone gets restless!"
"Okay," I sputtered, realizing that I hadn't said one word since meeting her.
I found my way back to the buffet, trying to choose between piles of freshly shaved, cured meats, mouthwatering platters of fresh fruit, pastries, cheese, and the crepe and omelet bar. I never wanted to go home.
I heard the telltale sound of a microphone being tapped and turned to face the front of the room.
Emily was holding a mic and grinning.
"Hello, everyone! I'm so glad that you've all arrived safe and sound! Welcome to the Motherhood Better Bootcamp Finale!"
Everyone cheered.
"I want you to take your time eating, drinking and mingling. Your only job here is to have a great time. You've earned it."
Heather "whooped" from inside the crowd.
"My number-one goal since I started the Emily Walker empire has been to inspire and support moms. I hope that the Motherhood Better Bootcamp has done that for you. No matter who is crowned as the winner in two days, I want you to know that, in my book, you're all queens."
Applause broke out. I could feel myself getting misty. If I hadn't had a plate full of ham and cheese omelets, mandarin-orange crepes topped with fresh cream and about six different kinds of meat, I would have clapped, too. I wished every mom could know what it felt like to be recognized like this.
I found an empty table in the back and proceeded to attack my plate.
Just when I'd stuffed a prosciutto-covered piece of cantaloupe into my face, a voice distracted me. "Ashley? Hi, I'm Kimmie Reardon."
Kimmie Reardon. How could I forget? I'd seen her name all over the Motherhood Better boards. Mom of four. Lives in Los Angeles. Loves to bake. Completed all of the challenges with ease and always has ten or twelve photos to prove it.
I stood up.
"No, no, don't get up," Kimmie said, taking a seat beside me. "You look...busy."
She looked just like the photos she'd taken: five foot five, long, wavy brown hair, pretty almond-shaped eyes. She was dressed more casually than the others: suede calf-high boots, black leather pants and a white denim cropped jacket over a black tank top. Where do all of these moms shop? And how can so many of them wear white?
I forced the appetizer down my throat. "It's nice to meet you," I said. She daintily shook my hand, as if human contact wasn't something she relished.
I took a bite of my crepe, eyeing Kimmie to see if she was going to stay.
"So," she said, watching me intently. "How do you feel about your chances?"
"My chances for what?" I asked, my mouth full.
"Winning," she said, staring me dead in the eye, expressionless.
I chewed. "Well. There are a lot of great women here." I trailed off, hoping that would be a sufficient answer.
Kimmie scanned the room, her eyes narrowing. "They're okay." She turned back to face me. "Don't let your guard down just yet. The competition's not over."
She gave a saccharine smile before standing up abruptly and walking away.
An almost-full plate of food sat in front of me, but suddenly I wasn't as ravenously hungry as I was before. Kimmie the Ice Queen was right. This wasn't a vacation. It was the final lap.
When I finished my meal, I opened the welcome packet Anna had given me.
Dear Ashley Keller,
It's our absolute pleasure to welcome you to the Napa home of Emily Walker for the Motherhood Better Bootcamp Finale! We hope this time will be one of rejuvenation and community. Below are your accommodation details and schedule, along with a map of the estate.
Wednesday
11:30AM Welcome brunch
Feel free to spend the rest of today relaxing! The spa, pools and kitchen are at your full disposal. If you need anything, please page Anna or James (the house butler), and our staff will provide it.
6:30PM Dinner in the Outdoor Garden Dining Room with Emily and her family
Thursday
6AM Yoga on the south lawn with Emily & Sven
7AM Breakfast in the Main Dining Room
8AM Basket and Dream Catcher Making in the Craft Room
9AM Organic Smoothie Workshop with Chef Evelyn
10AM Makeovers!
Noon Lunch & Sharing
1-5PM Free Time
6PM Dinner on the North Lawn
Friday
5AM Hair & Makeup
7AM We go live!
11AM Farewell brunch
"So much for a relaxing vacation," I thought. At least the makeover sounded fun. I scanned the sheet to find my room assignment.
Accommodations
Ashley Walker: The Pink Peony Room (locate on the map)
Roommate: Kimmie Reardon
Just when I thought things couldn't get worse.
When I finally made it to the room through the labyrinth of doors, I was taken aback. Pink Peony wasn't just the name of the room, it was the theme. Pale pink and white flowers with dainty green leaves filled every inch of the slate walls. A bedside table adorned with an antique desk lamp and a glass vase full of delicate peonies separated two double beds. The only other furniture was a white leather loveseat and a tall, wide oak dresser.
The bathroom door on the far right of the room opened.
"Hi, roomie," Kimmie said slyly, as she walked out and sat on a bed covered in garment bags.
I placed my suitcase, which had been left just inside the door by the staff, on the remaining bed.
"Hi again, Kimmie," I responded. "Did you know we were roommates earlier?"
Kimmie threw her head back and laughed. "Oh, yeah. I was just waiting for you to figure it out."
I smiled weakly. "It's going to be great."
Kimmie swung her legs over the bed to face me. "I'm so happy we're together. I can't imagine being with some of the other women."
I opened my suitcase and began slowly taking out my belongings, hoping Kimmie wasn't judging them. I didn't own anything nice enough to warrant a garment bag.
"Oh, really? Why not?" I asked, making my way over to the dresser. I opened drawer after drawer to find they were already filled with silk panties, tops, jeans and more jeans.
"Sorry. I'm an overpacker. I left you some space in the closet," she said flippantly.
I opened the modest closet to find it two-thirds full. Six hangers remained. "Thanks."
Kimberly pulled a black compact out of her purse and began puckering her lips. "Some of the moms here...wow. I mean, you can tell they needed the challenge, but there's no way they're going to win. I'm talking totally dumpy. Frump city. It's sad."
I silently stacked my clothes on the shelf at the top of the closet, next to four pairs of Kimmie's boots.
"Motherhood will do that to you," I responded.
Kimmie dug through her purse and retrieved a small glass vial and wrapped hypodermic needle.
"Oh, not me. Letting yourself go is a choice." She unwrapped the needle and poked it into the top of the vial. "Do you want some? It's better than Botox," she said, peering into the mirror and sliding the needle into her forehead.
I watched, shocked. "Um...no. But thank you."
"Suit yourself. We're going to be on TV in just under forty-eight hours. Your fine lines will be even more pronounced in high definition."
I slid my empty suitcase under my bed and sat on the chair. It was so odd not to have a baby to change, feed or put down for a nap while worrying she will wake up any second. I folded my hands and realized that I had absolutely no idea what to do with myself. Sleep was out of the question with Kimmie sitting three feet away, injecting God knew what into her brow line.
I coughed. Make conversation, Ashley. It's not that hard, my inner voice urged.
"So, Kimmie...how did you hear about the Motherhood Better Bootcamp?"
Kimmie put the needle in a black plastic box and snapped it shut.
"Actually, I've known about it for months. Emily Walker's husband works with mine. They're investors," she said, smiling rather smugly.
"Investors? What do they invest in?" I asked, leaning my head on my hand.
"Everything. Tech, retail... They went to the same Ivy League and were even in the same frat. We were at each other's weddings."
"So, you know each other?" I asked, trying not to frown.
Kimmie stumbled over her words, "Well, yes, but no. We're in many of the same circles. Anyway, I'm going to take a shower before heading down for a swim. Let's sit together at dinner, okay? See ya," she said, standing up and tossing me a tight smile.
"Okay, bye."
Kimmie grabbed a plush robe from the closet before disappearing into the bathroom and closing the door behind her. I heard it lock, so it was clear she'd be in there for a while. I decided to go for a stroll.
This wasn't a house. It was its own village. Emily Walker's Napa estate had its own tennis court, two pools, a hot tub, a pool house with an area for manicures and massages, a room just for hot yoga, three kitchens—including one large enough for a full professional staff to prepare meals—four wings, four garages, a movie room and that's just what I'd seen so far. Did I mention there was an elevator? I wouldn't have been at all surprised to open a closet door to Narnia.
As I walked down a set of cement stairs from the main garden to the spa, I ran into a familiar face: Janice Paulsen, the do-gooder mom who matched foster kids to families. She wore a thoroughly bedazzled gray sweatsuit.
"Ashley! It is so wonderful to see your beautiful face! I'm Janice" she said in a Minnesota accent.
Ah, Janice. The needlepoint queen of the great Midwest. She'd found way to inject her love of craft needles into every single challenge. For the Marriage Challenge, she'd even knitted a set of yarn lingerie that I'd never be able to unsee.
"It's nice to meet you in person." I smiled, feeling like for once I was nailing a social interaction with someone old enough to use the bathroom alone.
Janice took my hand as if she was trying to prevent me from leaving too quickly. "Lauren," she yelled, calling to a woman at the bottom of the stairs who was tying her shoe. "Lauren, Ashley's here. Remember? The tush girl?" she said, waving Lauren over furiously.
Tush girl? They couldn't mean the first video chat fiasco. There's no way they were talking about me.
Lauren, a woman with chestnut hair in a low ponytail, wearing bedazzled jeans and a T-shirt, hightailed it up the stairs. I recognized her from a particularly long post about how bedazzling saved her life.
"Tush girl!" Lauren exclaimed, loudly enough for everyone in the zip code to hear. She ran over to me and gave me a bear hug. "I tell your story to everyone I meet. You're practically famous in my book club. I love your little tattoo, by the way!"
I tried to will my body to melt into the ground.
"Thank you...for...it's nice to meet..." My words left my brain again.
"Hey." Lauren touched my shoulder and drew me close. "If you need anything bedazzled you let me know. I brought my Rhinestanator 2000 and have been hooking everyone up." I looked the women up and down, and by the no less than six trillion plastic gems on their outfits sparkling in the sunlight, I knew she wasn't kidding.
"I'll let you know!"
Somehow I managed to slink away from the conversation before they asked to take a photo of my tattoo for their scrapbooks.
Once safely back in my room, I opened the bathroom door to find Kimmie standing as naked as the day she was born in the shower with her arms and legs spread wide. She was wearing some kind of protective goggles and a woman wearing the same eyewear was spraying her with a large canister attached by a hose to an even larger tub.
I screamed.
Kimmie pulled up one side of her goggles. "Geez, Ash. You almost gave me a heart attack. What happened to knocking?"
I shielded my eyes with my hand. "I'm sorry, it was unlocked. I'm sorry."
I backed away into the door and bumped against it.
"No need to freak out," Kimmie said, folding down her goggles. "Amanda, meet Ashley. Ashley, meet Amanda. She's my personal tanner. She's staying at a nearby hotel. There's no way I was going on TV without a fresh one, am I right?"
"Yes, right, right," I said, finally finding the doorknob with my eyes closed. "Okay, enjoy yourself."
I sat down on my bed and opened my computer. One missed FaceCall request from David. I clicked on the notification and it started dialing.
He picked up after one ring. I could hear running water and the sound of someone gagging.
"David? Are you there?" The screen only showed the bathroom ceiling.
"ASHLEY!" I heard David yell before gagging again. "ASHLEY, HER DIAPER EXPLODED!"
"David?"
His face popped up over the monitor. His eyes were full of fear and there was a bandana tied around his nose.
"Ashley, I'm dealing with a Level Ten Poopsplosion right here and am two seconds away from—" He retched loudly.
"Oh, David..." I could hear Aubrey giggling hysterically in the bathtub.
"Ashley. If I pass out I'm going to need you to call 911."
I tried to hold back my laughter. "David, you're not going to pass out. Are her clothes off yet? Let them soak a bit before you wash them—"
"Too late," he said, looking around wildly. "I had to cut them off. They were an unfortunate casualty."
It was then that I noticed he was wearing the yellow gloves I use to wash dishes.
"Feel free to burn those when you're done," I said.
David paused for a minute before I heard him say, "Oh, no, no, no, it's happening again. There's more coming out of her. Why is this happening? Is she possessed? Is she possessed by a demon? I need a young priest and an old priest. I gotta go, Ashley. I'll call you later."
"David, you're going to be okay." Before the camera clicked off, I'm almost positive I heard him chanting in Latin.
"Don't forget to get under my butt cheeks! They won't be on camera but I'll know!" I heard Kimmie scream from the bathroom.
I opened the bedside table drawer and found a pair of purple eye covers. They smelled lightly of lavender. I slipped them on over my head, lay back and, before I knew it, was in a deep sleep.
I woke up to Kimmie shaking me. "Ashley. ASHLEY! It's time for dinner. Geez, you sleep like a rock."
Kimmie walked over to the full-length mirror. She was stunning in a floor-length pale pink evening gown. Her wrists and neck were dripping with what I could only assume were real diamond and gold jewelry.
"You look beautiful," I said, pushing myself up to sitting.
"You look tired. Get dressed. You know dinner starts in fifteen minutes, right?"
"Fifteen minutes!" I flew out of bed and toward the closet. "Why didn't you wake me up earlier?"
Kimmie shrugged. "I'm not your mommy." I don't know if I imagined it, but I thought I saw a smirk. Was this her competitive side?
"I'll meet you down there."
Kimmie walked out the door and shut it behind her. I tore through my clothes and looked for something that would even come close to the level of elegance my roommate had achieved.
I found a dark blue maxi dress. It would have to do. One of the good things about having held Aubrey 24/7 for the last ten months of my life was that I was used to doing everything with one hand. Finally having two, I was able to get my hair and makeup decent in five minutes.
After getting lost twice, I finally found the outdoor garden dining room where we'd be dining. Everyone was already sitting at several large round tables, including Emily's family. There they were: her husband and five perfect children in the flesh. Emily was wearing a plum three-quarter-sleeved, calf-length dress and black heels, and her husband was dashing in gray slacks and a crisp white dress shirt with a gray sport jacket. Her three boys were wearing white (WHITE) short-sleeved shirts and camel-colored shorts, and her girls were wearing the same outfit in jumper form. They looked like the cover of a fashion catalog.
"Ashley, over here!" I heard Lauren call. I glanced over and saw Janice and Lauren waving wildly from a table at the far end of the patio.
The last thing I needed was to spend the evening being referred to as "tush girl." I waved politely and ducked behind a large plant.
I felt a hand touch my shoulder. "Ashley, would you like to sit with my family?"
I looked up. It was Emily. I stared into her blemish-free face for a full twenty seconds before sputtering out, "Yes."
I followed Emily to her table and noticed Kimmie glaring at me. Naturally, I beamed back at her.
"Ashley, I'd like to introduce you to my husband, Thomas."
I took in her husband's ruggedly handsome features and found myself staring. It was impossible not to get lost in his dreamy auburn eyes. I blushed. "Nice to meet you."
He nodded. "Likewise." He was holding Emily's youngest baby, eighteen-month-old Sage. He nuzzled up to his father. If Aubrey were here she'd be trying to pull down every table curtain in the joint.
"You met little Sage earlier today. These are my older children, three-year-old Willow, four-year old Henry, and my six-year-old twins, Eleanor and Gregory." All of her children smiled pleasantly at me. In the center of the round table were twinkling tea lights, and not a single child attempted to burn the place down.
Were they drugged, I wondered? I smiled. "Wow, you're all so well-behaved! And adorable!" I said, taking my seat beside Eleanor.
Emily sat down on my other side. "We actually try not to compliment them on their looks. It builds an unhealthy emphasis on the outer appearance."
"Yes, yes," I nodded, pretending to know what she was talking about.
Emily smiled. "It's best if children are raised knowing their true beauty comes from within."
I continued nodding, "Yes, the inside. Their internal...organs."
Emily cocked her head to the side. A member of the staff came by with a bottle of wine.
"Madame?"
Emily held up her hand. "No, thank you." She turned to me. "Breastfeeding. You know how it is."
I flushed. "Yes, but um...breastfeeding didn't really work out for us..." I said, trailing off.
"So your baby is on formula?" Eleanor asked. I was startled. What did a six-year-old know about formula?
I turned to the child. "Yes, she's on formula."
"Well, that's sad," said Eleanor, flatly.
"Eleanor," Emily interrupted sternly. "What did Mommy say about respecting the choices of others?"
Eleanor lowered her head slightly. "Know better, do better."
"That's right." Emily turned to me. "I wish I'd known. I would have introduced you to my naturopath. Have you considered donor milk at all?"
I motioned to the waiter for some wine.
"Not yet. There are so many preemies, you know. I wouldn't want to exhaust the supply."
The waiter filled my glass half full and I chugged the glass before motioning for a refill.
Emily eyed me. "That's so giving of you. You know what? I'm going to send you home with sixteen ounces of my own milk. How does that sound?"
"That sounds...amazing. Thank you," I said, trying not to choke.
Thomas grinned and took Emily's hand. "You're such a generous spirit," he said, gazing into his wife's eyes.
"And you are the love of my life," she said. They stared at each other ethereally.
I held my breath, not wanting to disturb whatever it was they were doing.
Kimmie popped up from out of nowhere.
"Oh, hi, Ashley! I just wanted to make sure you made it down alright." She was talking to me, but staring at Emily.
She went on. "Emily, Kimberly Reardon. From LA. I met you earlier. I just wanted to say how amazing and inspirational you are. The past few weeks have been incredible. My life has truly changed. Thank you." Kimmie held one hand to her heart.
Emily stood up and the two hugged. I tried to hold back my gag reflex.
"You are so welcome, Kimmie. Surely, there's space for one more. Would you like to join us?"
"Absolutely!" Before I could register what was happening, Kimmie was pushing her chair in between me and Emily.
When she was comfortably seated she gave me a tight smile. "Hi, roomie."
I shot venom at her with my eyes but smiled back. "Hi."
Within minutes Kimmie and Emily were lost in quiet whispering about the latest probiotic on the market.
"Ashley, what's your opinion on it?" Kimmie said to me, her eyes wide and innocent.
"I...uh, I love probiotics. I'm definitely pro-probiotic." I laughed, hoping other people would find my joke hilarious. Everyone at the table stared at me. Kimmie smirked.
The meal was halfway over when I saw Lauren and Janice make their way over to me. Oh, no.
"Ashley! Ashley, we just wanted to make sure we got this to you before the night was over."
Janice reached into her purse and pulled out a black T-shirt with the words Tush Girl emblazoned in pink rhinestones across the chest.
Kimmie covered her mouth and giggled. I saw Emily struggling to hold back a smile.
"What's a tush girl?" asked Eleanor.
"Oh, honey, it's for the tattoo on her tush," said Lauren, howling.
Eleanor's eyes grew wide. "You have a tattoo!" She burst into tears.
Emily rushed over to comfort her daughter. She looked up at me. "She's very sensitive. Unnatural body modifications upset her."
I took the T-shirt. "Thank you," I said without looking anyone in the eye.
Everyone was on their last cocktail when Emily tapped her water glass with her spoon.
"Before dessert comes out, I just want to say that I'm so glad all of you are here! I hope tomorrow you can experience the rest and relaxation you mama goddesses deserve! Have a wonderful evening!"
Everyone clapped politely. Despite the night turning out to be a royal mess, I was looking forward to getting pampered a little.
Waiters began placing large slices of a rich-looking chocolate cake with buttery chocolate cream frosting in front of every place setting.
"Mother," said Gregory. "Do we have any fruit salad?"
Emily grinned proudly and addressed the table. "The kids know they only eat refined sugar once every other month." To Gregory she said, "I can do even better than that!"
She turned toward Thomas. "Darling, will you ask the staff to bring out the date carob blueberry sweet potato tarts with the almond flour crust for the children?" She smiled at us, "I made them this afternoon."
Kimmie spoke up, "If it's okay, I'd love to try one of the tarts. I'm on a cleanse from refined sugars myself. Ashley, would you like one?"
I looked up from the piece of cake I was halfway through devouring and licked a glob of chocolate frosting from the corner of my mouth.
Before I could speak, Kimmie cut in. "Never mind. You look preoccupied."
Later, in our room, Kimmie couldn't stop raving about the night.
"Emily and I really hit it off," she gushed, sitting at the vanity, wiping makeup from her face with huge cloths. "I'd consider the night a win."
"Yeah, you really nailed it," I responded dryly, crawling under my sheets.
As I fell asleep I made a note to self: Don't trust Kimmie.
Thursday, March 7, 5:45 A.M.
My alarm beeped, waking me up with a start. It wasn't until I saw Kimmie standing in front of the mirror adjusting her top knot that I remembered where I was. I sat up. My body felt strange. I arched my back a little and tried to figure out what it was. It took me a minute to realize that what I was experiencing was...being rested. My mind was crystal clear. There was no pain behind my eyes. No sluggishness in my legs.
I felt rested. I hadn't felt like this since before Aubrey was born. I tried to wrap my head around the reality that some people feel like this every day.
"Good morning, sleepyhead," Kimmie sang. "Ready for yoga?"
I fake smiled in her direction and got out of bed. Rummaging through my suitcase I found a pair of sweats, sports bra and tank top. In two minutes I was dressed. As I leaned over the sink brushing my teeth, I heard Kimmie gasp.
I looked up. She was staring at me in abject horror. "Is that what you're wearing?"
I glanced downward at my blue-and-white tennis shoes, light gray sweats, black tank and blue zippered hoodie.
"Yes?" I asked.
Kimmie just scoffed before turning back to the mirror to perfect her cat-eye eyeliner. I took in her outfit.
Black and silver expensive-looking tennis shoes, skin-tight hot-pink Lycra leggings with black stripes going down the sides, a matching crop top that accentuated her perfectly flat stomach and a black headband. She looked like a fitness infomercial. I noticed the EW logo on the back of her pants.
"Is that from—"
"Emily Walker's line? Yes. I own every item. Ready to go?"
Next to Kimmie I was going to look like a garbageman making his weekly rounds, but we headed out anyway.
"No makeup?" Kimmie asked, as she shut our door.
"It's exercise."
"It's yoga," she corrected me.
It appeared Kimmie was right, because when we arrived at the South Lawn, there were only five other moms, and all of them were wearing makeup and Emily Walker's line of activewear.
"Good morning, ladies!" Emily was beautiful as always in a purple-and-white ensemble. "I'm tickled pink to see so many of you wearing my line!"
Her eyes settled on my hobo wear and she smiled sympathetically.
"I'd like to introduce you to Sven—if you read my blog, and I assume that you do, you already know he's my dirty little wellness secret." I heard one of the moms giggle.
Sven was six foot four of pure Greek male model. His dark brown hair accentuated his bright blue eyes. To the surprise (delight?) of many of the women, he was wearing only a small pair of black short shorts.
"Okay, everyone," Sven said with a deep Eastern European accent. "Grab a mat."
Sven and Emily led us through a variety of poses, each one more painful and impossible than the last.
"If you're a newbie to yoga, don't hesitate to take a break when you need one," Emily said, looking directly at me.
By the end I was a sweaty mess. I could see why everyone opted for synthetic materials. I had huge sweat stains in each armpit, a large one on my back, and to top it off, an embarrassingly large one in the crotch of my pants.
"Ashley, did you have an accident?" Kimmie asked in front of the entire class as we finished sitting cross-legged in deep meditation—a pose that exposed my swamp stain to the world.
Sven opened his eyes, looked at me and turned red.
"It's normal to experience these things during yoga, especially when your pelvic floor has weakened due to childbirth," said Emily calmly.
"I didn't pee. It's sweat," I said, humiliated, standing up.
"Yes," said Emily, obviously trying to preserve my dignity.
Kimmie snickered.
As we were stacking our mats, I placed mine on top of the pile.
"You can keep it," Sven whispered in my ear. I was mortified.
I assumed my nickname had morphed from Tush Girl to Pee Girl and ate my breakfast in my bedroom. Emily's assistant had been kind enough to grab me a muffin so I wouldn't have to face anyone.
I opened my computer and checked the time—7:15.
I had an email from David.
Hello supermom,
Everything's fine, don't worry. My mom is taking Aubrey to the zoo today. I hope you're enjoying yourself. A Realtor came by and said we can probably get market value for the house. Have a good time.
Love, David
I'd almost forgotten about the house. Unless I won the grand prize tomorrow, and things weren't looking great, we'd be moving in with Gloria soon after I came home. I snapped my laptop shut and took a few deep breaths. It wouldn't be that bad. At least I'd always have help just an arm's reach away...and eyes watching me all day long. I guess roaming the house in my underwear eating chocolate-hazelnut spread right out of the jar was out of the question.
I thought At least I have the La Lait moms, but remembered that after telling the truth, I wouldn't. I'd be trapped in Gloria's house all day and night. There was no way around it. I had to win this contest. I grabbed the schedule off of the vanity.
8AM Basket and Dream Catcher Making in the Craft Room.
Oh, crap. Crafts.
Janice and Lauren were sitting on either side of Emily at the long wooden bench table when I arrived. I had showered and changed into dark blue jeans and a pink Emily Walker sweatshirt—David gave it to me the night before I left and I figured this was the perfect time to wear it.
"Hi, everyone!" I said cheerily. Almost everyone was at the workshop, including my roommate, who was seated directly across from Emily. I took my seat next to her.
"Hi, Kimmie!" I said, forcing cheerfulness.
"Hi, Ashley," she responded with an equally saccharine tone. "Missed you at breakfast!"
I flipped my hair over my shoulder. "After yoga I like to spend some time in quiet meditation in order to realign my—"
"Your mama chakra system," Emily finished for me, her eyes bright with excitement. "Someone has been reading Motherhood Better!"
"Absolutely!" I said, ignoring Kimmie's mouth hanging open. "It's so important to clear yourself every morning. It has made the biggest difference in my life. My love tank is full." I clasped my hands together in silent prayer.
Janice and Lauren stared at me like I was from a different planet.
"That's absolutely wonderful!" Emily exclaimed.
"Namaste." I bowed to her.
Kimmie glared at me.
Emily's assistant placed an enormous bundle of loose wicker in front of each woman.
"Ooh, goodie! Is everyone ready? I trust you read over the instructional materials for Basket Making 101 in your welcome packet?"
The only thing I remember about the welcome packet was that it contained a bar of expensive chocolate.
Everyone flew into craft mode and began twisting and winding the pieces of wicker around long pieces of wood to create a frame for their baskets.
I watched Emily out of the corner of my eye and copied every movement she made. To my surprise, I was actually keeping up.
"Good job, Ashley! You're really a pro at this," Emily said, grinning.
"I love crafts," I lied through my teeth. Turning to Kimmie, I eyed her progress. She was clearly struggling to manipulate the wicker. It wasn't easy, considering her long, acrylic nails. "Do you need some help, Kim?" I asked.
"I'm fine," she said through clenched teeth.
"Well, don't hesitate to ask. The key to success in motherhood and in life is to reach out when you need to." I'd memorized that quote from Emily's book during breakfast.
Emily looked up and absolutely beamed at me.
Kimmie was silent.
I started to really get into it and added my own personal flair to my basket by alternating different shades of wicker. So this is what the big fuss about crafting is about? I thought. It was actually pretty relaxing!
The craft was just wrapping up. To my utter surprise, I finished my basket first! It wasn't perfect, but it was done. My first successful craft was complete!
"Wow, Ashley! You're the first one done. Go ahead and use the paring knife to smooth out the splinters. Brava!"
"I'm also done!" shouted Kimmie. I looked at her basket. It appeared to have been run over by a truck.
"Good effort, Kimmie! I guess we have a tie!"
I stood up and rushed over to the knife station, determined to finish fine-tuning my basket before Kimmie. She must have sensed my intention because she jumped up at the same time. We walk-ran awkwardly over to the table and I picked up the small knife first.
"Shame, you'll just have to wait," I said, tightly.
Kimmie grabbed the knife out of my hand. "I guess you will," she hissed, out of Emily's earshot.
I tried to wrestle it away from her. "You know, you've been getting under my skin since we got here. What's your problem?"
Kimmie grabbed the knife back. "My problem is that you don't belong here. Look at you. Mellie the dog mom would have been a better contestant."
"Oh, yeah? At least I'm not a complete phony. I'd be surprised if you even had any kids." Kimmie's face fell. I went to grab the knife back but at the last second she lowered it, causing the blade to go directly into my palm.
A stream of blood spouted up and onto the front of my sweatshirt.
I screamed. Emily and several women rushed over.
"Oh, my!" Emily yelled. She grabbed an apron off of a wall hook and pressed it to my wound. "What happened?"
I looked over at Kimmie who had gone as white as a sheet. Her eyes were filled with tears.
"I slipped," I said.
"I'll take you to First Aid. We had a doctor stay for the week just in case something like this happened."
Kimmie stepped forward. "No, I'll take her. She's my roommate."
Kimmie and I were silent as we walked to the main house. It wasn't until the doctor had seen me and put some gauze over my palm (which turned out to have just a surface wound) and left the room that she burst into tears. Not tears—more like heaving sobs.
I was stunned. "Kimmie, it was an accident. I shouldn't have reached for the knife like that," I said, sitting across from her.
The tears continued to fall and snot poured out of her nose. I handed her a tissue.
She blew her nose. "It's not that. I'm so sorry for how I've been treating you, Ashley. You didn't deserve it."
I wanted to say, "No, I didn't," but this didn't seem the right time to rub it in.
"It's just that..." Kimmie blew her nose again and struggled to stop crying "... I know I'm not going to win the contest. I'm a crap mom. I can't cook. I can't craft. I lied on almost all of my journal entries. I'm a complete fraud. Compared to someone like you, I'm a complete mess."
Huh?
"Kimmie. Someone like me? Just what kind of mom do you think I am?"
Kimmie shot me an "oh, you know what I mean" look. "Come on, Ashley. I couldn't survive without my nanny and getting meals delivered daily. You do it all by yourself. You're probably so hands-on and patient all the time. You're the perfect mom."
I couldn't help it, I started to laugh. "Kimmie, I am not the perfect mom. I almost lit my entire house on fire during the craft challenge. I wear the same pants for three, four, seven days in a row. I'd do anything to have a body and sense of style like you."
Kimmie sniffled. "You think I have a nice body?"
I laughed. "Okay, let's go back to the group."
As we made our way back, things felt different. More relaxed. Not having Kimmie as my enemy was pretty awesome. Turns out she didn't know anything about probiotics and was totally talking out of her backside.
As we were walking, I decided to get some air.
"Kimmie, I'll meet up with you later. I'm going to take a walk."
"Are you sure?"
I nodded. She squeezed my shoulder. "Thanks...for understanding."
We parted ways and I followed a path through lush greenery and took in the view. Emily's house was slightly raised, making it possible to see the rows and rows of vineyards the area was famous for. The morning sun felt like heaven on my skin and a light breeze tickled the hair on the back on my neck. I felt like I was in paradise.
A twinge of guilt formed a knot in my stomach: Aubrey. I was sure she was fine, but felt a little bad enjoying myself so deeply. Then I remembered what was waiting for me when I returned. It was almost a sure reality that we'd be moving. I'd known when David started his business that it was a risk, but I'd had so much faith that everything would magically turn out perfectly that I hadn't considered what would happen if it didn't. He must be feeling so bad right now. While I'd been worrying about finding friends and losing weight, he'd been quietly fighting his own battle for the financial security of his family.
I sat down on a charming wooden bench in front of a koi pond. A dozen big orange, black, white and red fish swam lazily among the water lilies and lotus flowers. I kicked a smooth white stone with my foot and it plopped into the water, creating a shockwave of circular ripples.
And there was still the matter of my La Lait friends back home. I'd procrastinated long enough. Maybe the best thing to do was send Nina an email to read to the group while I was here. Yes, that's what I'd do. The bit of geographical distance was just the courage I needed. At the same time, I'd email David and apologize for everything that had happened in the last few months. What he needed now was a strong wife who was by his side 100 percent.
I took a deep breath. It was time to face my problems. I stood up and was about to walk back to my room when a stunning red koi with black stripes down its back caught my eye. "Aubrey would love to see that," I thought to myself. Joy was always taking photos of interesting things to share with Ella and George. She called them "experience boosters." George did have the most amazing vocabulary for his age.
I pulled my phone out of my pocket and focused on the fish before snapping a quick pic. I examined my work. Too blurry. I needed to get closer.
Carefully, I made my way through the ankle-deep shrubbery toward the edge of the pond and snapped another photo. Better, but it was hard to make out the details in his scales.
I planted one foot firmly on the ground, rested the other one against a smooth rock wedged in the corner of the pond for leverage and leaned in. My phone's camera clicked. I examined my work without moving. Absolutely perfect. It looked almost professional. I couldn't wait to post this one to Facebook. As I lowered my foot from the rock, it hit a wet patch, sending my body lurching forward, and before I could think, I was completely submerged in cold water.
My arms and legs flailed wildly as I struggled to stand. After a few moments of rising and then falling again on the slippery pond floor I found myself soaking wet in chest-high water, my phone nowhere to be found.
"This isn't happening," I muttered to myself, trying not to cry as I, with the elegance of a sea manatee, made my way out of the pond on my chest.
My jeans and tank top were stuck to my skin. My top, which was only meant to be worn under my Emily Walker sweatshirt, was completely see-through. I pulled the fabric away from my chest and looked around. The gauze on my hand was soaking wet and stung. Thankfully, there was no one in sight.
I was pushing strands of wet hair out of my face and trying to get my bearings back when I heard a woman's voice.
"Absolutely not!" she yelled. It was Emily Walker. I turned my head toward the sound. It was coming from the balcony above me. I had just enough time to run toward the wall and hide under the terrace before she stepped out onto it.
I froze.
"Thomas, you promised to be here tonight to help with the kids. I'm hosting a very important dinner!"
She paused.
"Okay, when will you be back? You can't expect me to do this all on my own. I need your support. Sage is teething—I can't stay up with him all night and be ready for taping tomorrow..." Emily's voice cracked.
A breeze swept over my already cold body, sending a chill down my arms. A sneeze began to build but I managed to squelch it before it erupted from my nose.
"Why is it that your work is always more important than mine?"
I looked right and left, trying to find a means of escape, but there was no way Emily wouldn't notice a soaking wet woman darting across the grass.
"Don't you dare throw the nanny in my face. I'm still their mother and I need you here! I'm exhausted. All of this is exhausting. I can't do everything by myself anymore, I just—"
Emily paused as if she'd been interrupted.
"Fine. Just do whatever you want."
I heard her sigh deeply and then sniff as if holding back tears.
I shivered. I felt another sneeze rising in the back of my nose and covered my mouth but it erupted before I could stop it. My heart skipped a beat.
"Hello?" Emily's voice cut through the silence. "Is someone there?"
I awkwardly walked out from under the balcony and tried to appear casual.
I waved. "Oh, hey, Emily! I was just passing by!"
Emily quickly wiped a tear from her eye. "Hi...Ashley. Um...are you wet?"
I looked down at my shirt and to my horror, the cold had affected much more than just my nose. I did my best to appear nonchalant.
"Oh, that, yes. I was swimming. I went on a swim."
Emily cocked her head to the side. "With your clothes on?"
I smiled like an idiot. "I'm shy."
Emily nodded, but it was clear from her expression that she thought I was mad.
"Well, I hope you're enjoying yourself. If you need anything don't hesitate to ask," she said, smiling tightly.
"Thanks so much!" I responded with too much enthusiasm before scurrying off.
It took me twice as long as it should have to get back to my room. I had to do plenty of ducking behind furniture and into stairwells to avoid running into anyone else with my pencil-pointed nipples.
When I finally closed the door behind me, I sank behind it to the floor. Thankfully Kimmie was nowhere to be found. Two thoughts ran through my head.
I'd just made a complete fool out of myself AGAIN in front of Emily. If the "tush girl" incident hadn't taken me out of the running, "swimming with my clothes on" certainly had.
Emily is far more normal than I realized. I must have had that exact conversation with David a million times. I knew her blog was supposed to be all rainbows and sunshine, but it was weird that she never talked about feeling overwhelmed.
I stood up and walked into the pristine bathroom to take off my clothes. As I undressed and hung my wet jeans on the shower rack, I felt a twinge in my chest. Aubrey. She had to be up from her nap by now. What time was it? I looked around for my phone for a moment before remembering it was at the bottom of a pond surrounded by majestic fish. Great. Just what I needed. Another bill.
6 P.M.
I stood in front of the bathroom mirror and studied my outfit. The black wrap dress I'd purchased for the date night that never happened looked great on me, paired with black pumps I'd borrowed from Joy. It was long-sleeved with a bit of a V-neck and hit perfectly at my upper calves, showing off a little leg. I had skipped the makeovers I'd been so looking forward to in favor of showering after my dip in the koi pond, but Kimmie had volunteered, or insisted, rather, that she do my makeup and the results were surprising. Every time I tried to pull off a smoky eye, it looked like I'd been hit in the face with a baseball bat, but she'd created the look flawlessly.
"You don't use lip liner?" Kimmie had asked while drawing on my lips.
"I pretty much only use lip gloss," I responded, trying to keep my mouth still.
She shook her head as if the information was too much to comprehend.
I twirled in the full-length mirror. I looked good. Amazing. I looked like the woman I was before Aubrey.
As much as I wanted to revel in my Cinderella moment, my heart was heavy.
An hour earlier I'd FaceCalled with Aubrey and David on my laptop, which had been bittersweet.
"Say hi to Mama!" David sang, while holding Aubrey up to the camera. Her sweet little face gazed innocently at me on the screen and it was all I could do to hold back the tears. I missed her so much. I wondered for a second if it had been a mistake to leave her. All I'd wished for the past ten months was a break, and now that I had one, I was dying to have her in my arms.
"I love you, baby!" I said, waving at her, and she broke out into a huge grin at the sound of my voice.
"So, how's Napa?" David asked, juggling Aubrey, who was wearing a pair of too-small yellow pajamas.
"It's good," I said. My mind flashed back to my accidental dip in the koi pond. "Really good."
"I'm glad," he said. I could tell his words were sincere, despite the solemn look in his eyes.
"David, are you sure this is what you want?" I asked gently. "I just can't believe this is happening. What about a business loan?"
David pursed his lips. "I've already tried, Ashley. We really needed the DentaFresh account."
I sighed. "So when do we move?"
Aubrey giggled.
"I found a Realtor who thinks that if we price it right, we'll have an offer in two weeks."
My heart sank. "How are Ross and Donnie doing?" Ross and Donnie were David's partners and both fathers with families. I figured they were as devastated as David. I tried not to cry.
He shrugged. "Nobody's happy, obviously, but they're young. They'll find work easily."
His voice tightened up. I knew this was hard for him.
"And Melissa?" I asked, trying to come off nonchalant.
David scowled. "I could care less."
I blinked. "What happened?"
"Oh, I didn't tell you? She's the reason we lost the DentaFresh account."
"What?"
"Yeah. An old buddy of mine on one of their accounts told me they passed on us because someone on our team sent them an email pretending to be a rival company to light a fire underneath them. She denied it, of course, but I checked up on it and the email definitely came from our server's network. What was she thinking?"
My body flushed with heat and I couldn't breathe.
"What...what are you going to do?" I managed to say, practically trembling.
"I fired her yesterday," he said, shaking his head. "I can't believe she'd do that to us."
"You can't," my voice said without permission from my brain.
"What?" David stared into the camera.
I moved backward on the bed, as if trying to create distance in addition to the thousands of miles already between us.
"You can't fire her. Not like this." I was shaking.
"Ashley, if—"
"It was me, David," I blurted out. "I sent the email."
David looked like he was going to faint as he took in my words.
"You? Ashley...why...when?"
I held my face with my hands. "I was trying to help, I knew you were worried, oh, my gosh, David, I'm so sorry. It's all my fault."
I covered my face and breathed deeply, waiting for him to speak.
He took a deep breath and his face relaxed. Relief washed over me. Then he spoke.
"Yeah. It is."
My breath caught in my throat. "What?"
"I can't believe you did this," he said, dryly. He stared at me as if trying to recognize a stranger.
Tears sprung into my eyes. "David, I said I was sorry..."
He stood up out of the frame. All I could see were Aubrey's feet dangling from his hip.
"I can't talk to you right now. I'll call you tomorrow."
"David."
"Bye."
The camera went black.
I sat there in shock. He had every right to be upset, but I wasn't expecting this.
What was I thinking? I sat on the bed, staring at my hands. I hadn't been thinking. I'd been in a sleep-deprived haze that day, but that was no excuse. I should have thought. I should have talked to him first. I was just scared for him, trying to help. He'd never forgive me for this. A tear slid down my cheek. I just wanted to be at home, not here in some mansion pretending to be someone I'm not.
I wiped my face. May as well let the other shoe drop.
I clicked on the email icon on my computer and without thinking composed a letter to Nina and Lola.
To: Nina Pikkering and Lola Vetter
From: Ashley Keller
Subject: The truth about me
Hello Nina, Lola and everyone at La Lait. I have something to confess that has been weighing heavily on me. I'm not who you think I am. I'm not breastfeeding and never was. What happened in the café when we first met was all a misunderstanding and then, because I was so desperate for friends, and you were all so wonderful to me, I led you to believe that I was one of you. Well, I'm not. I'm sorry for lying. I won't contact you again.
Ashley
I pressed Send before I could chicken out then clicked my computer shut. I took another deep breath. I didn't feel scared. I didn't feel sad. I didn't feel anything. I glanced around the room and noticed the welcome basket sitting on the dresser. Kimmie had already rifled through it and probably snagged all the good stuff, but a mini bottle of champagne remained. Not feeling the need for formalities like ice or glasses, I uncorked it and helped myself to a few long, bubbly sips. Within a few minutes I felt refreshingly peppy. When did I become such a lightweight?
I gazed at myself in the bathroom mirror. Two months ago I would have been thrilled to know I'd be standing right here, all dressed up, about to have dinner in Emily Walker's home. Two months ago this would have been my dream.
"Are you coming, Ashley?" I heard Kimmie call from the bedroom.
I walked toward the door and stumbled a little before catching my step.
"Note to self, don't fall over," I whispered, giggling. I hadn't drunk that much, but the tension from my call with David seemed to make the alcohol go straight to my head.
Kim raised an eyebrow at me as I walked toward her. She looked gorgeous in her red strapless minidress and matching red heels. Her makeup was even more dramatic than mine—from the cat eye to the bold, crimson lipstick, she looked like she'd jumped right out of a luxury car commercial. How did this person have children?
I stumbled again.
"Someone's been enjoying themselves a little too much! Wish you'd saved some of that good stuff for me!" she said, laughing.
I picked my purse up off of the bed and offered Kim my elbow. "Shall we?"
She hooked her elbow in mine. "We shall."
So what if I'd lost my house, my friends and my husband's trust? Tonight, I was determined to have one night of fun before facing the music that was waiting for me at home.
The large dining room had the air of a sophisticated French restaurant. Twinkling lights hung from the brick accent wall, which was draped with real ivy. The long, beautiful table was set with glass vase centerpieces bursting with white hydrangeas, and tall cream-colored candles adorned the silver runner. The entire table was dotted with tea lights that flickered against dimly lit walls. It was breathtakingly romantic.
Even in my state, I could appreciate how stunning the room was. A butler, with a white tea towel on his arm, stood at attention by the door.
"May I help you ladies to your seats? Madame Keller and Madame Reardon, yes?"
Kim and I looked at each other before bursting into laughter.
"How did you know our names?" I asked incredulously.
The butler didn't smile. "We have been briefed on all guests. Please follow me."
We were led to seats at the head of the table. I picked up the pink and gray folded name card on my salad plate. Ashley Keller.
Kimmie was seated beside me. She whispered in my ear, "Ashley! You're sitting next to Emily! Lucky! Wanna switch?" She tried to edge her way past me.
"Not on your life!" I yell-whispered back, sitting down quickly.
A woman appeared on my right. "Champagne, madame?"
"Yes, please!" I answered.
The woman gently took my flute and filled it.
When Kimmie's glass was full we cheered and sipped. The bubbly liquid was like a calming balm against my anxieties.
I turned to Kimmie and put a hand on her shoulder.
"I love this. I love you." A carefree laugh escaped out of my mouth and became a snort.
Kimmie's eyes grew wide. She nudged me. "Well, you'd better pull it together because here comes Queen Bee."
Everyone rose, as if a dignitary had just entered the room. I stood too quickly, causing my chair to fall backward. For some reason, I found it hilarious and dissolved into cheery laughter.
Janice, who was seated directly across from me, exchanged glances with Lauren.
"Whoops!" Emily bent down to help me right my chair. "Good evening, Ashley. How is your hand?"
I lifted up my palm. "As good as new. I can barely feel my hand. Or my face." I giggled.
"I'm...glad to hear it," she said, kindly ignoring the second half of my statement.
Emily looked stunning, as always, in a pale pink and lavender knee-length tea dress with white sling-backs. Her hair was pulled back into an elegant bun. She wore a pearl necklace and matching earrings. Her makeup was subtle but polished: a mauve lip, long dark lashes and charcoal shadow.
Emily took her place at the head of the table, to my right, and everyone took their seats.
"It's so nice to see all of you tonight. I can't tell you how excited I am about the Motherhood Better Bootcamp Finale tomorrow. Who's ready to find out who's going to be crowned as the Motherhood Better champion?"
Everyone clapped politely. I hooted. Janice coughed and gave me a disapproving look.
"Before we dig into this glorious meal that my chef, Lorenzo, put together, I just want to thank all of you for sharing so much of yourselves and being so willing to put yourselves out there. It means everything, not just to me, but to the thousands of women who will hear about your journeys tomorrow."
The women nodded politely. A chiseled Latin man wearing a chef's hat and black apron appeared behind Emily.
"Ah, Lorenzo! Everyone, this is the chef whose amazing recipes grace the pages of EmilyWalker.com. He's been feeding my family since before my eldest could walk."
Lorenzo took off his hat, revealing a luscious head of black ear-length curls. It was as if the room suddenly grew warmer. I saw a few ladies shift in their seats.
"It's very nice to meet all of you. I hope you enjoy your meal. Bon appetit!" he said, nodding.
I raised my hand.
Emily looked at me, confused.
"Yes, Ashley?"
I heard myself speak. "Actually, I have a question for Lorenzo."
Emily laughed nervously. "Okay."
Lorenzo stared at me, curious.
I took a sip of my champagne and tried to look scholarly.
"Do you have any advice for mothers who hate cooking?"
The table burst out into laughter. Emily blinked, wide-eyed.
I glanced at Janice and noticed that her face was red with laughter.
Lorenzo chuckled and then placed his finger on his chin.
"Takeout?"
Everyone burst into rowdy guffaws again. Even Emily had her napkin against her mouth to hide her chuckles.
Emily put her hands up. "Okay, okay, everyone. Very funny, Ashley. Who's ready to eat?"
Everyone clapped and hollered. I'm not sure if it was the promise of food, the champagne or my question, but the mood had relaxed significantly.
A flurry of waitstaff placed appetizers on everyone's plates.
Mine arrived—a set of three mini puff pastries, all stuffed with unique fillings. There was creamy chive, some sort of smoked fish and one overflowing with a fragrant relish.
Once everyone had been served, Emily raised her fork. "Dive in!"
And we did! Course after course continued to arrive. I lost count after five. The main dish was half a crispy, perfectly roasted duck with roasted garlic potatoes and asparagus. I hadn't eaten that well since my wedding.
"So, moms," Emily said, dabbing her lips with a linen napkin. "Before we go live tomorrow, I want to hear what your bootcamp experiences have really been like. Feel free to be perfectly honest."
A woman in her late twenties wearing a green cardigan and skirt set with black curly hair raised her hand. I recognized her as Lillian Pearson. She had three-year-old twin girls and had written the most thoughtful journal entry about starting a food drive in her city.
"Yes, Lillian!" Emily said, taking a most un-Emily-like swig from her wineglass. Was that her fourth glass?
Lillian stood. She smoothed the front of her sweater. "I just want to say that this has been the best experience of my life," she began shyly. "Usually, it's just me and the kids at home all day, not really talking to anyone. Since starting the Motherhood Better Bootcamp, I've felt like I have real friends and—" Her voice broke and she took a second to compose herself. "I feel like people understand me."
I could feel tears welling in my eyes. Glancing at Kimmie, I noticed her wipe the corner of her eye with her napkin. Even Janice was misting up.
Lillian continued. "I want to thank you, Emily, for putting this together. I've admired you for a long time and it has been an honor."
Emily stood up and, without saying a word, pushed out her chair, walked over to Lillian and gave her a long hug.
My heart swelled. This is what it's all about, I thought. This is all I want and need in motherhood. People who get it.
Emily made her way back to her seat, wiping her eyes with her fingers the whole way. She took another sip. "Does anyone else want to share?"
My hand shot up.
Emily smiled. "Ashley? The floor is all yours."
I stood up and felt myself get a little dizzy. My two glasses of champagne had gone right to my head. I used Kimmie's shoulder for balance. She laughed into her glass.
Once upright, I cleared my throat. "Everyone. Emily." I turned to face my host. "I'm not like all of you. I don't bake. Not anything very edible, anyway. I can't crochet my own baby clothes. I'd rather order pizza than make anything." I looked up and saw that everyone was staring at me, most with jaws dropped, but nothing was going to stop me now. "My house is always a mess and I'm genuinely surprised that a family of possums hasn't moved in." I paused, trying to find my words. My eyes met Emily's.
"I'm not like you. You're perfect, Emily. I've always wanted to be the kind of mom you are and I'll never be that. You make organic gluten-free apple butternut squash scones. I eat peanut butter off of a spoon in my underwear on the couch while my baby naps. You recycle old clothes into keepsake quilts. I sometimes buy new pants to avoid doing laundry. You make the most beautiful crafts out of mason jars and buttons. I don't know where my passport is."
I heard someone giggle.
"Point is, I know I shouldn't win tomorrow, because before me is a group of women—" I turned to Kimmie "—not you, Kimmie. You're just as messy as I am. Women who inspire me and make me feel insanely jealous and inadequate. I want to raise my glass to all of you."
I thrust my wineglass in the air, sending a stream of chardonnay directly into my face.
"Ow!" I screamed as the liquid burned my eyes.
Emily jumped up and put a napkin to my face, helping me back into my seat.
I blinked my eyes until everything came into focus.
Emily began to speak. "That was...quite the speech, Ashley, I—"
"I HATE MY HUSBAND," said a voice to my left.
It was Serena Hossfield, mother of four and bake-sale fundraising expert. Emily and I both stared.
She stood up, suddenly shy. "I mean, I love him, but I hate him at the same time. He doesn't understand my life at all. He pretends to take a crap and plays on his phone for hours at a time."
Other moms nodded enthusiastically and murmured. I exhaled sharply. Was this happening?
"I HATE CRAFTS!" a petite mousy brunette shouted, standing up. Tanya Gregory, mom of three. I'd recognize that face anywhere. She'd practically flooded the portal with photos of her creations: keepsake boxes, scrapbooking ideas and shadow boxes.
"I HATE THEM!" she screamed again. Her eyes were wide and wild. She took a long drink of the brown liquid on the rocks in her glass. "I only do them because they make me feel better than other moms who can't. It's my gift and my curse. But deep down, I'd like to douse my craft room and set it ablaze."
From her seat, Emily tried to regain control of the rapidly spiraling room. "Okay, okay, everyone," she said, pushing down with her hands.
"Breastfeeding sucks!" shouted a tall woman with a black bob next to Janice. She stood up. Her sweater dress accentuated her slim build.
"I hated every minute of it, but my doula convinced me my baby would be a dumb-ass if I didn't do it. That's crazy. My nephew was breastfed for two years and he's the slowest kid I know."
Emily stood up. "That's quite enough, everyone. I know our lives aren't easy but..." Her voice trailed off and she stared at the empty seat directly across from hers. The one meant for her husband.
"You know what? Screw this." Emily threw her napkin down on the table and everyone stared at her like they would a mother who had finally snapped.
Emily picked up her drink. "I'm tired of being little miss perfect. Life is freaking hard sometimes. It's hard. Kids don't listen. Husbands act like jackasses and I do EVERYTHING! I do everything! I'm tired of making organic quinoa cakes when I just want to order a pizza. I love chocolate cake. I love gluten. I LOVE GLUTEN." Emily gestured toward her lower half.
Everyone cheered.
"To gluten!" she said, raising her wineglass. We all raised ours with her.
Emily put her other hand on the table and leaned forward. "Who wants to get crazy?"
Everyone hooted. Emily smiled. "Lorenzo! We're gonna need more wine!"
Friday, March 8, 6 A.M.
I woke up with a splitting headache. I put my hands on my head, trying to quell the throbbing coming from within my brain.
Opening my eyes, I noticed that I wasn't in my bed. I wasn't inside. I was lying in a pool chair next to the hot tub. Beside me was Janice, hunched over on a beach towel propped up against a table. I scanned the crime scene. Among the bottles, bags of chips, empty pizza boxes and wet bikinis were passed-out moms. Then I noticed Emily. She was fast asleep, curled up on a pile of robes under a patio table.
I sat up. Kimmie was on the next beach chair over.
I pushed her shoulder. "Kimmie. Kimmie, wake up." She grumbled and struggled to open her eyes.
"Kimmie, what time is it? Aren't we taping today?"
Kimmie's eyes flew open. She jumped up with the strength of a dozen toddlers. "You have got to be kidding me! I need my injections!" And with that she gathered her shoes and ran toward the main house.
"Emily! Emily!" I could see Anna running across the lawn toward us with her trademark clipboard in hand.
When she finally reached us, Anna stopped dead in her tracks, trying to take in the carnage.
"What. Happened. Here?" she whispered.
I stood up and wobbled a bit. "We got a little...um, wild last night after dinner."
"I can see that," Anna said through her teeth.
Anna stomped over to Emily and gently prodded her shoulder. "Emily. EMILY."
Emily woke up with a start and tried to rise, hitting her head on the bottom of the table.
"Oh, my, what time is it?" Emily said, rubbing her eyes.
"We're an hour from taping. The set is ready and the whole crew is here."
"No, no, no, no, no." Emily crawled out from under the table and wrapped a towel around herself. "Anna, why didn't you wake me earlier?"
"I couldn't find you! Hurry, you need to go to wardrobe. We don't have time for a rehearsal."
Emily stood up and faced the group of exhausted, half-sleeping, hungover women in various states of dress.
"Everyone! Wake up! We're going live in an hour! Go get dressed! Meet me in the main lobby in half an hour for makeup! Chop-chop!" she said, clapping her hands.
Women began to move, sliding off patio chairs and coming out from under tables. It was like a zombie invasion.
Emily and Anna were about to scurry off. I grabbed Emily by the arm.
"Emily, I'm so sorry, I—"
Emily raised a hand. "Ashley. Best. Night. Ever." She ran off and I stood there smiling.
It was showtime.
Back in the room, Kimmie was spinning around like a Tasmanian devil.
"I can't believe we partied last night! The night before we were supposed to go on live TV in front of millions of people!" she said frantically, throwing cosmetics and outfits in every direction.
"Relax, Kimmie," I said, removing last night's eye makeup with a baby wipe. "Just jump in the shower and get dressed."
Kimmie turned to face me. "I don't just 'jump in the shower and get dressed.' I had my routine all planned out and I'm about six hours behind on it."
She walked into the bathroom and slammed the door.
I'd planned to shower, but what was another day without one? Anyway, I was pretty sure I'd been in the hot tub at some point, which was as good as a shower.
My stomach fluttered. Tonight I'd see Aubrey and David. Hopefully he'd settled down a bit and wasn't still so angry with me.
I looked in the vanity mirror. The area under my eyes was streaked with dark makeup, my complexion was blotchy and my hair was a knotted mess, but I couldn't help but smile. I'd had fun. For the first time in a very long time, I'd had carefree fun. I hadn't even drunk that much, just gotten carried away with a group of women who were all having their first fun night in ages. I laughed as the night came back to me. I'm pretty sure Lorenzo brought out organic lychee Jell-O shots at one point, and Emily did a cannonball in the pool.
I wiped the rest of my makeup from my face and brushed out my hair.
Time to change. Thankfully, I'd already planned my outfit. I stood up and pulled a hanger out of the closet. The producers of The Emily Walker Show had emailed guidelines for what not to wear, which included blue (in case they used a blue screen), complicated patterns and wild colors. They hadn't said no to yoga pants and XXL T-shirts, but I assumed they were also discouraged.
I quickly changed into a slimming heather-gray skirt suit. I had plenty of these from my office days, but none of those fit, so I'd had to buy one the day before we took off. I knew we didn't have the money for new clothes but I considered it the last little splurge before we tightened up, and how often would I be on national TV? This moment would be frozen in history; I wanted to at least look pulled together.
I could still hear the shower running when I left the room. Kimmie was probably in there pumping her face full of a chemical cocktail.
* * *
The set was larger than life.
Large cameras and microphones on robotic arms, wires everywhere, men and women wearing all black hustling to and fro and staring at large monitors. How they'd managed to turn the room where we'd had brunch just two days prior into a real live set, I'd never know.
I tried to take it all in. At the front of the room were three large couches and Emily Walker's signature pink armchair. I presumed that was where we'd be sitting. My stomach flipped. I was going to be on live television. What if I threw up?
"Are you looking for makeup?" a college-aged man in thick horn-rimmed glasses asked me.
"Yes," I said, trying not to appear as flustered as I was.
"Right this way," he said, leading me through a tangle of thick black cords. As we made our way through the equipment jungle, I realized that today was the day. The winner of the Motherhood Better Bootcamp was going to be announced.
Before I knew it, we were in a corner of the room with several tall stools and women being painted by a crew of artists.
"Take a seat," a man with hair down to his lower back said to me, and I did.
I shifted. "I'm hoping for a natural look, I don't wear a lot of..."
He lifted his finger to his lips. "Shh. Fabio will take care of you."
I closed my eyes. I could feel him pressing a foam applicator to my face, then an eye pencil, lip liner, some type of tickly brush. I flinched as he tweezed my brows. After ten minutes I heard his voice.
"All done."
I opened my eyes, and saw him holding a round hand mirror to my face.
I took it and, with feelings of trepidation running through my veins, looked in.
I didn't recognize myself. I looked like me, but richer. Better. Beautiful. He'd used the contouring method I'd seen on several online videos and had tried once to emulate, which resulted in tiger stripes up and down my face.
I marveled at my reflection.
"Good, right?" Fabio said, grinning.
"Not good. Amazing. Thank you!"
"Ten minutes until we're live!" yelled a stagehand.
Out of nowhere, Kimmie ran into me. She was fully dressed in a stunning navy blue minidress and sky-high white heels. Her hair and makeup made her look like a Miss America contestant.
"Kimmie! When did you get your makeup done?" I didn't recall seeing her being made up.
She flipped her layered, bouncy hair. "I had my own makeup and hair team scheduled to meet me in the room. We barely had enough time."
Emily Walker appeared in the center of the room. She looked flawless in a pink blazer, white skirt and pink heels. A hush fell over everyone.
"Hello, everyone! I know we had a...special night, but I'm so proud of all of you for making it here on time! This is the moment you've all been waiting for. In a few minutes, we'll be live on television to crown the Motherhood Better Bootcamp champion!"
Everyone cheered.
"And then we'll have breakfast."
A wave of nausea ran over me. I heard a woman say, "No, thanks."
I grabbed a bottle of water from a nearby basket.
"Five minutes until we're live!"
A man popped up next to me. "Ashley? Let's get you miked up," he said, affixing a microphone to the top collar of my blouse.
Kimmie grabbed my hand. "Are you ready?"
"Are you nervous, Kimmie?" I asked, teasing.
She took her hand back. "Absolutely not," she said, smiling sheepishly.
As a group, the women and I made our way up to the stage. Assistants directed us to specific seats. I was just one contestant away from Emily.
Emily sat down in her armchair with a handful of notes.
"Okay, everybody. We didn't have time for a rehearsal, so just act natural, answer the questions and don't be nervous."
Easy for her to say. She'd done this before!
I squirmed under the bright lights. This was the moment the last six weeks had been leading up to. I was a little sad it was all coming to an end, but excited, too. I knew my journey hadn't been as perfect as the others', but I still had a shot, right?
"Thirty seconds until we're live!" a woman shouted and I felt my stomach flip-flop again. "Don't throw up," I willed my body.
"Ten, nine, eight, seven, six, five, four..." A man next to the largest camera motioned to Emily.
I felt a hot flash run through my body. This was happening.
Emily beamed her million-dollar smile at the camera. "Good morning, and welcome to The Emily Walker Show!"
A camera on a long metal arm panned over the three couches. I tried to smile naturally and not like I was being held hostage.
Emily went on. "As you know, this is the grand finale of the Motherhood Better Bootcamp! The moms you see before you spent the last six weeks being mentored by me on how to become the women they've always known they could be. I'd like to introduce you to these women."
Emily went down the line and, as the camera panned across the couches, introduced us by name. I was petrified. Millions of people were staring at us now. By the time she got to me, I was just doing my best not to visibly shake.
"Ashley Keller, mom of ten-month-old Aubrey!" I heard Emily's voice say. I stared like a deer in headlights at a large camera with a flashing red dot indicator. Smile, Ashley, smile, I heard my brain saying, and I managed a nervous grimace.
I could already see the Twitter hashtag. #WhatsWrongWithAshley. It'd be trending before the day was over.
Emily leaned into the camera and smiled her perfect smile. "I'm SO proud of these incredible women! They've changed themselves, their homes and their communities in huge ways. Before I announce the grand prize winner, I have a little surprise for them."
A large, flat LCD screen was wheeled in by an assistant. The women began to murmur curiously. What was going on?
Emily stood next to the screen with a remote in hand. "Ladies, you're not the only ones proud of how far you've come. We have a little secret. We spoke to those who know you best and asked them to share their thoughts."
Emily pointed the remote at the screen and pushed a button.
The EW logo swirled across the screen in pink and white. Suddenly, a man in his forties with toddler twin girls in his lap was sitting on a couch in a modest living room. "Lillian has always inspired me to be better." Lillian covered her mouth and began to tear up.
"Watching her pour herself into this challenge just reminded me of how strong she truly is. I love you, Lil."
Lillian began to sob. "We wuv you, Mommy!" the girls said in unison. I noticed Kimmie quickly wipe a runaway tear from her cheek.
One by one, the women soaked up praise from their spouses and children. I wasn't surprised when a well-dressed man in designer glasses, sitting in what looked like a lavish mansion, turned out to be Kimmie's husband. "You're a winner, babe!" he said, winking.
Kimmie beamed and winked back at the screen. I coughed into my hand to hide my giggle.
When I looked back at the screen, there were David and Aubrey, sitting in our living room. They were on our old couch, which meant this was taped weeks ago. My breath caught in my throat. I missed that living room. I missed my life before I messed everything up and tried to become someone I'm not. I missed my family.
"Ashley is the most incredible, loving woman I know. She's an amazing mother and blows me away every day with her dedication to our daughter. If she didn't change a thing, she'd still be perfect. Perfect for us."
I felt a sob rise in my throat and, despite my best efforts, was in full ugly cry mode in less than five seconds. I couldn't stop. Sob after chest-racking sob consumed me. I had no idea David saw me like that.
A blurry woman handed me a box of tissues. It was Emily Walker, she was standing by my side.
"Beautiful, weren't they?" She spoke into the camera, with one hand on my shoulder. I blew into my tissue. The hashtag had probably changed to #GetAshleySomeHelp.
Emily continued. "When we get back from commercial, I'll announce the winner of the Motherhood Better Bootcamp challenge, live, right here on The Emily Walker Show. You won't want to miss it."
"Commercial!" someone yelled, and a flurry of makeup artists descended on the stage.
"Good emotion, Ashley!" Emily said, giving me a thumbs-up as someone dabbed at her eyelids.
I smiled weakly.
Kimmie touched my hand. "Are you going to be alright?"
I blew my nose again. "Yeah, I just..." I trailed off.
Kimmie waved the air in front of her. "No need to explain. When Max said, 'You're a winner, babe,' I would have lost it, too, but I remembered that we're on camera."
Kimmie side hugged me. I could tell she was trying to be sweet.
A makeup artist approached me. "Would you like me to, um...?"
"Yes. Yes, please," I said, bunching up my tissues.
A few moments later, besides slightly red eyes, I was TV ready.
"Twenty seconds!" someone yelled.
Anna appeared to my right.
"Ashley, we need you to move to the first couch."
"What?" My hands began shaking. I was moving closer to Emily? This had to be good!
I swapped seats with another mom and wound up right next to Emily Walker.
"Doing alright, Ashley?" she asked between powder poofs from the makeup crew.
"Absolutely," I said, still a little embarrassed.
Emily smiled kindly.
"We're back in five, four, three..." a man's voice boomed. The crew vanished as quickly as they'd arrived.
Emily flashed her pearly whites at the camera. "We're back live with the Motherhood Better Bootcamp contestants, ready to announce the winner of the $100,000 grand prize! Are you ready?"
Several of the women grabbed the hands of the people on either side of them. I wrung mine together and tried not to barf all over our host.
"The winner...of Motherhood Better Bootcamp is...."
I couldn't breathe. I felt like I was going to pass out. Just say it! I thought. Every second felt like an hour.
"Fiona Martin!" I heard the name being said and felt my heart shatter. I knew my chances were slim, but until that moment, hadn't let hope die.
Fiona, the mom of three who made hats for premature babies in NICU burst into tears. She and Emily stood and the two hugged before Fiona was presented with a huge check.
I forced myself to smile and clap politely. Glancing over at Kimmie, I saw that her smile was tight and her eyes narrowed. I stifled a laugh.
"Stay with us after the break!" Emily said.
"Commercial!" the voice boomed.
Emily turned to face all of us. "I'd like to formally present the winner of Motherhood Better Bootcamp, Fiona Martin!" Once again, everyone clapped. Fiona was beside herself. Large tears streamed down her cheeks and a trickle of snot was threatening to make its way down her lip.
"You guys are all winners to me," Emily continued. "Which is why I'm giving you all the Emily Walker Home set, absolutely free. If you paid for it, you'll be reimbursed. I'm also treating you to a spa day in your city. I have loved getting to know each and every one of you, and I'm going to miss you terribly. Please stay in touch!"
With that, everyone rose and crowded around Emily for a group hug. I didn't even know who I was squeezing as I embraced my new sisters. I may not have won the grand prize, but I in no way felt like a loser.
"We're back in two minutes!" a voice yelled again.
"Okay, Anna will take you to breakfast! We have gift bags for everyone! Thank you, ladies!" Emily said, waving frantically.
I couldn't believe it was all over. I didn't want to go home to my real life where I'd be moving in with my mother-in-law, be friendless yet again and have to face my husband. I wanted to stay here in TV world.
I found my bag and began making my way over to the exit to have one last meal at the Emily Walker estate when Anna stopped me.
"You're not done. Emily needs you for the next segment."
"Next segment?" I repeated, confused.
"Follow me." Anna led me back toward the set where the couches had been replaced by another pink armchair facing Emily's.
I took the seat. Emily took hers and winked at me. What was going on?
"Five, four, three, two...!" the voice yelled.
"Hello, viewers! You just saw me announce the winner of the Motherhood Better Bootcamp, but I wanted to introduce you to one very special contestant, Ashley Keller."
I tried my best not to appear as confused as I was.
I managed a weak wave.
"Ashley," Emily said, placing her hand on mine. "If you watch The Emily Walker Show, and I know you do, you know that every so often, we honor a mom who takes a stand for what she believes in. Today, you are that mom. Please watch the footage."
The room went dark, and behind us, a screen began to play a shaky video of the inside of an airplane. It looked oddly familiar.
A woman with crazy hair—me—was standing up and yelling. "Why don't you have the decency to let this mother tend to her baby in peace!" It was me! On the plane! Defending the mom!
At the end of my rambling speech the lights went back on.
"Someone filmed it?" I managed to sputter.
"Yes, Ashley. Not only did someone film your courageous act, they uploaded it to MyTube. The video of you standing up for a mom being poorly treated received 600,000 views in less than twenty-four hours. Now it's up to 1.5 million!"
"WHAT?" I yelled, forgetting I was on live television. Emily laughed.
"It's not easy being a mom today," she said. "There are so many expectations. You not only helped this one mom feel accepted in the world, but you helped all moms feel less alone when they watched that video."
I felt hot tears stream down my cheeks.
"For that, we'd like to present you with the Emily Walker Hero award and a check for $10,000."
I couldn't control myself any longer. I began to sob.
"I can't believe this. Thank you. Thank you," I sputtered. I leaned over and hugged Emily, crying even harder.
"No, thank you!" Emily said.
A crew member leaned in and handed Emily a box of tissues. She handed them to me and I dabbed at my face, unable to stop the flow of tears. Offstage, I saw all of the moms smiling proudly at us. A new flood opened up.
"When we come back, I'll show you three ways to upcycle used peanut butter containers!"
"Commercial!"
Emily and I stood up at the same time.
"Emily... this means so much. Thank you," I blubbered.
Emily put her hands on my shoulders.
"Ashley, you are an amazing person. Last night you helped remind me why I do this."
We hugged.
"I've got one more segment left—five baby arugula smoothies your toddler will love."
"Sounds delish," I said, and made my way to the group of moms waiting for me.
As soon as we were in the hallway and out of earshot of the set, they swarmed me.
"Go, Ashley!"
"Congratulations!"
Kimmie walked up to me. Her face was emotionless as she stood, her nose six inches away from mine.
"I'm so happy for you!" she said, and threw her arms around my neck, practically choking the life out of me.
To my surprise, I heard her sniffle. I hugged her back, shocked. "Thank you, Kimmie!"
She let go of my neck and wiped her eyes. "It's just that, I know how that woman on the plane felt. Every time I take the kids to the country club I feel so stressed out that they'll make too much noise. Everyone just glares." She flapped her hands emphatically. "But what am I supposed to do? Stay at home 24/7?"
I smiled, nodding. Kimmie's problems always sounded so glamorous.
Anna popped up with her trademark clipboard.
"Hello, ladies! It seems as if the overwhelming consensus is that a full breakfast isn't in the cards because of your...adventure last night." Anna looked up from her clipboard. "So we've taken the opportunity to pack each of you a lunch for your travel home."
Chef Lorenzo and his kitchen staff walked down the hall carrying cute pink bags with pink-ribbon handles.
"Good morning, ladies!" Lorenzo looked as dashing as ever in his pristine white chef's uniform with shiny silver buttons running down the front and a red apron. His crew began distributing the lunches.
"I've packed you all cold, slow-roasted, aged peppercorn beef sandwiches with our local buttery cheddar cheese," he began. Someone behind me dry heaved.
Lorenzo's eyes widened. "Perhaps I will not go into the details right now. You had some night."
Lorenzo leaned into my ear. "Lovely tattoo, by the way."
My body flushed. The skinny-dipping. I'd completely forgotten. He'd been there?
When I got back to my room I grabbed my computer and, typing faster than I ever have before, logged into Facebook to see if any of my new friends had posted incriminating photos from last night and to gauge the response to my televised tear fest. To my relief, there were only a few photos that included me. In all of them, I was smiling and fully clothed. Phew. And I wasn't trending on Twitter. What a relief.
I was just about to check Instagram when Kimmie walked into the room.
"Crazy morning, huh?" she said, throwing items into her bag. "You know..." She stopped packing and stared at me. "I'm going to miss you and all of the moms here. You're not the type of person I'd usually hang out with, or even notice, but I like you."
"Thank you?" I said, getting up to start packing myself.
The rest of the morning flew by. After packing we headed downstairs where all the contestants stood in the foyer, surrounded by bags.
After a few more hugs and exchanges of email addresses, it was time to go. You'd think I'd be sad to leave the gorgeous mansion, catered meals and excellent sleep, but all I could think about was seeing Aubrey and David. I couldn't wait to apologize for how nuts I'd been behaving and hold my baby in my arms.
It was already 11:30. My car was scheduled to arrive at noon to take me to the airport.
"My car's here!" Kimmie said, lowering her sunglasses. She stared at me as if trying to comprehend my entire existence. "You're a doll. It's been real, hun."
"It was great to meet you, Kimmie," I said, giving her a hug.
"Congrats again on the prize. You deserve it, Ashley. You're a good person."
I smiled. If only she knew about La Lait and the DentaFresh debacle. I still hadn't received an email back from Nina or Lola. Or anyone.
"Thanks, Kimmie."
"What are you going to do with the money?" she said. "If you're going to invest it in yourself, something I highly recommend, I know a great plastic surgeon."
I laughed.
Anna appeared before I could think of an answer. She was holding a ziplock bag that contained my cell phone covered in moss.
"The groundskeeper discovered this for you," she said flatly. "You do realize there are security cameras everywhere, right?"
I flushed red. "Sorry about that." I quickly took the phone.
"You also have a phone call."
"Oh, thank you."
I knew who it had to be. I quickly said goodbye to Kimmie and followed Anna to a waiting phone.
"Thanks," I said, cupping the receiver, but she didn't budge.
I awkwardly turned my back to her.
"Hello?"
"Mama," a small voice said. My mouth hung open and I was speechless. Even though it was the first time I'd heard her say the word, I knew my daughter's voice. Tears began flowing down my face.
"Baby," I managed to choke out.
"Did you hear her?" David's voice was breathless with excitement. "She said Mama!"
"I know! It's amazing! When did she first say it?" I was shaking with emotion.
"She saw you on TV and pointed to you and just said Mama."
A fresh batch of tears cascaded down my cheeks and began to form a damp spot on my shirt.
I heard Anna take a few steps away from me to give me a bit of space, but she still remained close.
"I can't believe it. Tell her I love her so much!"
"She knows," David said softly.
The line was quiet for a few moments.
We started talking at the same time.
"David—"
"Ashley—"
We both stopped.
"I want to go first," I said, turning back to see how close Anna was to me. She'd given me a respectable distance of about six feet.
I leaned into the receiver and lowered my voice.
"I am so, so, so, so, sorry. What I did was wrong. I should have told you. I just need you to forgive me."
David sighed. "Ashley, you were trying to help. I know that. I made so many mistakes and the biggest one was making you think you were the only reason DentaFresh passed on us."
"What do you mean?"
"We're a young company. They wanted someone with more experience. I think I just used that email as an excuse to make me feel better. They wouldn't have gone with us, anyway."
"I'm sorry, David. Things will get better."
"No, Ashley. Folding the company is the right thing to do. I need to think about you and Aubrey."
As amazing as it would be to have David home at a normal hour and not be stressed out, I could hear the pain in his voice and knew I couldn't let him do this.
I clenched my fist.
"No. David, I won't let you do this. We'll use the prize money to help with bills until you get the company back on its feet. I know you can do this. This has been your dream forever. I believe in you."
As I said the words, I knew they were true. There was silence on the other end of the phone.
"What do you say?" I asked. "All in?"
After a few moments I heard David clear his throat, the way he does when he's trying not to cry. "All in. I'm all in. I love you, Ashley."
I smiled like a girl on prom night. "I love you, too, David. I can't wait to see both of you."
"You, too, babe."
When we hung up, Anna ran over to me quickly, her black adult-sized Mary Janes clicking on the marble.
"Before you go, Emily would like to speak to you."
She took my arm and we run-walked over to a small office just off of the foyer.
Emily was sitting in a makeup chair in front of a mirror framed by bright lights and wearing a pink robe. Her hair was in rollers.
"Ashleeeey!" she squealed. She hugged me, rocking me back and forth like a giant baby. "Were you surprised?"
I held my cheeks. "I almost fainted! I didn't even know anyone had filmed what happened on the plane! I was just speaking from my heart."
Emily sat back down on her chair and motioned for me to take a seat in the one beside her.
"That's exactly what I wanted to talk to you about."
I sat down.
"What do you mean?"
A woman began taking the curlers out of Emily's hair, sending her hair cascading down her neck like a mini waterfall.
Emily kept her face forward and talked to my reflection in the mirror.
"Ashley, you have a voice. A raw, honest voice that I think mothers everywhere would love. I want you to come work for me."
I laughed. "Me? Work for you? I can't cook, clean or make crafts..." I shook my head, confused.
Emily grinned. "I know. That's why I want you for this. You're real and messy..."
I cleared my throat, "Messy?"
Emily laughed diplomatically. "In the best possible way, of course. Moms relate to you. I want to add a more...relatable aspect to the blog. I want normal, everyday moms to feel part of the Emily Walker family. My marketing team thinks you're perfect and I agree."
I was stunned. I wasn't exactly thrilled to be such an obvious mess, but I totally got it. Emily wanted to inject a dose of reality into her scripted Insta-world.
"Emily, I—"
"Just say yes."
I stared at her, perfect Emily Walker in her robe with full makeup looking like a vision of everything I'd wanted to be. She didn't want me to change. I didn't need to be anyone other than who I already was. I never imagined that someone would want to pay me for that.
"Yes."
"Good. You start next week. Air kisses!" She pursed her lips in my direction and sucked twice.
"Your car is here, Mrs. Keller," said Anna, who had been waiting by the door.
"Bye, Emily...thank you...for everything."
Emily winked at me.
Before I lowered myself into the black Town Car, Anna handed me a white manila envelope.
"It's your check. Congratulations. I'll be in touch about the column." She smiled. I could sense that she was as shocked that I'd be working for Emily as I was.
"Thanks, Anna."
And we were off to the airport.
1 P.M.
I was sitting in first class again. The flight attendant had offered me a glass of champagne, but I passed. Somehow I'd managed to avoid a terrible hangover but my body still felt like I'd run a marathon on stilts.
There was another baby on the flight, this time accompanied by a mother and father in their early thirties. The toddler couldn't have been more than two and was raising absolute hell.
"WANT IPAD NOW!" he shrieked as his father unsuccessfully tried to get him to doze off.
"Sammy, the iPad is dead. Would you like to color?"
His high-pitched growl sounded only partially human. Sammy didn't want to color.
I glanced back and saw his mother trying to buy his silence with a pack of gummy bears.
The passengers around him looked like they were trying to will themselves onto another plane. I smiled. Note to self: If I ever fly with Aubrey when she's a toddler, bring a charged iPad, I thought before turning around.
Aubrey. I couldn't wait to see her face. Two months ago I was bored to tears every single day, but now, all I wanted to do was spend a long afternoon on the floor playing blocks.
I looked out the window at the clouds. Everything just felt better somehow, and nothing had really changed. Well, except my phone was dead. I wondered if anyone tried to get in touch with me since the show aired.
I fished my laptop out from under the seat in front of me and fired up my email. Forty-three new messages! Most of them were old coworkers and friends saying they saw me on TV.
There was one from Nina. She'd sent it last night.
To: Ashley Keller
From: Nina Pikkering
Subject: Re: The truth about me
Ashley, we know. We've known for some time now. It's not every day someone thinks "nipple confusion" means a baby can't decide which breast to feed from first. We love you. Can't wait to see you at the next meeting.
PS. You can stop feeding Aubrey in the bathroom now. We don't care. Why should you?
For the second time that day, I was crying. Thank you was all I could write. There was so much to say. I'd say it the next time I saw them.
I saw an email from Joy and clicked on it.
We all watched you on TV together! Congratulations! You were beautiful. You looked a little tired and puffy though—what did I say about making sure you got enough sleep the night before? Check Instagram when you get a minute. When did you get a tattoo?
No. No. No. No.
I'd deal with that later, too. I closed my laptop and placed it in my bag under the seat.
My hand hit a paper bag. It was the pink lunch bag that Lorenzo had packed. I was starting to get a little hungry.
I put my tray down and set the gorgeous pink-and-white checked bag in front of me.
Inside a mesh cooler was a plastic container. Through the lid I could see a delicious-looking artisanal sandwich and some kind of potato salad, separated by dividers. Yum!
I opened the plastic and BAM: the scent hit me like a punch to the face. A wave of nausea rolled through my insides and quickly rose in me like a snake. I closed the container and jumped over the empty seat next to me before sprinting down the aisle.
Once inside the bathroom, my entire guts spilled out into the toilet. I didn't even have time to lock the door. I held it closed with the back of my foot.
I took a deep breath. Maybe I was more hungover than I thought. I tried to make sense of this. I'd been feeling okay a minute ago.
Another wave came and I heaved into the toilet.
After a few moments I flushed, pulled myself up to the sink and washed my hands and face. I looked into the mirror. My eyes were bloodshot and my face ashen, but I felt better.
I opened the door.
A flight attendant was standing in the small hallway of the plane. He looked at me, concerned.
"Ma'am, are you okay?"
I tried to not look like I'd just left all of my internal organs in the flying porta-potty.
"Yes," I said, steadying myself against some turbulence with the wall. "Just a bit sick from a long night."
He smiled knowingly.
"That's not it," said the elderly woman in a green pleated skirt and matching argyle sweater seated in A1.
"Excuse me?" I replied, confused.
The woman looked up from a ball of peach-colored yarn and two quickly moving knitting needles. She wasn't a day under eighty-five. She stared at my face as if she were studying every cell.
"I said, that's not it. You're pregnant." She pointed a needle at my abdomen.
The flight attendant laughed.
"What? I'm sorry, ma'am, but..." My voice trailed off.
My period. It was late.
My eyes widened in abject terror and I looked down at the woman. She smiled, as if taking delight in my realization.
"I'm pregnant."
* * * * *
Acknowledgments
Thank you to my agent, Holly Bemiss at the Susan Rabiner Literary Agency. You made this possible. To my editor, Emily Ohanjanians at MIRA Books, thank you for saying yes.
ISBN-13: 9781488022883
Confessions of a Domestic Failure
Copyright © 2017 by Bunmi Laditan
All rights reserved. By payment of the required fees, you have been granted the non-exclusive, non-transferable right to access and read the text of this e-book on-screen. No part of this text may be reproduced, transmitted, down-loaded, decompiled, reverse engineered, or stored in or introduced into any information storage and retrieval system, in any form or by any means, whether electronic or mechanical, now known or hereinafter invented, without the express written permission of publisher, Harlequin Enterprises Limited, 225 Duncan Mill Road, Don Mills, Ontario, M3B 3K9 Canada.
This is a work of fiction. Names, characters, places and incidents are either the product of the author's imagination or are used fictitiously, and any resemblance to actual persons, living or dead, business establishments, events or locales is entirely coincidental. This edition published by arrangement with Harlequin Books S.A.
® and ™ are trademarks of the publisher. Trademarks indicated with ® are registered in the United States Patent and Trademark Office, the Canadian Intellectual Property Office and in other countries.
www.Harlequin.com
| {
"redpajama_set_name": "RedPajamaBook"
} | 3,038 |
Matías Osadczuk (Buenos Aires, 22 de abril de 1997) é um jogador de rugby sevens argentino.
Carreira
Osadczuk rompeu o ligamento de um joelho contra a Austrália no torneio Hong Kong Sevens 2017 e precisou de uma cirurgia antes de retornar à ação competitiva no torneio Sydney Sevens 2018. Ele integrou Seleção Argentina de Rugby Sevens nos Jogos Olímpicos de Verão de 2020 em Tóquio, quando conquistou a medalha de bronze após derrotar a equipe britânica por 17–12.
Ligações externas
Naturais de Buenos Aires
Jogadores olímpicos de rugby sevens da Argentina
Jogadores de rugby sevens nos Jogos Olímpicos de Verão de 2020
Medalhistas nos Jogos Olímpicos de Verão de 2020 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,698 |
#pragma once
#include <modules/animation/animationmoduledefine.h> // for IVW_MODULE_ANIMATION_API
#include <modules/animation/factories/interpolationfactoryobject.h> // IWYU pragma: keep
#include <modules/animation/factories/trackfactoryobject.h> // IWYU pragma: keep
#include <memory> // for unique_ptr, make_unique
#include <string> // for string
#include <vector> // for vector
namespace inviwo {
class InviwoApplication;
namespace animation {
class AnimationManager;
/**
* \class AnimationSupplier
* Base class to derive your module from if your module should add to the animation framework
*/
class IVW_MODULE_ANIMATION_API AnimationSupplier {
public:
AnimationSupplier(AnimationManager& manager);
AnimationSupplier(InviwoApplication* app);
AnimationSupplier(const AnimationSupplier&) = delete;
AnimationSupplier& operator=(const AnimationSupplier&) = delete;
virtual ~AnimationSupplier();
/**
* Register a Track with the Track Factory
*/
template <typename T>
void registerTrack();
/**
* Register an Interpolation with the Interpolation Factory
*/
template <typename T>
void registerInterpolation();
/**
* Register connection between a property and a track.
* Used to create typed tracks for a property.
* @param propertyClassID Property::getClassIdentifier
* @param trackClassID PropertyTrack::getIdentifier()
* @see AnimationManager
*/
void registerPropertyTrackConnection(const std::string& propertyClassID,
const std::string& trackClassID);
void unRegisterAll();
private:
void registerTrackObject(std::unique_ptr<TrackFactoryObject> obj);
void registerInterpolationObject(std::unique_ptr<InterpolationFactoryObject> obj);
AnimationManager& manager_;
std::vector<std::unique_ptr<TrackFactoryObject>> tracks_;
std::vector<std::unique_ptr<InterpolationFactoryObject>> interpolations_;
};
template <typename T>
void AnimationSupplier::registerInterpolation() {
registerInterpolationObject(std::make_unique<InterpolationFactoryObjectTemplate<T>>());
}
template <typename T>
void AnimationSupplier::registerTrack() {
registerTrackObject(std::make_unique<TrackFactoryObjectTemplate<T>>());
}
} // namespace animation
} // namespace inviwo
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,377 |
{"url":"https:\/\/statproofbook.github.io\/P\/ug-lme","text":"Index: The Book of Statistical ProofsStatistical Models \u25b7 Univariate normal data \u25b7 Univariate Gaussian \u25b7 Log model evidence\n\nTheorem: Let\n\n$\\label{eq:ug} m: \\; y = \\left\\lbrace y_1, \\ldots, y_n \\right\\rbrace, \\quad y_i \\sim \\mathcal{N}(\\mu, \\sigma^2), \\quad i = 1, \\ldots, n$\n\nbe a univariate Gaussian data set with unknown mean $\\mu$ and unknown variance $\\sigma^2$. Moreover, assume a normal-gamma prior distribution over the model parameters $\\mu$ and $\\tau = 1\/\\sigma^2$:\n\n$\\label{eq:UG-NG-prior} p(\\mu,\\tau) = \\mathcal{N}(\\mu; \\mu_0, (\\tau \\lambda_0)^{-1}) \\cdot \\mathrm{Gam}(\\tau; a_0, b_0) \\; .$\n\nThen, the log model evidence for this model is\n\n$\\label{eq:UG-NG-LME} \\log p(y|m) = - \\frac{n}{2} \\log (2 \\pi) + \\frac{1}{2} \\log \\frac{\\lambda_0}{\\lambda_n} + \\log \\Gamma(a_n) - \\log \\Gamma(a_0) + a_0 \\log b_0 - a_n \\log b_n$\n\nwhere the posterior hyperparameters are given by\n\n$\\label{eq:UG-NG-post-par} \\begin{split} \\mu_n &= \\frac{\\lambda_0 \\mu_0 + n \\bar{y}}{\\lambda_0 + n} \\\\ \\lambda_n &= \\lambda_0 + n \\\\ a_n &= a_0 + \\frac{n}{2} \\\\ b_n &= b_0 + \\frac{1}{2} (y^\\mathrm{T} y + \\lambda_0 \\mu_0^2 - \\lambda_n \\mu_n^2) \\; . \\end{split}$\n\nProof: According to the law of marginal probability, the model evidence for this model is:\n\n$\\label{eq:UG-NG-ME-s1} p(y|m) = \\iint p(y|\\mu,\\tau) \\, p(\\mu,\\tau) \\, \\mathrm{d}\\mu \\, \\mathrm{d}\\tau \\; .$\n\nAccording to the law of conditional probability, the integrand is equivalent to the joint likelihood:\n\n$\\label{eq:UG-NG-ME-s2} p(y|m) = \\iint p(y,\\mu,\\tau) \\, \\mathrm{d}\\mu \\, \\mathrm{d}\\tau \\; .$\n\nEquation \\eqref{eq:ug} implies the following likelihood function\n\n$\\label{eq:UG-LF-class} \\begin{split} p(y|\\mu,\\sigma^2) &= \\prod_{i=1}^{n} \\mathcal{N}(y_i; \\mu, \\sigma^2) \\\\ &= \\prod_{i=1}^{n} \\frac{1}{\\sqrt{2 \\pi} \\sigma} \\cdot \\exp\\left[ -\\frac{1}{2} \\left( \\frac{y_i-\\mu}{\\sigma} \\right)^2 \\right] \\\\ &= \\frac{1}{(\\sqrt{2 \\pi \\sigma^2})^n} \\cdot \\exp\\left[ -\\frac{1}{2 \\sigma^2} \\sum_{i=1}^{n} \\left( y_i-\\mu \\right)^2 \\right] \\end{split}$\n\nwhich, for mathematical convenience, can also be parametrized as\n\n$\\label{eq:UG-LF-Bayes} \\begin{split} p(y|\\mu,\\tau) &= \\prod_{i=1}^{n} \\mathcal{N}(y_i; \\mu, \\tau^{-1}) \\\\ &= \\prod_{i=1}^{n} \\sqrt{\\frac{\\tau}{2 \\pi}} \\cdot \\exp\\left[ -\\frac{\\tau}{2} \\left( y_i-\\mu \\right)^2 \\right] \\\\ &= \\left( \\sqrt{\\frac{\\tau}{2 \\pi}} \\right)^n \\cdot \\exp\\left[ -\\frac{\\tau}{2} \\sum_{i=1}^{n} \\left( y_i-\\mu \\right)^2 \\right] \\end{split}$\n\nusing the inverse variance or precision $\\tau = 1\/\\sigma^2$.\n\nWhen deriving the posterior distribution $p(\\mu,\\tau|y)$, the joint likelihood $p(y,\\mu,\\tau)$ is obtained as\n\n$\\label{eq:UG-NG-LME-s1} \\begin{split} p(y,\\mu,\\tau) = \\; & \\sqrt{\\frac{\\tau^{n+1} \\lambda_0}{(2 \\pi)^{n+1}}} \\, \\frac{ {b_0}^{a_0}}{\\Gamma(a_0)} \\, \\tau^{a_0-1} \\exp[-b_0 \\tau] \\cdot \\\\ & \\exp\\left[ -\\frac{\\tau \\lambda_n}{2} \\left( \\mu - \\mu_n \\right)^2 -\\frac{\\tau}{2} \\left( y^\\mathrm{T} y + \\lambda_0 \\mu_0^2 - \\lambda_n \\mu_n^2 \\right) \\right] \\; . \\end{split}$\n\nUsing the probability density function of the normal distribution, we can rewrite this as\n\n$\\label{eq:UG-NG-LME-s2} \\begin{split} p(y,\\mu,\\tau) = \\; & \\sqrt{\\frac{\\tau^{n}}{(2 \\pi)^{n}}} \\sqrt{\\frac{\\tau \\lambda_0}{2 \\pi}} \\sqrt{\\frac{2 \\pi}{\\tau \\lambda_n}} \\, \\frac{ {b_0}^{a_0}}{\\Gamma(a_0)} \\, \\tau^{a_0-1} \\exp[-b_0 \\tau] \\cdot \\\\ & \\mathcal{N}(\\mu; \\mu_n, (\\tau \\lambda_n)^{-1}) \\, \\exp\\left[ -\\frac{\\tau}{2} \\left( y^\\mathrm{T} y + \\lambda_0 \\mu_0^2 - \\lambda_n \\mu_n^2 \\right) \\right] \\; . \\end{split}$\n\nNow, $\\mu$ can be integrated out easily:\n\n$\\label{eq:UG-NG-LME-s3} \\begin{split} \\int p(y,\\mu,\\tau) \\, \\mathrm{d}\\mu = \\; & \\sqrt{\\frac{1}{(2 \\pi)^{n}}} \\sqrt{\\frac{\\lambda_0}{\\lambda_n}} \\, \\frac{ {b_0}^{a_0}}{\\Gamma(a_0)} \\, \\tau^{a_0+n\/2-1} \\exp[-b_0 \\tau] \\cdot \\\\ & \\exp\\left[ -\\frac{\\tau}{2} \\left( y^\\mathrm{T} y + \\lambda_0 \\mu_0^2 - \\lambda_n \\mu_n^2 \\right) \\right] \\; . \\end{split}$\n\nUsing the probability density function of the gamma distribution, we can rewrite this as\n\n$\\label{eq:UG-NG-LME-s4} \\int p(y,\\mu,\\tau) \\, \\mathrm{d}\\mu = \\sqrt{\\frac{1}{(2 \\pi)^{n}}} \\sqrt{\\frac{\\lambda_0}{\\lambda_n}} \\, \\frac{ {b_0}^{a_0}}{\\Gamma(a_0)} \\, \\frac{\\Gamma(a_n)}{ {b_n}^{a_n}} \\, \\mathrm{Gam}(\\tau; a_n, b_n) \\; .$\n\nFinally, $\\tau$ can also be integrated out:\n\n$\\label{eq:UG-NG-LME-s5} \\iint p(y,\\mu,\\tau) \\, \\mathrm{d}\\mu \\, \\mathrm{d}\\tau = \\sqrt{\\frac{1}{(2 \\pi)^{n}}} \\sqrt{\\frac{\\lambda_0}{\\lambda_n}} \\, \\frac{\\Gamma(a_n)}{\\Gamma(a_0)} \\, \\frac{ {b_0}^{a_0}}{ {b_n}^{a_n}} \\; .$\n\nThus, the log model evidence of this model is given by\n\n$\\label{eq:UG-NG-LME-s6} \\log p(y|m) = - \\frac{n}{2} \\log (2 \\pi) + \\frac{1}{2} \\log \\frac{\\lambda_0}{\\lambda_n} + \\log \\Gamma(a_n) - \\log \\Gamma(a_0) + a_0 \\log b_0 - a_n \\log b_n \\; .$\nSources:\n\nMetadata: ID: P203 | shortcut: ug-lme | author: JoramSoch | date: 2021-03-03, 10:25.","date":"2021-08-03 07:17:28","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 2, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9289763569831848, \"perplexity\": 739.0395624604669}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-31\/segments\/1627046154432.2\/warc\/CC-MAIN-20210803061431-20210803091431-00523.warc.gz\"}"} | null | null |
\section{Introduction}
Metasurfaces have been heralded as a revolutionary platform for realizing complex functionalities and compact form factors inaccessible to conventional refractive or diffractive optics~\cite{yu2011light,khorasaninejad2017visible,chen2018broadband,engelberg2020advantages}.
Meanwhile, an emerging ``end-to-end'' paradigm in computational imaging, in which an optical frontend is optimized in conjunction with an image-processing backend, has received increasing attention due to successful applications in diffractive optics~\cite{sitzmann2018end,baek2020end}. More recently, the end-to-end paradigm has been introduced to full-wave vectorial nanophotonic and metasurface frontends~\cite{lin2021end,burgos2021design,tseng2021neural}, demonstrating an enhanced capability for physical data acquisition and manipulation. So far, these early endeavors have been limited to two-dimensional (2D) RGB imaging or classification problems. In this paper, we present end-to-end metaoptics inverse design for single-shot \emph{multi-channel} imaging beyond 2D RGB information: reconstruction of several depth, spectral and polarization channels \emph{simultaneously} from a single monochrome image (Section~\ref{sec:theory}). As a key result, we show that, even though demultiplexing is not a designated/prescribed objective, inverse design automatically leads to \emph{spatial demultiplexing} of the multiple channels into \emph{spontaneous domains}---distinct regions in the detected image for different channels, whose locations are not pre-designated but are optimally discovered during the course of optimization (Sections~\ref{sec:results}~and~\ref{sec:discuss}). In contrast to data-driven approaches such as neural networks~\cite{baek2020end}, our framework is physically interpretable, does not overfit despite a small generic training set, and is fully validated against ground truths vastly different from those of the training set. Specifically, we present metasurface designs for 16-color imagers with $5$--$12$\% reconstruction error (under 1\% image noise), a 4-color/4-depth imager with 5\% error, and a 2-color/2-depth/4-polarization imager with 2\% error (Section~\ref{sec:results}~and~Appendix~B). All the presented designs take into account fabrication constraints and are compatible with large-scale metasurface lithography~\cite{li2021inverse}. In practice, our method only requires a single calibration step (via measurement or calculation of the point spread function) and is amenable to arbitrary material platforms and differentiable reconstruction algorithms. Our results highlight the power of full-wave optics design with subwavelength components, whereas scalar diffractive optics could struggle to distinguish different wavelengths and polarizations due to limited dispersion and polarization sensitivity~\cite{engelberg2020advantages}.
A major aspiration of metasurface technology has been to realize aberration-free focusing via an ultra-thin interface, directly replacing traditional bulky lenses~\cite{khorasaninejad2017visible}. While there has been significant progress towards this goal~\cite{chen2018broadband}, most metalenses suffer from fundamental space-bandwidth limits on wave focusing~\cite{presutti2020focusing}. Although nanophotonic inverse design has introduced several innovations to metaoptics architectures~\cite{molesky2018inverse,sell2017large,lin2018topology,lin2019topology,pestourie2018inverse,shi2020continuous}, further disruptive improvements await the advent of mature three-dimensional (3D) nanofabrication~\cite{lin2021computational,roques2021towards,camayd2020multifunctional}. In contrast, recent studies in end-to-end inverse design~\cite{lin2021end,burgos2021design,tseng2021neural} have unveiled ``computationally aware'' nanostructures that bear little semblance to a lens and offer capabilities beyond optics-only or computation-only designs. On the other hand, several computational techniques have been developed for retrieving depth, spectral and polarization information from a scene~\cite{pentland1987new,guo2019compact,levin2007image,greengard2006depth,monakhova2020spectral,sahoo2017single,yang2019single,rubin2019matrix}. Such techniques operate by combining multiple bulky refractive, diffractive and/or absorptive elements, often involve time-domain multiplexing (for example, scanning a scene to accumulate different shots), and typically enable the reconstruction of a single additional dimension (e.g. depth, color, \emph{or} polarization). A universal framework is still lacking, by which a \emph{single-piece} nanophotonic structure can be optimally designed to extract \emph{any and all} channels \emph{simultaneously} from a \emph{single filter-free} monochrome exposure. Our proposed end-to-end framework enables inverse design of an ultra-thin single-layer metasurface in conjunction with a simple Tikhonov-regularized reconstruction algorithm. In particular, the Tikhonov regularization is agnostic to the nature of the information channels under consideration and is thus capable of extracting any and all channels (whether they be depth, spectral, polarization, or any combination thereof).
\begin{figure}
\centering
\includegraphics[width=1.0\textwidth]{multichannel_concept_v3-01.png}
\caption{(a,b) A multi-channel ground truth object consists of depth, spectral and polarization channels and can be represented by a set of two-dimensional (2D) intensity arrays indexed by $(z,\lambda,p)$: a three-dimensional (3D) object can be naturally sectioned into a collection of 2D ``depth'' slices; each depth slice can be further decomposed into different ``color'' slices; each color slice is, in turn, decomposed into different ``polarization'' slices. (c) End-to-end inverse design: a metasurface frontend is optimized in conjunction with a computational reconstruction backend to minimize the reconstruction error evaluated at the end of the full pipeline.}
\label{fig:intro}
\end{figure}
\section{Theory}
\label{sec:theory}
\subsection{Image formation model}
In conventional imaging, the optical frontend is usually modeled by an elementary phase-shift function $e^{i 2 \pi h(x,y) / \lambda}$, where $\lambda$ is the free-space wavelength and $h(x,y)$ the surface profile of the diffractive optical element~\cite{goodman2005introduction}. In nanophotonics and metaoptics, involving sub-wavelength scatterers, more detailed electromagnetic simulations are required, which must take into account richer wave effects such as multiple scattering~\cite{yu2011light,khorasaninejad2016metalenses,lin2018topology,lin2019topology,lin2019overlapping,pestourie2018inverse}. In this work, we use a Chebyshev-interpolated surrogate model ($\mathbf{T}$) under a locally periodic approximation (LPA) to efficiently simulate the transmitted electric field through a large-area metasurface~\cite{pestourie2018inverse}. Specifically, a metasurface is defined by a vector $\mathbf{g}$ characterizing the geometry of meta-atoms (such as width, height and orientation of nanopillars) while the surrogate model maps each parameter $g$ in a periodic unit cell to complex transmission coefficients. The transmitted electric field is then given by $\mathbf{E}_\text{transmitted} = \mathbf{T} (\mathbf{g}) \cdot \mathbf{E}_\text{incident}$.
In general, any ground-truth object $\mathbf{u}$ can be numerically discretized into a tensor of five dimensions including three-dimensional real space as well as color and polarization dimensions. For convenience, we denote $\mathbf{u}$ as a set of 2D $(x,y)$ intensity arrays: $\mathbf{u} \equiv \{ u_{z,\lambda,p} \}$, where each 2D array $u$ is indexed by depth ($z$), wavelength ($\lambda$) and polarization ($p$) channels (see Fig.~\ref{fig:intro}a,b). Such a ``multi-channel'' representation is naturally made for a multi-channel image-formation model, in which a single 2D monochrome image $v$ is formed by the sum of convolutions of the object channels with the corresponding point spread functions (PSFs) also indexed by $(z,\lambda,p)$:
\begin{align}
v &= \sum_{z,\lambda,p} \mathrm{PSF}_{z,\lambda,p} \circledast u_{z,\lambda,p} + \eta, \\
z &\in \{ z_1, z_2, ..., z_{n_z} \}, \notag \\
\lambda &\in \{ \lambda_1, \lambda_2, ..., \lambda_{n_\lambda} \}, \notag \\
p &\in \{ p_x, p_y, p^R_{xy}, p^I_{xy} \} \notag,
\end{align}
where $\eta$ is a generic noise term (typically modeled by zero-mean Gaussian white noise with standard deviation $\sigma$: $\eta \sim \mathcal{N}(0,\sigma^2)$~\cite{sitzmann2018end}). Note that in our model, we assume shift-invariant PSFs (valid in the paraxial regime) and only consider object intensities under incoherent illumination~\cite{goodman2005introduction}. The PSFs are computed from the surrogate model followed by near-to-far-field propagation, given a specific metasurface geometry $\mathbf{g}$. While there is no limit to the number of depths ($n_z$) or wavelength channels ($n_\lambda$), four polarization channels are sufficient to reconstruct the full Stokes vector~\cite{damask2004polarization} ($n_p \leq 4$). Those components can be understood as follows: $x$-polarized intensity channel ($p_x$), $y$-polarized intensity channel ($p_y$), the real part of the correlation between $x$ and $y$ polarizations ($ p^R_{xy}$) and the imaginary part ($ p^I_{xy} $).
\subsection{Inverse scattering and end-to-end optimization}
Given the multi-channel image formation model, the corresponding reconstruction problem (also called inverse scattering problem) is posed as:
\begin{align}
\min_{\{\mu_{z,\lambda,p}\}} ~ \Big\lVert v - \sum_{z,\lambda,p} \mathrm{PSF}_{z,\lambda,p} \circledast \mu_{z,\lambda,p} \Big\rVert^2 + R(\{\mu_{z,\lambda,p}\}). \label{eq:recon}
\end{align}
The reconstructed object, denoted by $\mathbf{\hat{u}} = \{ \hat{u}_{z,\lambda,p} \}$, is the solution that minimizes the problem ($\ref{eq:recon}$). Here, a regularization term $R(\cdot)$ is usually needed to make the inverse problem well-posed and well-conditioned as well as to impose any prior information such as sparsity or smoothness. A simplest choice (with minimal prior information) is the so-called Tikhonov regularization or $L_2$ norm~\cite{tarantola2005inverse} where $R(\cdot) = \alpha \lVert \cdot \rVert^2$, leading to:
\begin{align}
\mathbf{\hat{u}} = \left( \mathbf{G^TG} + \alpha \mathbf{I} \right)^{-1} \mathbf{G^Tv}, \label{eq:reconsol}
\end{align}
where, for convenience, the convolutions have been recast into a matrix notation,
\begin{align}
\mathbf{G} &=
\begin{bmatrix}
\mathrm{PSF}_{z_1,\lambda_1,p_x} \circledast & \ldots & \mathrm{PSF}_{z,\lambda,p} \circledast & \ldots
\end{bmatrix}
\end{align}
Typically, the matrix $\mathbf{G}$ is large and dense, easily reaching over $10^5 \times 10^5$ in dimension. We use matrix-free FFT-based convolutions~\cite{goodman2005introduction,frigo2005design} in both forward and inverse scattering models to efficiently compute the action of $\mathbf{G}$ or $\mathbf{G^T}$ on arbitrary vectors without storing $\mathbf{G}$ explicitly. In particular, in Eq.~\ref{eq:reconsol}, $\mathbf{\hat{u}}$ can be obtained by the iterative conjugate-gradient method~\cite{strang2007computational}, within $\sim 100$ iterations, instead of directly computing a matrix inverse. Our end-to-end inverse design considers the entire pipeline (see Fig.~\ref{fig:intro}c) and can be formulated as minimizing the average reconstruction error:
\begin{align}
&\min_{\mathbf{g},\alpha} \quad L(\mathbf{\hat{u}},\mathbf{u}) \stackrel{\triangle}= \langle \lVert \mathbf{u} - \mathbf{\hat{u}} \rVert^2 \rangle_{\mathbf{u},\eta} \\
&\mathbf{\hat{u}} = \left( \mathbf{G^TG} + \alpha \mathbf{I} \right)^{-1} \mathbf{G^Tv} \notag \\
&v = \sum_{z,\lambda,p} \mathrm{PSF}_{z,\lambda,p} \circledast u_{z,\lambda,p} + \eta \notag \\
&\mathrm{PSF} = |\mathrm{FF}\left( \mathbf{T} (\mathbf{g}) \cdot \mathbf{E}_\text{incident} \right)|^2. \notag
\end{align}
Here, $\langle \cdot \rangle_\mathbf{u,\eta}$ denotes averaging over training data as well as image noise; the training dataset consists of a few randomly-generated ground truths (e.g., random patterns drawn from a uniform distribution). $\mathrm{FF}$ denotes the near-to-far-field propagation to the detector plane---a convolution of the transmitted electric fields with the free-space Green's function~\cite{goodman2005introduction}. In our end-to-end framework, the gradients are back-propagated through the entire pipeline all the way to the metasurface parameters, and are efficiently handled by an in-house implementation of the adjoint method~\cite{strang2007computational} (see Appendix A) instead of solely relying on popular automatic differentiation libraries~\cite{maclaurin2015autograd} which perform poorly for differentiating through iterative algorithms such as the conjugate-gradient method. The reconstruction accuracy of an optimized design is validated over vastly different ground truths (distinct from training objects).
\section{Results}
\label{sec:results}
\begin{figure}
\centering
\includegraphics[width=0.98\textwidth]{16color.pdf}
\caption{(a) Design of a metasurface multi-spectral imager that can reconstruct 16 color channels from 450 nm (blue) to 660 nm (red). Inset: zoom-in of the design. (b) Each unit cell has a period of $465~\mathrm{nm}$, consisting of a square nanopillar. The pillar has a height of $600~\mathrm{nm}$ and a width of $60~\mathrm{nm} \leq w \leq 405~\mathrm{nm}$. (c) Monochrome image of the synthetic object shown in (d). The wavelengths are spatially demultiplexed onto distinct domains on the single-shot monochrome image, captured 1 mm away from the metasurface by a CCD array of $400\times 400$ pixels (each pixel has an area of $1.4 \times 1.4~\mathrm{\mu m}^2$). (d) Reconstruction of a synthetic ground truth---a multi-spectral picture of letters `a' to `p', situated 2~cm away from the metasurface and each letter emitting a different wavelength. Note that the letters in the ground truth cannot be distinguished by the naked eye (inset on the left of the ground truth row). Computationally, the ground truth is represented by a set of 16 intensity arrays, each of which is a $50\times 50$-pixel image of a letter (with $25~\mathrm{\mu m}$ resolution). The ground truth and the reconstruction are color-coded for a visual interpretation of the wavelengths. The reconstruction error is $12.5\%$ under $1\%$ image noise.}
\label{fig:16color}
\end{figure}
We now show how our framework can be utilized to inverse-design metaoptics with multi-channel reconstruction capability (depth, spectral, and polarization). We denote the dimensions of a ground truth object as $n_\text{ch} \times m\times m$---a set of $n_\text{ch}$ arrays each with $m \times m$ pixels (note that $n_\text{ch}=n_z n_\lambda n_p$), while the monochrome image is a \emph{single} 2D array of $n \times n$ pixels. In this work, we choose $n^2 \geq n_\text{ch} m^2$, that is, there are at least as many image pixels as the \emph{total} size of the object---an over-determined inverse problem, suitable for Tikhonov regularization which harbors minimal assumptions about the nature of the object.
First, we design a 16-color metasurface imager made up of $600~\mathrm{nm}$-tall TiO$_2$ pillars on silica (Fig.~\ref{fig:16color}a,b)---a design platform compatible with large-area lithographic fabrication as recently demonstrated in millimeter-scale achromatic metasurfaces~\cite{li2021inverse}. A Chebyshev-interpolated surrogate model maps the width of each pillar inside a unit cell (465 nm period) to transmission coefficients at 16 different wavelengths across the visible spectrum ($450 - 660~\mathrm{nm}$). The \emph{single-shot monochrome} image shows \emph{spatial demultiplexing} of the wavelength channels (Fig.~\ref{fig:16color}c). Interestingly, the imager does not solely rely on the demultiplexing effect; for example, there is channel replication, e.g. $\lambda_2$ (460 nm) channel, and a small degree of hybridization, e.g. between $\lambda_1$ (450 nm) and $\lambda_2$ (460 nm) channels. While the human eye is not equipped to recover all the information encoded in hybridization and redundancy, these apparent ``imperfections'' do not necessarily represent information loss. In particular, the apparent mixing between different channels does not preclude information recovery since the channels can be readily reconstructed by computation (as long as the corresponding PSFs are distinctly non-degenerate), leading to a reconstruction error of $12.5\%$ under $1\%$ Gaussian image noise (Fig.~\ref{fig:16color}e). We note that a signal-to-noise ratio of $\sim 100$ (1\% noise) can be readily achieved by modern electronic sensors~\cite{sitzmann2018end}. Furthermore, the apparent residual fine-grain noise in the reconstruction of non-random objects can be easily removed by simple de-noising routines.
In this example, we considered a simple geometry (a square pillar) suited for photo-lithographic mass production; utilizing a more complex geometry, such as a holey pillar, allowing for more degrees of freedom to manipulate incident wavefronts, leads to even better performance (5\% error with 1\% noise, see Appendix B). Our methods are also amenable to inverse-design techniques allowing for freeform geometries, involving domain decomposition methods with larger unit cells and full topology optimization~\cite{molesky2018inverse,lin2019overlapping}. We emphasize that our framework does not seek a ``heavily-processed imitation'' of the ground truth; it looks for a faithful reconstruction which is \emph{stable} under moderate noise, and should be applicable for imaging \emph{any} object, including random ones (see Appendix B). If desired, additional processing may be used, such as convolutional neural networks, which can be trained to ``interpolate'' a particular distribution of objects, enhance the reconstruction of \emph{that} class of objects, perform image segmentation, or classification on the reconstructed objects.
\begin{figure}
\centering
\includegraphics[width=0.98\textwidth]{depspec.pdf}
\caption{Depth-spectral imager. (a) Metasurface depth-spectral imager design. (b) Monochrome image of a synthetic multi-dimensional object consisting of 4 depths $\times$ 4 color channels. The channels in the test object are artificially synthesized as $m \times m$-pixel images of the channel indices ($m=50$). The monochrome image has $n \times n$ pixels ($n=400$) and is corrupted by 1\% noise, leading to (c) a reconstruction error of 5.3\%. Note that $z_i \in \{2,4,6,8\}~\mathrm{cm},~\lambda_j \in \{ 470,520,582,660\}~\mathrm{nm}$.}
\label{fig:depspec}
\end{figure}
Apart from spectral imagers, our framework is powerful in that it is straightforward to extract \emph{any and all} kinds of channels. For example, we design a depth-spectral imager (Fig.~\ref{fig:depspec}) that can reconstruct 4 depth channels $\times$ 4 wavelength channels. Additionally, as a proof of concept, we also design an ``all-in-one'' imager (Fig.~\ref{fig:spd}) that can reconstruct 2 depth channels $\times$ 2 wavelength channels $\times$ 4 polarization channels. In that case, spontaneous spatial demultiplexing discovered via inverse design is observed for channels that are a combination of a given depth and polarization (i.e. channels sharing the same depth but having different polarizations are also demultiplexed, and vice-versa). On the other hand, a greater degree of hybridization is seen to arise in between the depth channels. This originates from the limited geometric control of the \emph{local} metasurface design we have chosen, which cannot provide sufficiently strong \emph{spatial} dispersion to fully separate the depth channels. In future works, we will engineer larger unit cells, higher diffraction orders, and cascaded metamaterials to induce strongly \emph{non-local}, spatially-dispersive effects~\cite{lin2018topology,lin2021computational}.
\begin{figure}
\centering
\includegraphics[width=0.98\textwidth]{spd.pdf}
\caption{Spectro-polarimetric-depth imager. (a) The metasurface consists of TiO$_2$ nanopillars, each characterized by width ($w$), breadth ($b$) and orientation angle ($\theta$), where $60~\mathrm{nm}\leq w,b \leq 299~\mathrm{nm}$. (b) Monochrome image of a synthetic multi-dimensional object consisting of 2 depths $\times$ 2 colors $\times$ 4 polarization channels. The channels in the test object are artificially synthesized as pictures of the channel indices with $m \times m$ pixels ($m=50$). The monochrome image has $n \times n$ pixels ($n=400$) and is corrupted by 1\% noise, leading to (c) a reconstruction error of 2\%. Note that $z_i \in \{1.7,3.4\}~\mathrm{cm},~\lambda_j \in \{ 532,488\}~\mathrm{nm}$.}
\label{fig:spd}
\end{figure}
\section{Discussion and Outlook}
\label{sec:discuss}
The central result of this work is the realization of metaimaging based on \emph{spontaneous} demultiplexing of multi-channel information into distinct spatial domains, whose locations appear irregular but are optimally determined by end-to-end inverse design. This is in contrast to the situation where such domains would be dictated by a user, as would be the case for conventional optics-only designs such as color splitters~\cite{presutti2020focusing}, or even hybrid systems~\cite{rubin2019matrix}. The end-to-end automated discovery naturally leads to an optimal demultiplexing scheme with minimal hybridization between channels; in contrast, a human-designated scheme, such as a regular lattice of focal spots, may not be permitted by the available degrees of freedom in the metasurface, resulting in noisy crosstalk, sub-optimal PSFs, and poor resolution. Intuitively, the demultiplexing effect is enabled by the Tikhonov reconstruction backend, which does not attempt to learn from the specific training data, but ``judiciously'' nudges the optical frontend to separate the incoming channels in order to reduce the reconstruction error. Therefore, our method is physically interpretable and data-efficient. It only requires a small training set, for example, as few as 30 training data drawn from a uniform distribution in the case of the 16-color imager (Fig.~\ref{fig:16color}). At the same time, the final optimized designs achieve robust reconstruction performance with consistent accuracy over vastly different sets of ground truths (whether they are pictures like letters or patterns like random dots, see Appendix B). This is in contrast to recent works~\cite{baek2020end} using phase masks and neural networks, which require large, diverse and carefully curated training sets and do not lead to spatial demultiplexing.
One conceivable limitation of our multi-channel imagers is that the transverse dimensions of the object must be significantly smaller than those of the detector; therefore, the device is not suitable for reconstructing the entire natural field of view corresponding to the size of the detector. In practice, a narrower operational field of view may be realized by an appropriate aperture, a directed flash, or by selective illumination (a common technique in microscopy)~\cite{saleh2019fundamentals,mertz2019introduction}. The field of view can be enlarged by designing larger-area metasurfaces or by taking into account out-of-field-of-view light in the image-formation model. On the other hand, the inverse problem is under-determined if we choose the same transverse dimensions for the object and the detector. Such a problem requires additional priors on the object, and a regularization scheme like Tikhonov may not be sufficient. One powerful prior in image processing is sparsity, and a theoretically rigorous technique for reconstructing sparse objects is called compressed sensing~\cite{donoho2006compressed}. In another manuscript under preparation, we will present a fully end-to-end inverse design framework with a compressed-sensing backend. Ultimately, future backends may be realized by new architectures that combine classical algorithms (such as Tikhonov and CS, which are theoretically rigorous and physically interpretable) and deep neural networks (which are best suited for learning deep data priors). Moreover, the performance of ultra-compact nanophotonic devices (such as depth and spectral sensitivities) can be further enhanced if we transcend the limitations imposed by LPA and expand the available degrees of freedom to encompass the full Maxwell physics. In future work, we hope to explore end-to-end inverse design using more sophisticated domain decomposition methods~\cite{lin2019overlapping} and scattering-matrix formulations~\cite{benzaouia2021quasi}, or by cascading non-local metamaterials and 3D photonic crystals with local metasurfaces.
\section*{Funding}
Z.~Lin, C.R.C., R.P., M.S. and S.G.J. were supported in part by the U.~S.~Army Research Office through the Institute for Soldier Nanotechnologies under award number W911NF-18-2-0048. Z.~Lin and R.P. were partially supported by the MIT-IBM Watson AI Laboratory under Challenge 2415. Z.~Li and F.C. were supported by MURI AFOSR grant FA9550-21-1-0312.
| {
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Název Boreč má více míst:
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The Beautiful American
QUANT, Mary
Quant by Quant
New York: Ballantine, 1967. First Paperback Edition. Octavo. (18cm x 10cm) 224 pp. ills. Photo pictorial wrappers. Very short, closed tear to bottom verso. Very modest toning. Near fine. Item #103
Mary Quant's fashion designs so greatly influenced popular culture during the mid 1960s, it is difficult to look back on photos from that era without finding someone wearing "Mary Quant". It was obviously apparent in the ubiquitous "mini-skirt", a garment at least coined, if not invented, by Quant. An icon of the 1960s youth-quake, known as the "Mod" movement, Quant opened her first store, "Bazaar", in London's Chelsea neighborhood, assuring that Chelsea would become the center of the cultural youth movement. Appointed to the Officer of the Order of the British Empire (OBE) in 1966, Mary Quant's belief that clothing should be cheap, accessible, optimistic and most of all, exciting and fun, changed modern culture. You see it in the Beatle's "Hard Days Night" and in the Mini Cooper. And of course, the mini-skirt. A stubbornly popular autobiography of an unsual genius, this book is hard to find in any early edition.
See all items in Art & Design, Mass Market, Women
See all items by Mary QUANT
136 Hutton Street
© 2023 The Beautiful American. All rights reserved. Site Map | Site by Bibliopolis | {
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Located between Mill Pond and Centerport Harbor, Mill Dam Bridge was once the site of a functioning mill. To keep this historic road intact GBI restored the bridge and its amenities. Before they could begin they had to install a steel sheeting coffer dam on both sides of the bridge and dewater the construction site with well points so that they could work in dry conditions. GBI then removed the existing bridge and abutments, constructed new reinforced concrete abutments, a pre-stressed pre-cast bridge deck, concrete barriers, asphalt approach ramps and street lighting. To keep the pond healthy GBI fabricated and installed wooden tidal gates which maintain Mill Pond's water levels at low tide while allowing tidal flushing at high tide. | {
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\subsection{Evidence of colour}
\begin{figure}[htb]
\centerline{\epsfysize = 2.2cm \epsfbox{eehadrons.eps}}
\caption{Feynman diagram for $e^+e^-\to \mbox{\rm hadrons}$.}
\label{fig:eediagram}
\end{figure}
A direct test of the colour quantum number can be obtained from the
ratio
\begin{equation}\label{eq:R_ee}
R_{e^+e^-} \equiv
{\sigma(e^+e^-\to \mbox{\rm hadrons})\over\sigma(e^+e^-\to\mu^+\mu^-)} \, .
\end{equation}
The hadronic production occurs through
$e^+e^-\to\gamma^*, Z^*\to q\bar q\to \mbox{\rm hadrons}$.
Since quarks are assumed
to be confined, the probability to hadronize is just one; therefore,
the sum over all possible quarks in the final state will give the total
inclusive cross-section into hadrons.
At energies well below the $Z$ peak, the cross-section is
dominated by the $\gamma$-exchange amplitude;
the ratio $R_{e^+e^-}$ is then given by the sum of the
quark electric charges squared:
\begin{equation}\label{eq:R_ee_res}
R_{e^+e^-} \approx N_C \, \sum_{f=1}^{N_f} Q_f^2 \, = \,
\left\{
\begin{array}{cc}
\frac{2}{3} N_C = 2\, , \qquad & (N_f=3 \; :\; u,d,s) \\
\frac{10}{9} N_C = \frac{10}{3}\, , \qquad & (N_f=4 \; :\; u,d,s,c) \\
\frac{11}{9} N_C = \frac{11}{3} \, ,\qquad & (N_f=5 \; :\; u,d,s,c,b)
\end{array}\right. .
\end{equation}
\begin{figure}[bht]
\vspace{-0.4cm}
\centerline{\epsfxsize = 12cm \epsfbox{reepdg.ps}} \vspace{-0.3cm}
\caption{Measurements of $R_{e^+e^-}$ \protect\cite{PDG:94}.
The two continuous curves are QCD fits.}
\label{fig:Ree}
\end{figure}
\begin{figure}[thb]
\centerline{\epsfysize=3cm \epsfbox{TauDecay.ps}}
\caption{$\tau$-decay diagram.}
\label{fig:tau}
\end{figure}
The measured ratio is shown in Fig. \ref{fig:Ree}. Although
the simple
formula \eqn{eq:R_ee_res} cannot explain the complicated
structure around the different quark thresholds,
it gives the right average
value of the cross-section (away from the thresholds),
provided that $N_C$ is taken to be three.
The agreement is better at larger energies.
Notice that strong
interactions have not been taken into account;
only the confinement hypothesis has been used.
The hadronic decay of the $\tau$ lepton provides additional evidence
for $N_C=3$. The decay proceeds through the $W$-emission diagram
shown in Fig.~\ref{fig:tau}. Since the $W$ coupling to the charged
current is of universal strength, there are $(2+N_C)$ equal
contributions
(if final masses and strong interactions are neglected)
to the $\tau$-decay width. Two of them correspond
to the leptonic decay modes $\tau^-\to\nu_\tau e^-\bar\nu_e$ and
$\tau^-\to\nu_\tau \mu^-\bar\nu_\mu$, while the other $N_C$
are associated with the possible colours of the quark--antiquark
pair in the $\tau^-\to\nu_\tau d_\theta u$ decay mode
($d_\theta\equiv \cos\theta_C d + \sin\theta_C s$).
Hence, the branching ratios for the different channels are expected
to be approximately:
\
\begin{eqnarray}\label{eq:B_l}
B_{\tau\to l}\equiv
&\!\!\!\!\!\! & \!\!\!\!\!\!
{\rm Br}(\tau^-\to\nu_\tau l^-\bar\nu_l)
\approx {1\over 2+N_C} = {1\over 5} = 20 \% \, , \quad
\\ \label{eq:R_tau}
R_\tau &\!\!\!
\equiv &\!\!\!
{\Gamma(\tau^-\to\nu_\tau + \mbox{\rm hadrons})\over
\Gamma(\tau^-\to\nu_\tau e^-\bar\nu_e)} \approx N_C = 3 \, ,
\end{eqnarray}
which should be compared with the experimental averages \cite{PDG:94}:
\begin{eqnarray}\label{eq:B_l_exp}
B_{\tau\to e} = (18.01\pm 0.18)\% \, , \qquad\qquad
B_{\tau\to \mu} = (17.65\pm 0.24)\% \, ,
\\ \label{eq:R_tau_exp}
R_\tau = (1-B_{\tau\to e}-B_{\tau\to \mu})/B_{\tau\to e}
= 3.56\pm 0.04 \, . \qquad\qquad
\end{eqnarray}
The agreement is fairly good. Taking $N_C=3$, the naive predictions
only deviate from the measured values by about 20\%.
Many other observables, such as the partial widths of the $Z$ and $W^\pm$
bosons, can be analyzed in a similar way to conclude that $N_C=3$.
A particularly strong test is obtained from the $\pi^0\to\gamma\gamma$ decay,
which occurs through the triangular quark loops in Fig.~\ref{fig:triangle}.
The crossed vertex denotes
the axial current
$A_\mu^3\equiv (\bar u \gamma_\mu\gamma_5 u - \bar d \gamma_\mu\gamma_5 d)$.
One gets:
\begin{equation}\label{eq:pi_decay}
\Gamma(\pi^0\to\gamma\gamma) = \left( {N_C\over 3}\right)^2
{\alpha^2 m_\pi^3\over 64 \pi^3 f_\pi^2} = 7.73 \, {\rm eV} ,
\end{equation}
where the $\pi^0$ coupling to $A_\mu^3$,
$f_\pi = 92.4$ MeV, is known from the
$\pi^-\to\mu^-\bar\nu_\mu$ decay rate (assuming isospin symmetry).
The agreement with the measured value,
$\Gamma = 7.7\pm 0.6$ eV \cite{PDG:94}, is remarkable.
With $N_C=1$, the prediction would have failed by a factor of 9.
The nice thing about this decay is that it is associated with an
{\it anomaly}: a global flavour symmetry
which is broken
by quantum effects (the triangular loops). One can then proof that
the decay amplitude \eqn{eq:pi_decay} does not get corrected by
strong interactions \cite{AB:69}.
\begin{figure}[htb]
\centerline{\epsfysize = 3cm \epsfbox{pi0gg.ps}}
\caption{Triangular quark loops generating the decay $\pi^0\to\gamma\gamma$.}
\label{fig:triangle}
\end{figure}
Anomalies provide another compelling theoretical reason to
adopt $N_C=3$. The gauge symmetries of the Standard Model of
electroweak interactions have also anomalies associated with
triangular fermion loops
(diagrams of the type shown in Fig.~\ref{fig:triangle}, but with
arbitrary gauge bosons --$W^\pm,Z,\gamma$-- in the external legs and
Standard Model fermions in the internal lines).
These gauge anomalies are deathly because
they destroy the renormalizability of the theory. Fortunately,
the sum of all possible triangular loops cancels if $N_C=3$.
Thus, with three colours, anomalies are absent and the Standard
Model is well-defined.
\subsection{Asymptotic Freedom}
\label{subsec:AF}
The structure of the proton can be probed through the scattering
$e^- p\to e^- p$. The cross-section is given by
\begin{equation}\label{eq:ep_ep}
{d \sigma\over d Q^2} =
{\pi\alpha^2\cos^2\! {\theta\over 2} \over
4 E^2 \sin^4\! {\theta\over 2} E E'}\,
\left\{
{|G_E(Q^2)|^2 + {Q^2\over 4 M_p^2} |G_M(Q^2)|^2 \over 1 + {Q^2\over 4 M_p^2}}
+ {Q^2\over 2 M_p^2} |G_M(Q^2)|^2 \tan^2{\! {\theta\over 2}}
\right\} ,
\end{equation}
where $E$ and $E'$ are the energies of the incident and scattered
electrons, respectively, in the proton rest-frame, $\theta$
the scattering angle, $M_p$ the proton mass and
\begin{equation}\label{eq:Q2}
Q^2\equiv - q^2 = 4 E E'\sin^2{\! {\theta\over 2}} \, ,
\end{equation}
with $q^\mu\equiv (k_e - k'_e)^\mu$ the momentum transfer through the
intermediate photon propagator.
$G_E$ and $G_M$ are the electric and magnetic form factors, respectively,
describing the proton electromagnetic structure; they would be equal to
one for a pointlike spin-$\frac{1}{2}$ target. Experimentally they are
known to be very well approximated by the dipole form
\begin{equation}\label{eq:dipole}
G_M(Q^2)/\mu_p \approx G_E(Q^2) \approx
\left( 1 + {Q^2\over 0.7 \, \mbox{\rm GeV}^2}\right)^{-2} \, ,
\end{equation}
where $\mu_p=2.79$ is the proton magnetic moment (in proton
Bohr magneton units). Thus, the proton is actually an extended object with a
size of the order of 1 fm.
At very low energies ($Q^2<< 1 \, \mbox{\rm GeV}^2$), the photon probe
is unable to get information on
the proton structure, $G_{M,E}(Q^2)\approx G_{M,E}(0) =1$, and
the proton behaves as a pointlike particle.
At higher energies, the photon is sensitive to shorter distances; the proton
finite size gives then rise to form factors, which suppress the elastic
cross-section at large $Q^2$, i.e. at large angles.
\begin{figure}[htb]
\centerline{\epsfysize = 4cm \epsfbox{epDIS.ps}}
\caption{Inelastic $e^-p\to e^-X$ scattering.}
\label{fig:ep_eX}
\end{figure}
One can try to further resolve the proton structure, by increasing the
incident energy. The inelastic scattering
$e^- p \to e^- X$ becomes then the dominant process. Making an inclusive
sum over all hadrons produced, one has an additional kinematical variable
corresponding to the final hadronic mass, $W^2\equiv P_X^2$. The scattering
is usually described in terms of $Q^2$ and
\begin{equation}\label{eq:nu}
\nu \equiv {(P\cdot q)\over M_p} = {Q^2 + W^2 - M_p^2 \over 2 M_p}
= E - E' \, ,
\end{equation}
where $P^\mu$ is the proton cuadrimomentum;
$\nu$ is the energy transfer in the proton rest-frame.
In the one-photon approximation, the unpolarized differential
cross-section is given by
\begin{equation}\label{eq:sigma_inel}
{d \sigma\over d Q^2 \, d \nu} =
{\pi\alpha^2\cos^2\! {\theta\over 2} \over
4 E^2 \sin^4\! {\theta\over 2} E E'}\,
\left\{ W_2(Q^2,\nu) + 2\, W_1(Q^2,\nu)\, \tan^2{\! {\theta\over 2}} \right\}
{}.
\end{equation}
The proton structure is then characterized by two measurable
{\it structure functions}.
For a pointlike proton, the elastic scattering \eqn{eq:ep_ep} corresponds to
\begin{equation}\label{eq:W-elastic}
W_1(Q^2,\nu) = {Q^2\over 4 M_p^2}\,\delta\!\left(\nu - {Q^2\over 2 M_p}\right)
,
\qquad\qquad
W_2(Q^2,\nu) = \delta\!\left(\nu - {Q^2\over 2 M_p}\right) .
\end{equation}
At low $Q^2$, the experimental data
reveals prominent resonances;
but this resonance structure quickly dies out as $Q^2$ increases.
A much softer but sizeable continuum contribution persists at large $Q^2$,
suggesting the existence of pointlike objects inside the proton.
To get an idea of the possible behaviour of the structure functions, one
can make a very rough model of the proton, assuming that it consist of
some number of pointlike spin-$\frac{1}{2}$ constituents (the so-called
{\it partons}), each one carrying a given fraction $\xi_i$ of the
proton momenta, i.e. ${p_i}^\mu = \xi_i P^\mu$. That means that we are
neglecting\footnote{\small
These approximations can be made more precise going to the
infinite momentum frame of the proton, where the transverse motion
is negligible compared with the large longitudinal boost of the partons.}
the transverse parton momenta, and $m_i = \xi M_p$.
The interaction of the photon-probe with the parton $i$ generates a
contribution to the structure functions given by:
\begin{eqnarray}\label{eq:W1}
W_1^{(i)}(Q^2,\nu) &=& {e_i^2 Q^2\over 4 m_i^2}\:
\delta\!\left(\nu - {Q^2\over 2 m_i}\right) =
{e_i^2\over 2 M_p}\, \delta\left(\xi_i - x\right) ,
\\ \label{eq:W2}
W_2^{(i)}(Q^2,\nu) &=& e_i^2 \delta\!\left(\nu - {Q^2\over 2 m_i}\right) =
e_i^2 {x\over\nu}\: \delta\left(\xi_i - x\right) ,
\end{eqnarray}
where $e_i$ is the parton electric charge and
\bel{eq:x_def}
x\equiv {Q^2\over 2 M_p\nu} = {Q^2\over Q^2 + W^2 - M_p^2} \, .
\end{equation}
Thus, the parton structure functions only depend on the ratio $x$,
which, moreover, fixes the momentum fractions $\xi_i$.
We can go further, and assume that in the limit $Q^2\to\infty$,
$\nu\to\infty$, but keeping $x$ fixed, the proton structure functions
can be estimated from an incoherent sum of the parton ones
(neglecting any strong interactions among the partons). Denoting
$f_i(\xi_i)$ the probability that the parton $i$ has momentum fraction
$\xi_i$, one then has:
\begin{eqnarray}\label{eq:W1p}
W_1(Q^2,\nu) &\!\!\! =&\!\!\! \sum_i \int_0^1 d\xi_i\, f_i(\xi_i)\,
W_1^{(i)}(Q^2,\nu) = {1\over 2 M_p} \sum_i e_i^2 f_i(x)
\equiv {1\over M_p}\, F_1(x) \, ,\quad
\\ \label{eq:W2p}
W_2(Q^2,\nu) &\!\!\! =&\!\!\! \sum_i \int_0^1 d\xi_i\, f_i(\xi_i)\,
W_2^{(i)}(Q^2,\nu) = {x\over \nu} \sum_i e_i^2 f_i(x)
\equiv {1\over \nu}\, F_2(x) \, .
\end{eqnarray}
This simple parton description implies then the so-called Bjorken
{\it scaling} \cite{BJ:69}: the proton structure functions only depend on the
kinematical variable $x$. Moreover, one gets the Callan--Gross relation
\cite{CG:69}
\bel{eq:CG}
F_2(x) = 2 x F_1(x) \, ,
\end{equation}
which is a consequence of our assumption of spin-$\frac{1}{2}$ partons.
It is easy to check that spin-0 partons would have lead to $F_1(x)=0$.
\begin{figure}[htb]
\vfill\centerline{
\begin{minipage}[t]{.47\linewidth}
\centerline{\mbox{\epsfxsize=7.7cm\epsfysize=7.0cm\epsffile{F2x.ps}}}
\vspace{-0.3cm}
\caption{Experimental data on $\nu W_2$ as function of $x$,
for different values of $Q^2$
\protect\cite{AT:80} (taken from Ref.~\protect\cite{AH:89}).}
\label{fig:W2x}
\end{minipage}
\hspace{0.7cm}
\begin{minipage}[t]{.47\linewidth}
\centerline{\mbox{\epsfysize=7.5cm\epsffile{F1F2rat.ps}}}
\vspace{-0.3cm}
\caption{The ratio $2xF_1/F_2$ versus $x$,
for different $Q^2$ values (1.5 GeV$^2 < Q^2 < 16$ GeV$^2$)
\protect\cite{PE:87} (taken from Ref.~\protect\cite{AH:89}).}
\label{fig:CG}
\end{minipage}
}\vfill
\end{figure}
The measured values of $\nu W_2(Q^2,\nu)$ are shown in Fig.~\ref{fig:W2x}
as function of $x$, for many different values of $Q^2$ between 2 and 18
GeV$^2$;
the concentration of data points along a curve indicates that Bjorken scaling
is correct, to a quite good approximation.
Fig.~\ref{fig:CG} shows that the Callan--Gross relation is also reasonably
well satisfied by the data, supporting the spin-$\frac{1}{2}$ assignment
for the partons.
The surprising thing of this successful predictions is that we have assumed
the existence of free independent pointlike partons inside the proton, in
spite of the fact that quarks are supossed to be confined by very strong
colour forces.
Bjorken scaling suggests that the strong interactions must have the
property of {\it asymptotic freedom}:
they should become weaker at short distances,
so that quarks behave as free particles for $Q^2\to\infty$.
This also agrees with the empirical observation in Fig.~\ref{fig:Ree},
that the free-quark description of the ratio $R_{e^+e^-}$ works
better at higher energies.
Thus, the interaction between a $q\bar q$ pair looks like some kind of
rubber band. If we try to separate the quark form the antiquark
the force joining them increases.
At some point, the energy on the elastic band is bigger than $2m_{q'}$, so
that it becomes energetically favourable to create an additional $q'\bar q'$
pair; then the band breaks down into two mesonic systems, $q\bar q'$ and
$q'\bar q$, each one with its corresponding half-band joining the quark pair.
Increasing more and more the energy, we can only produce more and more
mesons, but quarks remain always confined within colour-singlet bound states.
Conversely, if one tries to approximate two quark constituents into
a very short-distance region, the elastic band loses the energy and becomes
very soft; quarks behave then as free particles.
\subsection{Why \protect\boldmath $SU(3)$?}
Flavour-changing transitions have a much weaker strength than processes
mediated by the strong force. The quark-flavour quantum number is associated
with the electroweak interactions, while strong forces appear to be
flavour-conserving and flavour-independent.
On the other side, the carriers of the electroweak interaction
($\gamma$, $Z$, $W^\pm$) do not couple to the quark colour. Thus, it seems
natural to take colour as the charge associated with the strong forces
and try to build a quantum field theory based on it \cite{FGL:73}.
The empirical evidence described so far puts a series of requirements that
the fundamental theory of colour interactions should satisfy:
\begin{enumerate}
\item Colour is an exact symmetry $G_C$
(hadrons do not show colour multiplicity).
\item $N_C=3$. Thus, quarks belong to the triplet representation
$\underline{3}$ of $G_C$.
\item Quarks and antiquarks are different states. Therefore,
$\underline{3}^*\not= \underline{3}$, i.e. the triplet representation has
to be complex.
\item Confinement hypothesis: hadronic states are colour singlets.
\item Asymptotic freedom.
\end{enumerate}
Among all compact simple Lie groups there are only four having 3-dimensional
irreducible representations; moreover, three of them are isomorphic to
each other. Thus, we have only two choices: $SU(3)$ or
$SO(3)\simeq SU(2)\simeq Sp(1)$. Since the triplet representation of $SO(3)$
is real, only the symmetry group $SU(3)$ survives the conditions 1, 2 and 3.
The well-known $SU(3)$ decomposition of the products of $\underline{3}$
and $\underline{3}^*$ representations,
\begin{eqnarray}\label{eq:rep_products}
q\bar q: & & \underline{3}\otimes \underline{3}^* =
\underline{1} \oplus \underline{8} \, ,
\nonumber\\
qqq: && \underline{3}\otimes\underline{3}\otimes\underline{3} =
\underline{1} \oplus \underline{8} \oplus \underline{8}
\oplus \underline{10} \, ,
\nonumber\\
qq: && \underline{3}\otimes \underline{3} =
\underline{3}^* \oplus \underline{6} \, ,
\nonumber\\
qqqq: &&
\underline{3}\otimes\underline{3}\otimes\underline{3}\otimes \underline{3}=
\underline{3}\oplus\underline{3}\oplus\underline{3}\oplus\underline{6}^*
\oplus\underline{15}\oplus\underline{15}\oplus\underline{15}
\oplus\underline{15'} \, ,
\end{eqnarray}
guarantees that there are colour-singlet configurations corresponding to
meson ($q\bar q$) and baryon ($qqq$) states, as required
by the confinement hypothesis. Other exotic combinations such as diquarks
($qq$, $\bar q\bar q$) or four-quark states
($qqqq$, $\bar q\bar q\bar q\bar q$) do not satisfy this requirement.
Clearly, the theory of colour interactions should be based on
the $SU(3)_C$ group.
It remains to be seen whether such a theory is able
to explain confinement and asymptotic freedom as natural dynamical
consequences of the colour forces.
\setcounter{equation}{0}
\section{GAUGE SYMMETRY: QED}
\label{sec:qed}
Let us consider the Lagrangian describing a free Dirac fermion:
\bel{eq:l_free}
{\cal L}_0\, =\, i \,\overline{\Psi}(x)\gamma^\mu\partial_\mu\Psi(x)
\, - \, m\, \overline{\Psi}(x)\Psi(x) \, .
\end{equation}
${\cal L}_0$ is invariant under {\em global}
$U(1)$ transformations
\bel{eq:global}
\Psi(x) \,\stackrel{\mbox{\rms U(1)}}{\longrightarrow}\, \Psi'(x)\,\equiv\,\exp{\{i Q \theta\}}\,\Psi(x) \, ,
\end{equation}
where $Q\theta$ is an arbitrary real constant.
The phase of $\Psi(x)$ is then a pure convention-dependent
quantity without physical meaning.
However,
the free Lagrangian is no-longer invariant if one allows
the phase transformation to depend on the space-time coordinate,
i.e. under {\em local} phase redefinitions $\theta=\theta(x)$,
because
\bel{eq:local}
\partial_\mu\Psi(x) \,\stackrel{\mbox{\rms U(1)}}{\longrightarrow}\, \exp{\{i Q \theta\}}\,
\left(\partial_\mu + i Q \partial_\mu\theta\right)\,
\Psi(x) \, .
\end{equation}
Thus, once an observer situated at the point $x_0$
has adopted a given phase-convention, the same convention must
be taken at all space-time points. This looks very unnatural.
The ``Gauge Principle'' is the requirement that the $U(1)$
phase invariance should hold {\em locally}.
This is only possible if one adds some additional piece to the
Lagrangian, transforming in such a way as to cancel the
$\partial_\mu\theta$ term in Eq.~\eqn{eq:local}.
The needed modification is completely fixed by the transformation
\eqn{eq:local}: one introduces a new spin--1
(since $\partial_\mu\theta$ has a Lorentz index)
field $A_\mu(x)$, transforming as
\bel{eq:a_transf}
A_\mu(x)\,\stackrel{\mbox{\rms U(1)}}{\longrightarrow}\, A_\mu'(x)\,\equiv\, A_\mu(x) + {1\over e}\,
\partial_\mu\theta\, ,
\end{equation}
and defines the covariant derivative
\bel{eq:d_covariant}
D_\mu\Psi(x)\,\equiv\,\left[\partial_\mu-ieQA_\mu(x)\right]
\,\Psi(x)\, ,
\end{equation}
which has the required
property of transforming like the field itself:
\bel{eq:d_transf}
D_\mu\Psi(x)\,\stackrel{\mbox{\rms U(1)}}{\longrightarrow}\,\left(D_\mu\Psi\right)'(x)\,\equiv\,
\exp{\{i Q \theta\}}\,D_\mu\Psi(x)\,.
\end{equation}
The Lagrangian
\bel{eq:l_new}
{\cal L}\,\equiv\,
i \,\overline{\Psi}(x)\gamma^\mu D_\mu\Psi(x)
\, - \, m\, \overline{\Psi}(x)\Psi(x)
\, =\, {\cal L}_0\, +\, e Q A_\mu(x)\, \overline{\Psi}(x)\gamma^\mu\Psi(x)
\end{equation}
is then invariant under local $U(1)$ transformations.
The gauge principle has generated an interaction
between the Dirac spinor and the gauge field $A_\mu$,
which is nothing else than the familiar QED vertex.
Note that the corresponding electromagnetic
charge $eQ$ is completely arbitrary.
If one wants $A_\mu$ to be a true propagating field, one needs to add
a gauge-invariant kinetic term
\bel{eq:l_kinetic}
{\cal L}_{\!\!\mbox{\rm\scriptsize Kin}}\,\equiv\, -{1\over 4} F_{\mu\nu} F^{\mu\nu}\,,
\end{equation}
where
$F_{\mu\nu}\,\equiv\, \partial_\mu A_\nu -\partial_\nu A_\mu$
is the usual electromagnetic field strength.
A possible mass term for the gauge field,
${1\over 2}m^2A^\mu A_\mu$, is forbidden because it would violate
gauge invariance; therefore,
the photon field is predicted to be massless.
The total Lagrangian in \eqn{eq:l_new} and \eqn{eq:l_kinetic}
gives rise to the well-known Maxwell equations.
{}From a simple gauge-symmetry requirement, we have deduced
the right QED Lagrangian, which leads to a very successful
quantum field theory.
Remember that QED predictions have been tested
to a very high accuracy, as exemplified by the electron and
muon anomalous magnetic moments
[$a_l\equiv (g_l-2)/2$, where $\mu_l\equiv g_l \,(e \hbar/2m_l)$]
\cite{KI:90}:
\begin{eqnarray}\label{eq:a_e}
a_e&=&\left\{ \begin{array}{cc}
(115 \, 965 \, 214.0\pm 2.8) \times 10^{-11} & (\mbox{\rm Theory})
\\
(115 \, 965 \, 219.3\pm 1.0) \times 10^{-11} & (\mbox{\rm Experiment})
\end{array} \, , \right.\\
a_\mu&=&\left\{ \begin{array}{cc}
(1 \, 165 \, 919.2\pm 1.9)
\times 10^{-9} & (\mbox{\rm Theory})
\\
(1 \, 165 \, 923.0\pm 8.4) \times 10^{-9} & (\mbox{\rm Experiment})
\end{array} \, . \right.
\end{eqnarray}
\setcounter{equation}{0}
\section{THE QCD LAGRANGIAN}
\label{sec:QCDlagrangian}
Let us denote $q^\alpha_f$ a quark field of colour $\alpha$ and flavour $f$.
To simplify the equations, let us adopt a vector notation
in colour space:
$q_f \,\equiv\, \mbox{\rm column}(q^1_f,q^2_f,q^3_f) $ .
The free Lagrangian
\bel{eq:L_free}
{\cal L}_0 = \sum_f\,\bar q_f \, \left( i\gamma^\mu\partial_\mu - m_f\right) q_f
\end{equation}
is invariant under arbitrary global $SU(3)_C$ transformations in colour
space,
\bel{eq:q_transf}
q^\alpha_f \,\longrightarrow\,
(q^\alpha_f)' = U^\alpha_{\phantom{\alpha}\beta}\, q^\beta_f \, ,
\qquad\qquad
U U^\dagger = U^\dagger U = 1 \, , \qquad\qquad
\det U = 1 \, .
\end{equation}
The $SU(3)_C$ matrices can be written in the form
\bel{eq:U_def}
U = \exp\left\{-ig_s {\lambda^a\over 2}\theta_a\right\} \, ,
\end{equation}
where $\lambda^a$ ($a=1,2,\ldots,8$) denote the
generators of the fundamental representation of the
$SU(3)_C$ algebra,
and $\theta_a$ are arbitrary parameters. The matrices $\lambda^a$
are traceless and
satisfy the commutation relations
\bel{eq:commutation}
\left[\lambda^a,\lambda^b\right] =
2 i f^{abc} \, \lambda^c \, ,
\end{equation}
with $f^{abc}$ the $SU(3)_C$
structure constants, which are real and totally antisymmetric.
Some useful properties of $SU(3)$ matrices are collected in Appendix A.
As in the QED case, we can now require the Lagrangian to be also invariant
under {\it local} $SU(3)_C$ transformations, $\theta_a = \theta_a(x)$. To
satisfy this requirement, we need to change the quark derivatives by covariant
objects. Since we have now 8 independent gauge parameters, 8 different
gauge bosons $G^\mu_a(x)$, the so-called {\it gluons}, are needed:
\bel{eq:D_cov}
D^\mu q_f \,\equiv\, \left[ \partial^\mu - i g_s {\lambda^a\over 2}
G^\mu_a(x)\right]
\, q_f \, \equiv\, \left[ \partial^\mu - i g_s G^\mu(x)\right] \, q_f \, .
\end{equation}
Notice that we have introduced the compact matrix notation
\bel{eq:G_matrix}
[G^\mu(x)]_{\alpha\beta}\,\equiv\,
\left({\lambda^a\over 2}\right)_{\!\alpha\beta}\, G^\mu_a(x) \, .
\end{equation}
We want $D^\mu q_f$ to transform in exactly the same way as the colour-vector
$q_f$;
this fixes the transformation properties of the gauge fields:
\bel{eq:G_trans}
D^\mu \,\longrightarrow\, (D^\mu)'= U\, D^\mu\, U^\dagger \, ; \qquad
G^\mu \,\longrightarrow\, (G^\mu)'= U\, G^\mu\, U^\dagger
-{i\over g_s} \, (\partial^\mu U) \, U^\dagger \, .
\end{equation}
Under an infinitesimal $SU(3)_C$ transformation,
\begin{eqnarray}\label{eq:inf_transf}
q^\alpha_f &\longrightarrow & (q^\alpha_f)' =
q^\alpha_f -i g_s \left({\lambda^a\over 2}\right)_{\!\alpha\beta}
\delta\theta_a\, q^\beta_f \, ,
\nonumber\\
G^\mu_a &\longrightarrow & (G^\mu_a)' = G^\mu_a -\partial^\mu(\delta\theta_a)
+ g_s f^{abc} \delta\theta_b \, G^\mu_c \, .
\end{eqnarray}
The gauge transformation of the gluon fields is more complicated that the one
obtained in QED for the photon.
The non-commutativity of the $SU(3)_C$ matrices gives rise to an additional
term
involving the gluon fields themselves.
For constant $\delta\theta_a$, the transformation rule for the gauge fields
is expressed in terms of the structure constants $f^{abc}$ only; thus,
the gluon fields belong to the adjoint representation of the colour group
(see Appendix~A).
Note also that there is a unique $SU(3)_C$
coupling $g_s$. In QED it was possible to assign arbitrary electromagnetic
charges to the
different fermions. Since the commutation relation \eqn{eq:commutation} is
non-linear, this freedom does not exist for $SU(3)_C$.
To build a gauge-invariant kinetic term for the gluon fields, we introduce
the corresponding field strengths:
\begin{eqnarray}\label{eq:G_tensor}
G^{\mu\nu}(x) & \equiv & {i\over g_s}\, [D^\mu, D^\nu] \, = \,
\partial^\mu G^\nu - \partial^\nu G^\mu - i g_s\, [G^\mu, G^\nu] \, \equiv \,
{\lambda^a\over 2}\, G^{\mu\nu}_a(x) \, ,
\nonumber\\
G^{\mu\nu}_a(x) & = & \partial^\mu G^\nu_a - \partial^\nu G^\mu_a
+ g_s f^{abc} G^\mu_b G^\nu_c \, .
\end{eqnarray}
Under a gauge transformation,
\bel{eq:G_tensor_transf}
G^{\mu\nu}\,\longrightarrow\, (G^{\mu\nu})' = U\, G^{\mu\nu}\, U^\dagger \, ,
\end{equation}
and the colour trace
Tr$(G^{\mu\nu}G_{\mu\nu}) = \frac{1}{2} G^{\mu\nu}_aG_{\mu\nu}^a$
remains invariant.
Taking the proper normalization for the gluon kinetic term, we finally have
the $SU(3)_C$ invariant QCD Lagrangian:
\bel{eq:L_QCD}
{\cal L}_{\!\!\mbox{\rm\scriptsize QCD}} \,\equiv\, -{1\over 4}\, G^{\mu\nu}_aG_{\mu\nu}^a
+ \sum_f\,\bar q_f \, \left( i\gamma^\mu D_\mu - m_f\right)\, q_f \, .
\end{equation}
It is worth while to decompose the Lagrangian into its different pieces:
\begin{eqnarray}\label{eq:L_QCD_pieces}
{\cal L}_{\!\!\mbox{\rm\scriptsize QCD}} & = &
-{1\over 4}\, (\partial^\mu G^\nu_a - \partial^\nu G^\mu_a)
(\partial_\mu G_\nu^a - \partial_\nu G_\mu^a)
+ \sum_f\,\bar q^\alpha_f \, \left( i\gamma^\mu\partial_\mu - m_f\right)\,
q^\alpha_f
\qquad\nonumber\\ && \mbox{}
+ g_s\, G^\mu_a\,\sum_f\, \bar q^\alpha_f \gamma_\mu
\left({\lambda^a\over 2}\right)_{\!\alpha\beta} q^\beta_f
\\ && \mbox{}
- {g_s\over 2}\, f^{abc}\, (\partial^\mu G^\nu_a - \partial^\nu G^\mu_a) \,
G_\mu^b G_\nu^c
\, - \, {g_s^2\over 4} \, f^{abc} f_{ade} \, G^\mu_b G^\nu_c G_\mu^d G_\nu^e
\,
{}.
\nonumber
\end{eqnarray}
The first line contains the correct kinetic terms for the different fields,
which
give rise to the corresponding propagators. The colour interaction between
quarks and gluons is given by the second line; it involves the $SU(3)_C$
matrices
$\lambda^a$. Finally, owing to the non-abelian character of the colour group,
the $G^{\mu\nu}_aG_{\mu\nu}^a$ term generates the cubic and quartic gluon
self-interactions shown in the last line;
the strength of these interactions is given by the same coupling $g_s$ which
appears in the fermionic piece of the Lagrangian.
In spite of the rich physics contained in it, the Lagrangian \eqn{eq:L_QCD}
looks very simple, because of its colour-symmetry properties.
All interactions are given in terms of a single universal coupling $g_s$,
which is called the {\it strong coupling constant}.
The existence of self-interactions among the gauge fields is a new feature
that was not present in the QED case; it seems then reasonable to expect that
these gauge self-interactions could explain properties
like asymptotic freedom and confinement, which do not appear in QED.
\begin{figure}[ph]
\centerline{\epsfxsize = 7cm \epsfbox{3jetmod.eps}}
\caption{Three-jet event from the hadronic decay of a $Z$ boson (DELPHI).}
\label{fig:ThreeJets}
\end{figure}
Without any detailed calculation, one can already extract qualitative physical
consequences from ${\cal L}_{\!\!\mbox{\rm\scriptsize QCD}}$.
Quarks can emit gluons. At lowest-order
in $g_s$, the dominant process will be the emission of a single gauge boson.
Thus, the hadronic decay of the $Z$ should result in some $Z\to q\bar q G$
events,
in addition to the dominant $Z\to q\bar q$ decays discussed in
Section~\ref{sec:introduction}
Fig.~\ref{fig:ThreeJets} clearly shows that 3-jet events, with the required
kinematics, indeed appear in the LEP data. Similar events show up in
$e^+e^-$ annihilation into hadrons, away from the $Z$ peak.
In order to properly quantize the QCD Lagrangian, one needs to add
to ${\cal L}_{\!\!\mbox{\rm\scriptsize QCD}}$ the
so-called {\it Gauge-fixing} and {\it Faddeev--Popov} terms.
Since this is a rather technical issue, its discussion is relegated
to Appendix B.
\setcounter{equation}{0}
\section{QUANTUM LOOPS}
\label{sec:loops}
The QCD Lagrangian is rather economic in the sense that it involves a single
coupling $g_s$. Thus, all strong-interacting phenomena should be described in
terms of just one parameter. At lowest order in $g_s$ (tree-level),
it is straightforward
to compute all kind of scattering amplitudes involving quarks and gluons:
$q\bar q\to GG$, $qq\to qq$, $G q\to G q$, \ldots
Unfortunately, this exercise by itself does not help very much to understand
the
physical hadronic world.
First, we see hadrons instead of quarks and gluons. Second, we have learnt from
experiment that the strength of the strong forces changes with the
energy scale: the interaction is very strong (confining) at low energies, but
quarks behave as nearly free particles at high energies.
Obviously, we cannot understand both energy regimes with a single constant
$g_s$,
which is the same everywhere. Moreover, if we neglect the quark masses,
the QCD Lagrangian does not contain any energy scale;
thus, there is no way to decide when the energy
of a given process is large or small, because we do not have any
reference scale to compare with.
If QCD is the right theory of the strong interactions, it should provide
some dynamical scale through quantum effects.
\subsection{Regularization of loop integrals}
\label{sub:regularization}
The computation of perturbative corrections to the tree-level results
involves divergent loop integrals. It is then necessary to find a way of
getting finite results with physical meaning from a priori meaningless
divergent quantities.
\begin{figure}[htb]
\centerline{\epsfysize=3cm \epsfbox{gluonSE.ps}}
\caption{Gluon self-energy diagram.}
\label{fig:gluonSE}
\end{figure}
Let us consider the self-energy gluon loop in Fig.~\ref{fig:gluonSE}.
The corresponding contribution in momentum space can be easily obtained,
using standard Feynman rules techniques:
\bel{eq:gluon_se}
i \Pi^{\mu\nu}_{ab}(q) \, = \, - g_s^2 \delta_{ab} T_F \int
{d^4k\over (2\pi)^4}
{\mbox{\rm Tr}[\gamma^\mu\slashchar{k}\gamma^\nu (\slashchar{k}-\slashchar{q})]
\over k^2 (k-q)^2} \, .
\end{equation}
The result is proportional to $g_s^2$, because there are two $q\bar q G$
vertices, and there is a trivial $SU(3)_C$ factor, $T_F = {1\over 2}$,
coming from the colour trace
${1\over 4}\mbox{\rm Tr}(\lambda^a\lambda^b) = \delta^{ab} T_F$.
The problem appears in the momentum integration, which is clearly divergent
[$\sim \int d^4k (1/k^2) = \infty$].
We can define the momentum integral in many different (and arbitrary) ways.
For instance, we could introduce a {\it cut-off} $M$, such that only
momentum scales smaller than $M$ are integrated; obviously, the resulting
integral would be an increasing function of $M$.
Instead, it has become conventional to define the loop integrals through
{\it dimensional regularization}: the calculation is performed in
$D=4+2\epsilon$ dimensions. For $\epsilon\not=0$ the resulting integral is
well-defined:
\bel{eq:dimensional}
\int {d^Dk\over (2\pi)^D}\, {k^\alpha (k-q)^\beta \over k^2 (k-q)^2} \, = \,
{-i\over 6 (4\pi)^2} \left({-q^2\over 4\pi}\right)^\epsilon
\Gamma(-\epsilon) \, \left(1-{5\over 3}\epsilon\right)
\left\{ {q^2 g^{\alpha\beta}\over 2 (1+\epsilon)} + q^\alpha q^\beta\right\} \,
{}.
\end{equation}
The ultraviolet divergence of the loop appears at $\epsilon=0$,
through the pole of the Gamma function,
\bel{eq:gamma}
\Gamma(-\epsilon) \, = \, -{1\over\epsilon} - \gamma_E + {\cal O}(\epsilon^2) \, ,
\end{equation}
where $\gamma_E = 0.577215\ldots $ is the Euler constant.
Although the integral \eqn{eq:dimensional} looks somewhat funny, dimensional
regularization has many advantages because does not spoil the gauge symmetry
of QCD and, therefore, simplifies a lot the calculations.
One could argue that a cut-off
procedure would
be more {\it physical}, since the parameter $M$ could be related to some
unknown additional physics at very short distances. However, within the
QCD framework, both prescriptions are equally meaningless. One just introduces
a regularizing parameter, such that the integral is well-defined and the
divergence is recovered in some limit ($M\to\infty$ or $\epsilon\to 0$).
Since the momentum-transfer $q^2$ has dimensions, it turns out to be convenient
to introduce and arbitrary energy scale $\mu$ and write
\bel{eq:mu_scale}
\left({-q^2\over 4\pi}\right)^\epsilon\Gamma(-\epsilon) =
\mu^{2\epsilon} \left({-q^2\over 4\pi\mu^2}\right)^\epsilon\Gamma(-\epsilon) =
-\mu^{2\epsilon}\left\{{1\over\epsilon} +\gamma_E -\ln{4\pi}
+\ln{(-q^2/\mu^2)} + {\cal O}(\epsilon)\right\} \, .
\end{equation}
Obviously, this expression does not depend on $\mu$; but written in this form
one has a dimensionless quantity ($-q^2/\mu^2$) inside the logarithm.
The contribution of the loop diagram in Fig.~\ref{fig:gluonSE}
can finally be written as
\begin{eqnarray}\label{eq:g_se}
\Pi^{\mu\nu}_{ab} &\!\! = &\!\!
\delta_{ab}\,\left( -q^2 g^{\mu\nu} + q^\mu q^\nu\right)
\, \Pi(q^2) \, ,
\nonumber\\
\Pi(q^2) &\!\! = &\!\!
-{4\over 3} T_F \,\left({g_s\mu^\epsilon\over 4\pi}\right)^2
\left\{{1\over\epsilon} +\gamma_E -\ln{4\pi}
+\ln{(-q^2/\mu^2)} - {5\over 3} + {\cal O}(\epsilon)\right\} \, .
\end{eqnarray}
Owing to the ultraviolet divergence, Eq.~\eqn{eq:g_se} does not determine the
wanted self-energy contribution. Nevertheless, it does show how this effect
changes with the energy scale.
If one could fix the value of
$\Pi(q^2)$ at some reference momentum transfer $q_0^2$, the result
would be known at any other scale:
\bel{eq:pi_1_2}
\Pi(q^2) = \Pi(q_0^2) - {4\over 3} T_F \, \left({g_s\over 4\pi}\right)^2
\,\ln{(q^2/q_0^2)} \, .
\end{equation}
We can split the self-energy contribution into a meaningless divergent piece
and a finite term, which includes the $q^2$ dependence,
\bel{eq:Pi_splitting}
\Pi(q^2) \,\equiv\, \Delta\Pi_\epsilon(\mu^2) + \Pi_R(q^2/\mu^2)\, .
\end{equation}
This separation is of course ambiguous, because the finite $q^2$-independent
contributions can be splitted in many different ways. A given choice defines
a {\it scheme}:
\begin{equation}\label{eq:Pi_epsilon}
\Delta\Pi_\epsilon(\mu^2) \, =\, \left\{
\begin{array}{ll}
-{T_F\over 3\pi} {g_s^2\over 4\pi} \mu^{2\epsilon} \left[ {1\over\epsilon}
+ \gamma_E -\ln(4\pi) -{5\over 3}\right] \quad\qquad\qquad &
\;\; (\mu\mbox{\rm -scheme}) , \\
-{T_F\over 3\pi} {g_s^2\over 4\pi} \mu^{2\epsilon} {1\over\epsilon} \qquad &
(\mbox{\rm MS}\mbox{\rm -scheme}) , \; \\
-{T_F\over 3\pi} {g_s^2\over 4\pi} \mu^{2\epsilon} \left[ {1\over\epsilon}
+ \gamma_E -\ln(4\pi)\right] \qquad &
(\overline{\mbox{\rm MS}}\mbox{\rm -scheme}) ,
\end{array}\right.
\end{equation}
\begin{equation}\label{eq:Pi_R}
\Pi_R(q^2/\mu^2) \, =\, \left\{
\begin{array}{ll}
-{T_F\over 3\pi} {g_s^2\over 4\pi} \ln{(-q^2/\mu^2)} \qquad &
\;\; (\mu\mbox{\rm -scheme}) , \\
-{T_F\over 3\pi} {g_s^2\over 4\pi} \left[ \ln{(-q^2/\mu^2)}
+ \gamma_E -\ln(4\pi) -{5\over 3}\right] \qquad &
(\mbox{\rm MS}\mbox{\rm -scheme}) , \quad\\
-{T_F\over 3\pi} {g_s^2\over 4\pi} \left[ \ln{(-q^2/\mu^2)}
-{5\over 3}\right] \qquad & (\overline{\mbox{\rm MS}}\mbox{\rm
-scheme}) .
\end{array}\right.
\end{equation}
In the $\mu$-scheme, one uses the value of $\Pi(-\mu^2)$ to define the
divergent part.
MS and $\overline{\mbox{\rm MS}}$ stand for minimal subtraction
\cite{THO:73} and
modified minimal subtraction schemes \cite{BBDM:78};
in the MS case, one subtracts only
the divergent $1/\epsilon$ term, while the $\overline{\mbox{\rm MS}}$
scheme puts also the annoying $\gamma_E-\ln(4\pi)$ factor into the
divergent part.
Notice that the logarithmic $q^2$-dependence is always the same.
\begin{figure}[htb]
\centerline{\epsfysize=4cm \epsfbox{photonSE.ps}}
\caption{Photon self-energy contribution to $e^-e^-$ scattering.}
\label{fig:EEint}
\end{figure}
\subsection{Renormalization: QED}
\label{subsec:renormalization}
A Quantum Field Theory is called {\it renormalizable} if all ultraviolet
divergences can be reabsorbed through a redefinition of the original fields
and couplings.
Let us consider the electromagnetic interaction between two electrons.
At one loop,
the QED photon self-energy contribution is just given by
Eq.~\ref{eq:g_se}, with the changes $T_F\to 1$ and $g_s\to e$. The
corresponding scattering amplitude takes the form
\bel{eq:T_ee}
T(q^2) \,\sim\, -J^\mu J_\mu \, {e^2\over q^2} \, \left\{ 1 -\Pi(q^2) + \ldots
\right\} \, ,
\end{equation}
where $J^\mu$ denotes the electromagnetic fermion current.
At lowest order,
$T(q^2)\sim \alpha/q^2$ with $\alpha = e^2/(4\pi)$.
The divergent correction generated by quantum loops can be reabsorbed into a
redefinition of the coupling:
\bel{eq:alpha_R}
{\alpha_0\over q^2}\, \left\{ 1 -\Delta\Pi_\epsilon(\mu^2)
- \Pi_R(q^2/\mu^2)\right\} \,\equiv\,
{\alpha_R(\mu^2)\over q^2}\, \left\{ 1
- \Pi_R(q^2/\mu^2)\right\} \, ,
\end{equation}
\bel{eq:alpha_Rb}
\alpha_R(\mu^2) \, = \, \alpha_0 \,
\left\{ 1 + {\alpha_0 \over 3\pi} \mu^{2\epsilon}
\left[{1\over\epsilon} + C_{\!\!\mbox{\rm\scriptsize scheme}}\right] + \ldots
\right\} \, ,
\qquad\qquad
\alpha_0\,\equiv\, {e_0^2\over 4\pi}\ , \quad
\end{equation}
where $e_0$ denotes the {\it bare}
coupling appearing in the QED Lagrangian;
this bare quantity is, however, not directly observable. Making the
redefinition
\eqn{eq:alpha_R}, the scattering amplitude is finite and gives rise
to a definite prediction for the cross-section, which can be compared with
experiment; thus, one actually measures the {\it renormalized} coupling
$\alpha_R$.
The redefinition \eqn{eq:alpha_R} is meaningful, provided that it can be done
in a self-consistent way: all ultraviolet divergent contributions to all
possible scattering processes should be eliminated through the same
redefinition
of the coupling (and the fields). The nice thing of gauge theories, such as
QED or QCD, is that the underlying gauge symmetry guarantees the
renormalizability of the quantum field theory.
The renormalized coupling $\alpha_R(\mu^2)$ depends
on the arbitrary scale $\mu$ and on the chosen {\it renormalization scheme}
[the constant $C_{\!\!\mbox{\rm\scriptsize scheme}}$ denotes the different finite terms
in
Eq.~\eqn{eq:Pi_epsilon}]. Quantum loops have introduced a scale dependence in a
quite subtle way. Both $\alpha_R(\mu^2)$ and the renormalized self-energy
correction $\Pi_R(q^2/\mu^2)$ depend on $\mu$, but the physical scattering
amplitude $T(q^2)$ is of course $\mu$-independent: ($Q^2\equiv -q^2$)
\begin{eqnarray}\label{eq:mu_dep}
T(q^2) &\sim & -4\pi\, J^\mu J_\mu\,
{\alpha_R(\mu^2)\over q^2}\, \left\{ 1 +
{\alpha_R(\mu^2)\over 3\pi} \left[ \ln{\left(-q^2\over\mu^2\right)} +
C'_{\!\!\mbox{\rm\scriptsize scheme}}\right] + \ldots \right\}\nonumber\\
& = & 4\pi\, J^\mu J_\mu\,
{\alpha_R(Q^2)\over Q^2} \, \left\{ 1 +
{\alpha_R(Q^2)\over 3\pi} C'_{\!\!\mbox{\rm\scriptsize scheme}} + \cdots \right\}\, .
\end{eqnarray}
The quantity $\alpha(Q^2)\equiv\alpha_R(Q^2)$ is called the QED
{\it running coupling}.
The ordinary fine structure constant $\alpha=1/137$ is defined through the
classical Thomson formula; therefore, it corresponds to a very low scale
$Q^2= -m_e^2$. Clearly, the value of $\alpha$ relevant for LEP experiments
is not the same
[$\alpha(M_Z^2)_{\overline{\!\!\mbox{\rm\scriptsize MS}}} = 1/129$].
The scale dependence of $\alpha(Q^2)$ is regulated by
the so-called $\beta$-function:
\bel{eq:beta}
\mu {d\alpha\over d\mu} \,\equiv\, \alpha \,\beta(\alpha) \, ;
\qquad\qquad \beta(\alpha)\, =\, \beta_1 {\alpha\over \pi} +
\beta_2 \left({\alpha\over\pi}\right)^2 + \cdots
\end{equation}
At the one-loop level, the $\beta$-function reduces to the first coefficient,
which is fixed by Eq.~\eqn{eq:alpha_Rb}:
\bel{eq:beta_1}
\beta_1^{\!\!\mbox{\rm\scriptsize QED}} \, = \, {2\over 3}\, .
\end{equation}
The first-order differential equation \eqn{eq:beta} can then be easily solved,
with the result:
\bel{eq:alpha_run}
\alpha(Q^2) \, = \, {\alpha(Q_0^2)\over 1 - {\beta_1 \alpha(Q_0^2)\over 2\pi}
\ln{(Q^2/Q_0^2)}} \, .
\end{equation}
Since $\beta_1>0$, the QED running coupling increases with the energy scale:
$\alpha(Q^2)>\alpha(Q_0^2)$ if $Q^2>Q_0^2$;
i.e. the electromagnetic charge decreases at large distances. This can be
intuitively understood as the screening effect due to the virtual $e^+e^-$
pairs
generated, through quantum effects, around the electron charge.
The physical QED vacuum behaves as a polarized dielectric medium.
\begin{figure}[htb]
\centerline{\epsfysize=5cm \epsfbox{screening.ps}}
\caption{Electromagnetic charge screening in a dipolar medium.}
\label{fig:screening}
\end{figure}
Notice that taking $\mu^2=Q^2$ in Eq.~\eqn{eq:mu_dep} we have eliminated
all dependences on $\ln{(Q^2/\mu^2)}$ to all orders in $\alpha$.
The running coupling \eqn{eq:alpha_run} makes a resummation of all
leading logarithmic corrections, i.e
\bel{eq:alpha_logs}
\alpha(Q^2) \, = \, \alpha(\mu^2)\,\sum_{n=0}^\infty
\left[ {\beta_1 \alpha(\mu^2)\over 2\pi}
\ln{(Q^2/\mu^2)}\right]^n \, .
\end{equation}
This higher-order logarithms correspond to the contributions from an
arbitrary number of one-loop self-energy insertions along the intermediate
photon propagator in Fig.~\ref{fig:EEint}
$[1 - \Pi_R(q^2/\mu^2) + \left(\Pi_R(q^2/\mu^2)\right)^2 + \cdots]$.
\subsection{The QCD running coupling}
\label{subsec:AlphaRunning}
\begin{figure}[htb]
\centerline{\epsfxsize=14cm \epsfbox{ASren.ps}}
\caption{Feynman diagrams contributing to the renormalization of the
strong coupling.
The dashed loop indicates the {\it ghost} correction discussed in Appendix B.}
\label{fig:g_si}
\end{figure}
The renormalization of the QCD coupling proceeds in a similar
way. Owing to the non-abelian character of $SU(3)_C$, there are additional
contributions involving gluon self-interactions. From the
calculation of the relevant one-loop diagrams, shown in Fig.~\ref{fig:g_si},
one gets the value of the first $\beta$-function
coefficient \cite{GW:73,PO:73}:
\bel{eq:QCD_beta}
\beta_1 \, = \, {2\over 3} T_F N_f - {11\over 6} C_A
\, = \, {2 N_f - 11 N_C \over 6} \, .
\end{equation}
The positive contribution proportional to $N_f$ is generated by the
$q$-$\bar q$ loops and corresponds to the QED result (except for the $T_F$
factor).
The gluonic self-interactions introduce the additional {\it negative}
contribution proportional to $N_C$. This second term is responsible for the
completely different behaviour of QCD: $\beta_1 < 0$ if $N_f \leq 16$.
The corresponding QCD running coupling,
\bel{eq:QCD_run}
\alpha_s(Q^2) \, = \, {\alpha_s(Q_0^2)\over 1 - {\beta_1 \alpha_s(Q_0^2)\over
2\pi}
\ln{\left({Q^2/ Q_0^2}\right)}} \, ,
\end{equation}
decreases at short distances, i.e.
\bel{eq:af_limit}
\lim_{Q^2\to\infty} \, \alpha_s(Q^2) \, = \, 0 \, .
\end{equation}
Thus, for $N_f\leq 16$, QCD has indeed the required property of asymptotic
freedom.
The gauge self-interactions of the gluons {\it spread out} the QCD charge,
generating an {\it antiscreening} effect. This could not happen in QED, because
photons do not carry electric charge. Only non-abelian gauge theories,
where the intermediate gauge bosons are self-interacting particles, have this
antiscreening property \cite{CG:73}.
Although quantum effects have introduced a dependence with the energy, we
still need a reference scale to decide when a given $Q^2$ can be
considered large or small. An obvious possibility is to choose the scale
at which $\alpha_s$ enters into a strong-coupling regime (i.e.
$\alpha_s\sim 1$), where perturbation theory is no longer valid.
A more precise definition can be obtained from the solution of the
$\beta$-function differential equation \eqn{eq:beta}. At one loop, one gets
\bel{eq:Lambda_def}
\ln{\mu} + {\pi\over\beta_1\alpha_s(\mu^2)} \, = \,
\ln{\Lambda} \, ,
\end{equation}
where $\ln{\Lambda}$ is just an integration constant. Thus,
\bel{eq:alpha_Lambda}
\alpha_s(\mu^2) \, = \,
{2\pi\over -\beta_1 \ln{\left({\mu^2/\Lambda^2}\right)}} \, .
\end{equation}
In this way, we have traded the dimensionless parameter $g_s$ by the
dimensionful scale $\Lambda$.
The number of QCD free parameters is the same (1 for massless quarks), but
quantum effects have generated an energy scale.
Although, Eq.~\eqn{eq:QCD_run} gives the impression that the
scale-dependence of
$\alpha_s(\mu^2)$ involves two parameters, $\mu_0^2$ and
$\alpha_s(\mu_0^2)$, only the combination \eqn{eq:Lambda_def}
is actually relevant, as explicitly shown in
\eqn{eq:alpha_Lambda}.
When $\mu>>\Lambda$, $\alpha_s(\mu^2)\to 0$, so that we recover asymptotic
freedom. At lower energies the running coupling gets bigger; for
$\mu\to\Lambda$, $\alpha_s(\mu^2)\to \infty$ and perturbation theory breaks
down. The scale $\Lambda$ indicates when the strong coupling blows up.
Eq.~\eqn{eq:alpha_Lambda} suggests that confinement at low energies
is quite plausible
in QCD; however, it does not provide a proof because
perturbation theory is no longer valid when $\mu\to\Lambda$.
\subsection{Higher orders}
Higher orders in perturbation theory are much more important in QCD than in
QED, because the coupling is much bigger (at ordinary energies). Unfortunately,
the calculations are also technically more involved. Nevertheless, many
quantities have been already computed at ${\cal O}(\alpha_s^2)$ or even
${\cal O}(\alpha_s^3)$. The $\beta$-function is known to three loops; in the
$\overline{\mbox{\rm MS}}$ scheme, the computed higher-order coefficients
take the values \cite{CA:74}:
\bel{eq:beta_hl}
\beta_2 = -{51\over 4} + {19\over 12} N_f \, ; \qquad\qquad
\beta_3 = {1\over 64}\left[ -2857 + {5033\over 9} N_f
- {325\over 27} N_f^2 \right] \, .
\end{equation}
If $N_f\leq 8$, $\beta_2 <0$ \ ($\beta_3 < 0$ for $N_f\leq 5$)
which further reinforces the asymptotic freedom behaviour.
The scale dependence of the running coupling at higher-orders is given by:
\bel{eq:rsc_a} \!\!
\alpha_s(\mu^2) \, =\, \alpha_s(\mu_0^2) \,\left\{ 1 -
{\beta_1\over 2}{\alpha_s(\mu_0^2)\over\pi}
\ln{\left({\mu^2/\mu_0^2}\right)}
-{\beta_2\over 2}\left({\alpha_s(\mu_0^2)\over\pi}\right)^2
\ln{\left({\mu^2/\mu_0^2}\right)} + \cdots \right\}^{-1} \!\! ,
\end{equation}
or, in terms of $\Lambda$,
\bel{eq:rsc_b}
\alpha_s(\mu^2) \, =\,
{2\pi\over (-\beta_1) \ln{\left({\mu^2/\Lambda^2}\right)}}
\left\{ 1 - {\beta_2 \over \beta_1}
{2 \over (-\beta_1) \ln{\left({\mu^2/\Lambda^2}\right)}}
\ln{\left[{1\over 2}\ln{\left({\mu^2/\Lambda^2}\right)}\right]}
+ \cdots \right\} \, .
\end{equation}
When comparing different QCD fits to the data, it is worth while to have in
mind
that any given value of $\alpha_s$ refers to a particular selection of
scale and renormalization scheme. Moreover, the resulting numerical values can
be different if one works at leading (LO), next-to-leading (NLO)
or next-to-next-to-leading (NNLO) order.
Although the parameter $\Lambda$ does not depend on the scale, it is
a scheme-dependent quantity. For instance:
\bel{eq:L_scheme}
\Lambda^2_{\!\!\mbox{\rm\scriptsize MS}} \, = \, {\mbox{\rm e}^{\gamma_E}\over 4\pi}\,
\Lambda^2_{\overline{\!\!\mbox{\rm\scriptsize MS}}} \, .
\end{equation}
Moreover, $\Lambda_{\!\!\mbox{\rm\scriptsize LO}} \not= \Lambda_{\!\!\mbox{\rm\scriptsize NLO}}
\not= \Lambda_{\!\!\mbox{\rm\scriptsize NNLO}}$.
In fact, slightly different definitions of
$\Lambda$ can be given at NLO, depending on the way the integration constant
is chosen when solving the $\beta$-function differential equation.
Moreover, since in the MS and $\overline{\mbox{\rm MS}}$ schemes the
$\beta$-function coefficients depend on $N_f$, $\Lambda$ takes different
values when the number of flavours is changed. At NLO,
the relation between the $\Lambda$ scales for 3 and 4 flavours
is given by:
\bel{eq:Lf}
\Lambda_4\,\approx\,\Lambda_3 \left({\Lambda_3\over m_c}\right)^{2/25}
\,\left[\ln{\left({m_c^2/\Lambda_3^2}\right)}\right]^{-107/1875} \, .
\end{equation}
\setcounter{equation}{0}
\section{PERTURBATIVE QCD PHENOMENOLOGY}
\label{sec:QCDpert}
\subsection{\protect\boldmath $e^+e$\protect\unboldmath\mbox{}$^-$
\protect\boldmath $\to\; $
\protect\unboldmath hadrons}
\label{subsec:Rhadrons}
\begin{figure}[htb]
\centerline{\epsfxsize=14cm \epsfbox{eeqqhad.ps}}
\caption{$e^+e^-\to\gamma^*,Z^*\to\, $ hadrons.}
\label{fig:eeqqhad}
\end{figure}
The inclusive production of hadrons in $e^+e^-$ annihilation is a good
process for testing perturbative QCD predictions.
The hadronic production occurs through the basic mechanism
$e^+e^-\to\gamma^*,Z^*\to q\bar q$,
where the final $q$-$\bar q$ pair interacts through the QCD forces;
thus, the quarks exchange and emit gluons (and $q'$-$\bar q'$ pairs) in all
possible ways.
At high energies, where $\alpha_s$ is small, we can use perturbative
techniques to predict the different subprocesses:
$e^+e^-\to q\bar q,q\bar q G, q\bar q GG, \ldots$ However, we still do not
have a good understanding of the way quarks and gluons hadronize.
Qualitatively, quarks and gluons are created by the
$q$-$\bar q$ current at very short distances, $x\sim 1/\sqrt{s}$. Afterwards,
they continue radiating additional soft gluons with smaller energies.
At larger
distances, $x\sim 1/\Lambda$, the interaction becomes very strong and the
hadronization process occurs. Since we are lacking a rigorous description of
the confinement mechanism, we are unable to provide precise predictions of the
different exclusive processes, such as $e^+e^-\to 16\pi$. However, we can make
a quite accurate prediction for the total inclusive production of hadrons:
\bel{eq:sigma_total}
\sigma(e^+e^-\to\mbox{\rm hadrons}) = \sigma(e^+e^-\to
q\bar q + q\bar q G + q\bar q GG + \ldots) \, .
\end{equation}
The details of the final hadronization are irrelevant for the inclusive sum,
because the probability to hadronize is just one owing to our confinement
assumption.
\begin{figure}[bh]
\centerline{\hbox{\Large $\sigma\quad\;\sim\quad\; $}
\hbox{\epsfxsize=12.5cm \epsfbox[95 400 524 491]{PiBlob.ps}}}
\vspace{2.5cm}
\caption{Diagrammatic relation between the total hadronic-production
cross-section
and the two-point function $\Pi^{\mu\nu}(q)$.
The $q\bar q$ blob contains all possible QCD corrections. The dashed vertical
line
indicates that the blob is cut in all possible ways, so that the left and
right sides correspond to the production amplitude $T$ and its
complex-conjugate
$T^\dagger$, respectively, for a given intermediate state.}
\label{fig:PiBlob}
\end{figure}
Well below the $Z$ peak, the hadronic production is dominated by the
$\gamma$-exchange contribution.
Thus, we can compute the cross-sections of all subprocesses
$e^+e^-\to\gamma^*\to q\bar q, q\bar q G,\ldots $
(at a given order in $\alpha_s$), and make the sum. Technically,
it is much easier
to compute the QCD T-product of two electromagnetic currents
[$J^\mu_{\!\!\mbox{\rm\scriptsize em}} = \sum_f Q_f q_f\gamma^\mu q_f$]:
\bel{eq:Pi_def}
\Pi^{\mu\nu}(q)\equiv i \int d^4x \; \mbox{\rm e}^{iqx}\;
\langle 0| T\left( J^\mu_{\!\!\mbox{\rm\scriptsize em}}(x)
J^\nu_{\!\!\mbox{\rm\scriptsize em}}(0)^\dagger\right)|0\rangle
= \left(-g^{\mu\nu}q^2 + q^\mu q^\nu\right) \Pi_{\!\!\mbox{\rm\scriptsize em}}(q^2) \, .
\end{equation}
As shown in Fig.~\ref{fig:PiBlob}, the absorptive part of this object
(i.e. the imaginary part, which results from cutting --putting {\it on shell}--
the propagators of the intermediate exchanged quarks and gluons in all
possible ways) just corresponds to the sum of the squared moduli of the
different production amplitudes. The exact relation with the total
cross-section is:
\bel{eq:R_ee_QCD}
R_{e^+e^-} \equiv
{\sigma(e^+e^-\to \mbox{\rm hadrons})\over\sigma(e^+e^-\to\mu^+\mu^-)}
= 12 \pi \,\mbox{\rm Im}\Pi_{\!\!\mbox{\rm\scriptsize em}}(s)
\, .
\end{equation}
Neglecting the small (away from thresholds)
corrections generated by the non-zero quark masses, the ratio
$R_{e^+e^-}$ is given by a perturbative series in powers of $\alpha_s(s)$:
\begin{eqnarray}\label{eq:R_series}
R_{e^+e^-} &\!\!\! =\!\!\! & \left(\sum_{f=1}^{N_f} Q_f^2\right)
\, N_C \, \left\{ 1 +
\sum_{n\geq 1} F_n \left({\alpha_s(s)\over\pi}\right)^{\! n} \right\} \nonumber\\
&\!\!\! =\!\!\! & \left(\sum_{f=1}^{N_f} Q_f^2\right)
\, N_C \, \Biggl\{ 1 +
F_1 {\alpha_s(\mu^2)\over\pi} +
\left[ F_2 + F_1 {\beta_1\over 2} \ln\left({s\over\mu^2}\right)\right]
\left({\alpha_s(\mu^2)\over\pi}\right)^{\! 2}
\Biggr. \\
&\!\!\! +\!\!\! & \Biggl.
\left[ F_3 + F_2 \beta_1 \ln\left({s\over\mu^2}\right) + F_1
\left( {\beta_2\over 2} \ln\left({s\over\mu^2}\right)
+ {\beta_1^2\over 4} \ln^2\left({s\over\mu^2}\right)\right)\right]
\left({\alpha_s(\mu^2)\over\pi}\right)^{\! 3} +
{\cal O}(\alpha_s^4) \Biggr\} .\nonumber
\end{eqnarray}
The second expression, shows explicitly how the running coupling
$\alpha_s(s)$ sums an infinite number of
higher-order logarithmic terms.
So far, the calculation has been performed to order $\alpha_s^3$, with
the result (in the $\overline{\rm MS}$ scheme) \cite{CKT:79,GKL:91}:
\begin{eqnarray}\label{eq:F_results}
F_1 &\!\! = &\!\! 1 \, , \nonumber\\
F_2 &\!\! = &\!\! 1.986 - 0.115 N_f \, , \\
F_3 &\!\! = &\!\! -6.637 - 1.200 N_f - 0.005 N_f^2 - 1.240
{\left(\sum_f Q_f \right)^2\over 3 \sum_f Q_f^2 } \, . \nonumber
\end{eqnarray}
Note the different charge-dependence on the last term, which is due to the
contribution from three intermediate gluons (with a separate quark trace
attached to each electromagnetic current in Fig.~\ref{fig:PiBlob}).
For 5 flavours, one has:
\bel{eq:R_five}
R_{e^+e^-}(s) \, = \, {11\over 3} \left\{ 1 + {\alpha_s(s)\over\pi} +
1.411 \left({\alpha_s(s)\over\pi}\right)^2
-12.80 \left({\alpha_s(s)\over\pi}\right)^3 + {\cal O}(\alpha_s^4) \right\} \, .
\end{equation}
The perturbative uncertainty of this prediction is of order
$\alpha_s^4$, since the coefficient $F_4$ is unknown. This uncertainty also
includes the ambiguities related to the choice of renormalization scale and
scheme. Although, the total sum of the perturbative series is of course
independent of our renormalization conventions, different choices of scale
and/or scheme lead to slightly different numerical predictions for the
truncated series. For instance,
the perturbative series truncated at a finite order $N$,
$R_{e^+e^-}^{(N)}(s)\equiv\left(\sum_f Q_f^2 \right)\, N_C \, \left\{ 1 +
\sum_{n= 1}^N F_n \left({\alpha_s(s)\over\pi}\right)^n \right\}$,
has an explicit scale dependence of order $\alpha_s^{N+1}$:
\bel{eq:R_mu_dep}
{dR_{e^+e^-}^{(N)}\over d\mu^2}\sim\left({\alpha_s(\mu^2)\over\pi}\right)^{N+1}
{}.
\end{equation}
The numerical values of $\alpha_s$ and the $F_n$ ($n\geq 2$) coefficients
depend on our choice of scheme
(also $\beta_n$ for $n\geq 3$).
For instance, at second order\footnote{\small
Actually, at second order a scheme is completely specified by a single
parameter. Thus, scale and scheme dependence is just the same at this order.
The relations in Eqs.~\protect\eqn{eq:scheme_dep_a} and
\protect\eqn{eq:scheme_dep_F} are equivalent to a change of scale:
$\mu^2_{\!\!\mbox{\rm\scriptsize MS}} = (4\pi/{\rm e}^{\gamma_E})\,
\mu^2_{\overline{\!\!\mbox{\rm\scriptsize MS}}}$.},
the relation
between the MS and $\overline{\mbox{\rm MS}}$ schemes is:
\begin{eqnarray}\label{eq:scheme_dep_a}
\alpha_s^{\!\!\mbox{\rm\scriptsize MS}} &\!\!\! = &\!\!\!
\alpha_s^{\overline{\!\!\mbox{\rm\scriptsize MS}}} \left\{
1 + {\beta_1\over 2} \left[\ln{(4\pi)}-\gamma_E\right]
{\alpha_s^{\overline{\!\!\mbox{\rm\scriptsize MS}}} \over\pi} + \cdots \right\} \, ,
\\ \label{eq:scheme_dep_F}
F_2^{\!\!\mbox{\rm\scriptsize MS}} &\!\!\! = &\!\!\!
F_2^{\overline{\!\!\mbox{\rm\scriptsize MS}}} -
F_1 {\beta_1\over 2} \left[\ln{(4\pi)}-\gamma_E\right]
= 7.359 - 0.441 N_f \, .
\end{eqnarray}
The difference between both schemes is obviously a higher-order effect.
With $N_f=5$, the MS scheme leads to a second-order coefficient
$F_2^{\!\!\mbox{\rm\scriptsize MS}} = 5.156$, which is a factor 3.6 bigger than
$F_2^{\overline{\!\!\mbox{\rm\scriptsize MS}}}$. Thus, the perturbative series
looks more convergent with the $\overline{\mbox{\rm MS}}$ choice.
The theoretical prediction for $R_{e^+e^-}(s)$ above the $b$-$\bar b$
threshold is compared \cite{PDG:94}
in Fig.~\ref{fig:Ree} with the measured data,
taking into account mass-corrections and electroweak ($Z$-exchange)
contributions. The two curves correspond to
$\Lambda^{(N_f=5)}_{\overline{\!\!\mbox{\rm\scriptsize MS}}} = 60$ MeV (lower curve)
and 250 MeV (upper curve). The rising at large energies is due to the
tail of the $Z$ peak.
A global fit to all data between 20 and 65 GeV yields \cite{HA:93}
\bel{eq:alpha_ee}
\alpha_s(34\:\mbox{\rm GeV}) \, = \, 0.146\pm0.030\, .
\end{equation}
The hadronic width of the $Z$ boson can be analyzed in the same way:
\bel{eq:Z_hadrons}
R_Z\equiv{\Gamma(Z\to\mbox{\rm hadrons})\over \Gamma(Z\to e^+e^-)} =
R_Z^{\!\!\mbox{\rm\scriptsize EW}} N_C \left\{ 1 +
\sum_{n\geq 1} \tilde{F}_n \left({\alpha_s(M_Z^2)\over\pi}\right)^n
+ {\cal O}\left({m_f^2\over M_Z^2}\right) \right\} \, .
\end{equation}
The global factor
\bel{eq:R_Z_ew}
R_Z^{\!\!\mbox{\rm\scriptsize EW}}\, =\, {\sum_f (v_f^2 + a_f^2)\over v_e^2 + a_e^2}\;
(1 + \delta_{\!\!\mbox{\rm\scriptsize EW}} )
\end{equation}
contains the underlying electroweak $Z\to \sum_f q_f \bar q_f$ decay amplitude.
Since both vector and axial-vector couplings are present, the QCD-correction
coefficients $\tilde{F}_n$ are slightly different from $F_n$ for $n\geq 2$.
For instance, the $Z$ axial coupling generates the two-loop contribution
$Z\to t\bar t\to GG \to q\bar q$ (through triangular quark diagrams),
which is absent in the vector case; this leads to an additional
${\cal O}\left(\alpha_s^2 m_t^2/M_Z^2\right)$ correction.
In order to determine $\alpha_s$ from $R_Z$, one needs to perform a global
analysis of the LEP/SLC data, taking properly into account
the higher-order electroweak corrections \cite{BA:95,PI:94b}.
The latest $\alpha_s$ value reported by the LEP Electroweak Working Group
\cite{LEPEWG:94} is
\bel{eq:alpha_Z_fit}
\alpha_s(M_Z^2) \, = \, 0.125 \pm 0.005 \pm 0.002 \, .
\end{equation}
\subsection{\protect\boldmath $\tau$\protect\unboldmath\mbox{}$^-$
\protect\boldmath $\to\nu$\protect\unboldmath\mbox{}$_\tau$
\protect\unboldmath + hadrons}
\label{subsec:TauHadrons}
The calculation of QCD corrections to the inclusive decay of the $\tau$
lepton \cite{BR:88,NP:88,BNP:92,LDP:92a,PI:94}
looks quite similar from a diagrammatic point of view. One just puts
all possible gluon (and $q\bar q$) corrections to the basic decay diagram
in Fig.~\ref{fig:tau}, and computes the sum
\bel{eq:Tau_sum}
\Gamma(\tau^-\to\nu_\tau + \mbox{\rm hadrons}) =
\Gamma(\tau^-\to\nu_\tau + q\bar q) + \Gamma(\tau^-\to\nu_\tau + q\bar q G)
+ \Gamma(\tau^-\to\nu_\tau + q\bar q GG) + \cdots
\end{equation}
As in the $e^+e^-$ case, the calculation is more efficiently performed through
the two-point-function
\bel{eq:PiTau}
\Pi_L^{\mu\nu}(q)\equiv i \int d^4x \, \mbox{\rm e}^{iqx}\;
\langle 0| T\left( L^\mu(x) L^\nu(0)^\dagger\right)|0\rangle
= \left(-g^{\mu\nu}q^2 + q^\mu q^\nu\right) \Pi_L^{(1)}(q^2)
+ q^\mu q^\nu \,\Pi_L^{(0)}(q^2)\, ,\;
\end{equation}
which involves the T-ordered product of two left-handed currents,
$L^\mu = \bar u \gamma^\mu (1-\gamma^5) d_\theta$.
This object can be easily visualized through a diagram analogous to
Fig.~\ref{fig:PiBlob}, where the photon is replaced by a $W^-$ line and
one has a $\tau\nu_\tau$ pair in the external fermionic lines instead of
the $e^+e^-$ pair. The precise relation with the ratio $R_\tau$ is:
\begin{eqnarray}\label{eq:R_tau_int}
R_\tau &\!\!\! \equiv &\!\!\!
{\Gamma(\tau^-\to\nu_\tau + \mbox{\rm hadrons})\over
\Gamma(\tau^-\to\nu_\tau e^-\bar\nu_e)} \nonumber\\
&\!\!\! = &\!\!\!
12 \pi \int^{m_\tau^2}_0 {ds \over m_\tau^2 } \,
\left(1-{s \over m_\tau^2}\right)^2
\left\{ \left(1 + 2 {s \over m_\tau^2}\right)
\mbox{\rm Im} \Pi^{(1)}_L(s)
+ \mbox{\rm Im} \Pi^{(0)}_L(s) \right\} \, . \quad
\end{eqnarray}
The three-body character of the basic decay mechanism,
$\tau^-\to\nu_\tau u d_\theta$, shows here a crucial difference with
$e^+e^-$ annihilation. One needs to integrate over all possible neutrino
energies or, equivalently, over all possible values of the total hadronic
invariant-mass $s$. The spectral functions
$\mbox{\rm Im} \Pi^{(0,1)}_L(s)$ contain the dynamical information on the
invariant-mass distribution of the final hadrons.
The lower integration limit corresponds to the threshold for hadronic
production, i.e. $m_\pi$ (equal to zero for massless quarks). Clearly, this
lies deep into the non-perturbative region where confinement is crucial.
Thus, it is very difficult to make a reliable prediction for
the integrand in \eqn{eq:R_tau_int}.
\begin{figure}[bht]
\centerline{\epsfysize =7cm \epsfbox{contour.ps}}
\vspace{-0.5cm}
\caption{Integration contour in the complex $s$-plane used to obtain
Eq.~\protect\eqn{eq:circle}.}
\label{fig:circle}
\end{figure}
Fortunately, we have precious exact (i.e. non-perturbative) information on
the dynamical functions $\Pi^{(0,1)}_L(s)$, which allows us to accurately
predict the total integral \eqn{eq:R_tau_int}:
$\Pi^{(0,1)}_L(s)$ are analytic functions in the complex $s$-plane except for a
cut in the positive real axis. The physics we are interested in lies of course
in the singular region, where hadrons are produced.
We need to know the integral along the physical cut of
$\,\mbox{\rm Im} \Pi^{(0,1)}_L(s) = -{i\over 2}
[\Pi^{(0,1)}_L(s+i\epsilon)-\Pi^{(0,1)}_L(s-i\epsilon)]$.
However, we can use Cauchy's theorem (close integrals of analytic functions are
zero if there are no singularities within the integration contour), to express
$R_\tau$ as a contour integral
in the complex $s$-plane running
counter-clockwise around the circle $|s|=m_\tau^2$
\cite{BR:88,NP:88,BNP:92}:
\bel{eq:circle}
R_\tau =
6 \pi i \oint_{|s|=m_\tau^2} {ds \over m_\tau^2} \,
\left(1 - {s \over m_\tau^2}\right)^2
\left\{ \left(1 + 2 {s \over m_\tau^2}\right) \Pi^{(0+1)}_L(s)
- 2 {s \over m_\tau^2} \Pi^{(0)}_L(s) \right\} .
\end{equation}
The advantage of this expression
is that it requires dynamical information only for
complex $s$ of order $m_\tau^2$, which is significantly larger than the scale
associated with non-perturbative effects in QCD. A perturbative
calculation of $R_\tau$ is then possible.
Using the so-called {\it Operator Product Expansion} techniques
it is possible to show
\cite{NP:88,BNP:92,PI:94}
that non-perturbative contributions are
very suppressed [$\sim (\Lambda/m_\tau)^6$].
Thus, $R_\tau$ is a perfect observable for determining the strong coupling.
In fact, $\tau$ decay is probably the lowest energy process from which the
running coupling constant can be extracted cleanly, without hopeless
complications from non-perturbative effects.
The $\tau$ mass, $m_\tau = 1.7771{\,}^{+0.0004}_{-0.0005}$ GeV \cite{PDG:94},
lies fortuitously
in a {\it compromise} region where the coupling constant
$\alpha_s$ is large enough that $R_\tau$ is very sensitive to its
value, yet still small enough that the perturbative expansion
still converges well.
The explicit calculation gives \cite{BNP:92,PI:94}:
\bel{eq:r_tau_total}
R_{\tau} =
3 \left( |V_{ud}|^2 + |V_{us}|^2 \right)
S_{\!\!\mbox{\rm\scriptsize EW}} \left\{ 1 + \delta_{\!\!\mbox{\rm\scriptsize EW}}' +
\delta^{(0)} + \delta_{\!\!\mbox{\rm\scriptsize NP}}\right\}
\, ,
\end{equation}
where $S_{\!\!\mbox{\rm\scriptsize EW}} = 1.0194$ and
$\delta_{\!\!\mbox{\rm\scriptsize EW}}' = 0.0010$
are the leading and next-to-leading electroweak corrections, and
$\delta^{(0)}$ contains the dominant perturbative-QCD contribution:
\begin{eqnarray}\label{eq:delta_0}
\delta^{(0)} &\!\!\! =&\!\!\! {\alpha_s(m_\tau^2)\over\pi} +
\left[ F_2 - {19\over 24}\beta_1\right]
\left( {\alpha_s(m_\tau^2)\over\pi} \right)^2
\nonumber\\ &\!\!\! &\!\!\! \mbox{} +
\left[ F_3' - {19\over 12} F_2\beta_1 - {19\over 24}\beta_2 +
{265\over 288} \beta_1^2\right]
\left( {\alpha_s(m_\tau^2)\over\pi} \right)^3 + {\cal O}(\alpha_s^4) \\
&\!\!\! = &\!\!\! {\alpha_s(m_\tau^2)\over\pi} +
5.2023 \left( {\alpha_s(m_\tau^2)\over\pi} \right)^2
+ 26.366 \left( {\alpha_s(m_\tau^2)\over\pi} \right)^3
+ {\cal O}(\alpha_s^4) \, .
\end{eqnarray}
The remaining factor $\delta_{\!\!\mbox{\rm\scriptsize NP}}\approx -0.016\pm 0.005$
includes the estimated \cite{BNP:92,PI:94}
small mass-corrections and non-perturbative contributions.
Owing to its high sensitivity to $\alpha_s$ \cite{NP:88,BNP:92}
the ratio $R_\tau$ has been a subject of intensive study in recent years.
Many different sources of possible perturbative and non-perturbative
contributions have been analyzed in detail.
Higher-order logarithmic corrections have been resummed \cite{LDP:92a},
leading to very small renormalization-scheme dependences.
The size of the non-perturbative contributions has been
experimentally analyzed, through a study of the invariant-mass
distribution of the final hadrons \cite{LDP:92b}; the present data
implies \cite{ALEPH:93}
$\delta_{\!\!\mbox{\rm\scriptsize NP}}= (0.3\pm 0.5)\% $ confirming
the predicted \cite{BNP:92} suppression of non-perturbative
corrections.
An exhaustive summary of the $R_\tau$ analysis can be found
in Ref.~ \cite{PI:94}.
Using the Particle Data Group values for the $\tau$ lifetime and
leptonic branching ratios \cite{PDG:94}, the theoretical analysis
of $R_\tau$ results in a fitted value of $\alpha_s$ \cite{PI:94},
\bel{alpha_s_tau}
\alpha_s(m_\tau^2)\, = \, 0.33\pm 0.03 \, ,
\end{equation}
which is significantly larger than \eqn{eq:alpha_Z_fit}.
After evolution up to the scale $M_Z$, the strong coupling constant in
Eq.~\eqn{alpha_s_tau} decreases to
$\alpha_s(M_Z^2) = 0.120^{+0.003}_{-0.004}$, in excellent agreement
with the $Z$-width determination and with a smaller error bar.
This comparison provides a beautiful test of the predicted running of
$\alpha_s$.
\subsection{\protect\boldmath $e^+e$\protect\unboldmath\mbox{}$^-$
\protect\boldmath $\to\; $
\protect\unboldmath jets}
\label{subsec:jets}
\begin{figure}[htb]
\centerline{\epsfxsize = 14.5cm \epsfbox{eeqqG.ps}}
\caption{Gluon bremsstrahlung corrections to $e^+e^-\to q\bar q$.}
\label{fig:ee3J}
\end{figure}
At lowest-order in the strong coupling, the hadronic production in
$e^+e^-$ collisions proceeds through $e^+e^-\to q\bar q$. Thus,
at high-energies, the final hadronic states are predicted to
have mainly a two-jet structure, which agrees with the
empirical observations.
At ${\cal O}(\alpha_s)$, the emission of a hard gluon from a quark leg
generates the $e^+e^-\to q\bar q G$ transition, leading to
3-jet configurations. For massless quarks, the differential
distribution of the 3-body final state is given by:
\bel{eq:3J_dis}
{1\over\sigma_0}\, {d^2\sigma\over dx_1 dx_2} \, = \,
{2\alpha_s\over 3\pi}\, {x_1^2 + x_2^2 \over (1-x_1) (1-x_2)} \ ,
\end{equation}
where
\bel{eq:sigma0}
\sigma_0 \,\equiv\, {4\pi\alpha^2\over 3 s} \, N_C \,
\sum_{f=1}^{N_f} Q_f^2
\end{equation}
is the lowest-order $e^+e^-\to\gamma^*\to q\bar q$ cross-section.
The kinematics is defined through the invariants
$s\equiv q^2$ and
$s_{ij}\equiv (p_i + p_j)^2 = (q-p_k)^2 \equiv s (1-x_k)$
($i,j,k = 1,2,3$), where $p_1$, $p_2$ and $p_3$ are the quark,
antiquark and gluon momenta, respectively,
and $q$ is the total $e^+e^-$ momentum.
For given $s$, there are only
two independent kinematical variables since
\bel{eq:x_rel}
x_1 + x_2 + x_3 = 2 \, .
\end{equation}
In the centre-of-mass system [$q^\mu = (\sqrt{s}, \vec{0}\, )$],
$x_i = E_i/E_e = 2 E_i/\sqrt{s}$.
Eq.~\eqn{eq:3J_dis} diverges as $x_1$ or $x_2$ tend to 1.
This is a very different infinity from the ultraviolet ones
encountered before in the loop integrals.
In the present case, the tree amplitude itself is becoming singular in
the phase-space boundary. The problem originates in the infrared
behaviour of the intermediate quark propagators:
\bel{eq:infrared}
\begin{array}{c}
x_1\to 1 \qquad\Longleftrightarrow\qquad
(p_2+p_3)^2 = 2 \,(p_2\cdot p_3) \to 0 \ ;
\\
x_2\to 1 \qquad\Longleftrightarrow\qquad
(p_1+p_3)^2 = 2\, (p_1\cdot p_3) \to 0 \ .
\end{array}\end{equation}
There are two distinct kinematical configurations leading to
{\it infrared divergences}:
\begin{enumerate}
\item {\bf Collinear gluon}: The 4-momentum of the gluon is
parallel to that of either the quark or the antiquark.
This is also called a {\it mass singularity}, since the
divergence would be absent if either the gluon or the
quark had a mass
($p_3\| p_2$ implies $s_{23}=0$ if $p_2^2=p_3^3=0$).
\item {\bf Soft gluon}: $p_3\to 0$.
\end{enumerate}
In either case, the observed final hadrons
will be detected as a 2-jet configuration, because the $qG$ or
$\bar qG$ system cannot be resolved.
Owing to the finite resolution of any detector,
it is not possible (not even in principle) to separate those
2-jet events generated by the basic $e^+e^-\to q\bar q$ process,
from $e^+e^-\to q\bar q G$ events with a collinear or soft gluon.
In order to resolve a 3-jet event, the gluon should have an energy
and opening angle (with respect to the quark or antiquark)
bigger than the detector resolution.
The observable 3-jet cross-section will never include the
problematic region $x_{1,2}\to 1$; thus, it will be finite,
although its value will depend on the detector resolution and/or
the precise definition of {\it jet}
(i.e. $\sigma$ depends on the chosen integration
limits).
On the other side, the 2-jet configurations will include both
$e^+e^-\to q\bar q\; $ and $e^+e^-\to q\bar q G$ with an unobserved
gluon. The important question is then the infrared behaviour of the
sum of both amplitudes.
The exchange of virtual gluons among the quarks
generate an ${\cal O}(\alpha_s)$ correction to the $e^+e^-\to q\bar q$
amplitude:
\bel{eq:T_eeqq}
T[e^+e^-\to q\bar q] = T_0 + T_1 + \cdots
\end{equation}
where $T_0$ is the lowest-order (tree-level) contribution,
$T_1$ the ${\cal O}(\alpha_s)$ correction, and so on.
The interference of $T_0$ and $T_1$ gives rise to an
${\cal O}(\alpha_s)$ contribution to the $e^+e^-\to q\bar q$
cross-section.
\begin{figure}[htb]
\centerline{\epsfxsize = 14.5cm \epsfbox{eeqq_g.ps}}
\caption{1-loop gluonic corrections to $e^+e^-\to q\bar q$.}
\label{fig:eeqq(g)}
\end{figure}
We know already that loop diagrams have ultraviolet divergences
which must be renormalized. In addition, they also have infrared
divergences associated with collinear and soft configurations
of the virtual gluon.
One can explicitly check that the ${\cal O}(\alpha_s)$ infrared divergence
of $\sigma(e^+e^-\to q\bar q)$ exactly cancels the one in
$\sigma(e^+e^-\to q\bar q G)$, so that the sum is well-defined:
\bel{eq:infrared_sum}
\sigma(e^+e^-\to q\bar q) + \sigma(e^+e^-\to q\bar q G) + \cdots
= \sigma_0\,\left( 1 + {\alpha_s\over\pi} + \cdots\right) \ .
\end{equation}
This is precisely the inclusive result discussed
in Sect.~\ref{subsec:Rhadrons}.
This remarkable cancellation of infrared divergences is
actually a general result (Bloch-Nordsieck \cite{BN:37}
and Kinoshita--Lee--Nauenberg \cite{KLN:62} theorems):
for inclusive enough cross-sections both the
soft and collinear infrared divergences cancel.
\begin{figure}[tbh]
\centerline{\epsfysize = 4.5cm \epsfbox{jetdef.ps}}
\caption{2-jet configuration.}
\label{fig:jetdef}
\end{figure}
While the total hadronic cross-section is unambiguously defined,
we need a precise definition of jet in order to classify a given
event as a 2-, 3-, \ldots, or n-jet configuration.
Such a definition should be free of infrared singularities, and
insensitive to the details of the non-perturbative fragmentation
into hadrons.
A popular example of jet definition is the so-called
JADE algorithm \cite{JADE:86}, which makes use of an invariant-mass cut $y$:
\bel{eq:jade}
\mbox{\rm 3 jet} \qquad\Longleftrightarrow\qquad
s_{ij} \equiv (p_i + p_j)^2 > y s \qquad (\forall i,j=1,2,3) \ .
\end{equation}
Clearly, both the theoretical predictions and the experimental
measurements depend on the adopted jet definition.
With the JADE algorithm, the fraction of 3-jet events
is predicted to be:
\begin{equation}\label{eq:R3}
R_3 = {2\alpha_s\over 3\pi} \,\biggl\{
(3-6y) \ln{\!\left({y\over 1-2y}\right)}
+ 2 \ln^2{\!\left({y\over 1-y}\right)} + {5\over 2}
-6y -\frac{9}{2} y^2
+ 4 \mbox{\rm Li}_2\!\left({y\over 1-y}\right) -{\pi^2\over 3}
\biggr\} ,
\end{equation}
where
\bel{eq:Li}
\mbox{\rm Li}_2(z)\,\equiv\, -\int_0^z\,{d\xi\over 1-\xi}\,
\ln{\xi} \ .
\end{equation}
The corresponding fraction of 2-jet events is given by
$R_2 = 1 - R_3$.
The fraction of 2- or 3-jet events obviously depends on the
chosen cut $y$.
The infrared singularities are manifest in the divergent behaviour
of $R_3$ for $y\to 0$.
At higher-orders in $\alpha_s$ one needs to define the
different multi-jet fractions. For instance, one can
easily generalize the JADE algorithm an classify a
$\{p_1,p_2,\ldots,p_n\}$ event as a n-jet configuration
provided that $s_{ij}>y s$ for all $i,j=1,\ldots,n$.
If a pair of momenta does not satisfy this constraint, they are
combined into a single momentum and the event is considered
as a $(n-1)$ jet configuration (if
the constraint is satisfied by all other combinations
of momenta).
The general expression for the fraction of n-jet events takes the
form:
\bel{eq:R_n_frac}
R_n(s,y) \, = \, \left({\alpha_s(s)\over\pi}\right)^{n-2}
\sum_{j=0} C_j^{(n)}(y)\,\left({\alpha_s(s)\over\pi}\right)^j \ ,
\end{equation}
with $\sum_n R_n = 1$.
A few remarks are in order here:
\begin{itemize}
\item The jet fractions have a
high sensitivity to $\alpha_s$ [$R_n\sim \alpha_s^{n-2}$].
Although the sensitivity
increases with $n$, the number of events decreases
with the jet multiplicity.
\item Higher-order $\alpha_s(\mu^2)^j\ln^k(s/\mu^2)$ terms have
been summed into $\alpha_s(s)$. However, the coefficients
$C_j^{(n)}(y)$ still contain $\ln^k(y)$ terms.
At low values of $y$, the infrared divergence ($y\to 0$) reappears
and the perturbative series becomes unreliable.
For large $y$, the jet fractions $R_n$ with $n\geq 3$ are small.
\item Experiments measure hadrons rather than partons. Therefore,
since these observables are not fully inclusive, there is an
unavoidable dependence on the non-perturbative fragmentation into
hadrons. This is usually modelled through Monte Carlo analyses,
and introduces theoretical uncertainties which need to be estimated.
\end{itemize}
Many different jet algorithms and jet variables
(jet rates, event shapes, energy correlations, \ldots) have
been introduced to optimize the perturbative analysis.
In some cases, a resummation of
$\alpha_s(s)^n\ln^m\! (y)$ contributions with $m>n$ has been performed
to improve the predictions at low $y$ values \cite{CA:91}.
\begin{figure}[bth]
\centerline{\epsfysize=8.5cm \epsfbox{R3E.ps}}
\vspace{-0.5cm}
\caption{Energy dependence of 3-jet event production rates
$R_3(y=0.8)$, compared with predictions of analytic ${\cal O}(\alpha_s^2)$
QCD calculations, with the hypothesis of an energy independent $\alpha_s$
and with the abelian vector theory in ${\cal O}(\alpha_A^2)$
(taken from Ref.~\protect\cite{BE:93}).}
\label{fig:r3_e}
\end{figure}
Fig.~\ref{fig:r3_e} \cite{BE:93} shows the energy dependence of the
measured 3-jet
production fraction $R_3$ ($y=0.08$), compared with QCD
predictions. The data is in good agreement with QCD and
fits very well the predicted energy-dependence of the
running coupling. A constant value of $\alpha_s$ cannot
describe the observed production rates. The figure
shows also the predictions obtained with an abelian vector
theory at ${\cal O}(\alpha_A^2)$, which are clearly excluded.
Several measurements of $\alpha_s$, using different jet variables, have
been performed.
All measurements are in good agreement, providing a
good consistency test of the QCD predictions.
Combining the results from all experiments at LEP and SLC, one gets
the average value \cite{BE:94}:
\bel{eq:alpha_s_shapes}
\alpha_s(M_Z^2)\, = \,\left\{
\begin{array}{cc} 0.119\pm 0.006 \qquad & \left({\cal O}(\alpha_s)^2\right) \\
0.123\pm 0.006 \qquad & \left(\mbox{\rm resummed calculations}\right)
\end{array}\right. \, .
\end{equation}
The two numbers correspond to different theoretical approximations
used in the fits to extract $\alpha_s$.
3-jet events can also be used to test the gluon spin.
For a spin-0 gluon, the differential distribution is still
given by Eq.~\eqn{eq:3J_dis}, but changing the $x_1^2+x_2^2$ factor
in the numerator to $x_3^2/4$.
In general, one cannot readily be sure which hadronic jet emerges
via fragmentation from a quark (or antiquark), and which from a gluon.
Therefore, one adopts instead a jet ordering,
$x_1>x_2>x_3$, where $x_1$ refers to the most energetic jet, 2 to the next
and 3 to the least energetic one, which most likely would correspond to
the gluon.
When $x_2\to 1$ ($x_1\to 1$) the vector-gluon distribution is singular,
but the corresponding scalar-gluon distribution is not
because at that point
$x_3 = (1-x_1) + (1-x_2) \to 0$.
The measured distribution agrees very well with the QCD predictions with
a spin-1 gluon;
a scalar gluon is clearly excluded.
\begin{figure}[bth]
\vfill\centerline{
\begin{minipage}[b]{.47\linewidth}
\centerline{\mbox{\epsfxsize=7.5cm\epsffile{opalCACF.ps}}}
\vspace{-0.2cm}
\caption{68\% and 95\% CL contours in the
$T_F/C_F$ versus $C_A/C_F$ plane, from OPAL data \protect\cite{OPAL:94}.
Expectations from various gauge models are also shown.}
\label{fig:colour_factors}
\end{minipage}
\hspace{0.7cm}
\begin{minipage}[b]{.47\linewidth}
\centerline{\mbox{\epsfysize=9.5cm\epsffile{colfac.ps}}}
\vspace{-0.5cm}
\caption{Summary of colour-factor measurements \protect\cite{WE:94}.
The results refer to 5 active flavours with
$T_R\equiv N_f T_F =5 T_F$.}
\label{fig:colour_factors_comb}
\end{minipage}
}\vfill
\end{figure}
The predictions for jet distributions and event shapes are
functions of the colour-group factors $T_F=1/2$,
$C_F = (N_C^2-1)/(2 N_C)$ and $C_A=N_C$. These quantities,
defined in Eq.~\eqn{eq:invariants}, result from the
colour algebra associated with the different interaction vertices,
and characterize the colour-symmetry group.
If the strong interactions were based on a different gauge group,
the resulting predictions would differ in the values of these
three factors.
Since the vertices contribute in a different way to
different observables, these colour factors can be measured by
performing a combined fit to the data.
Fig.~\ref{fig:colour_factors} compares a recent OPAL
determination \cite{OPAL:94} of $C_A/C_F$ and $T_F/C_F$ with the values
of these two ratios for different colour groups.
The data is in excellent agreement with the $SU(3)$ values,
and rules out the Abelian model and many classical
Lie groups. Notice that
those groups shown by the open squares and circles are already excluded
because they do not contain three colour degrees of freedom for quarks.
Similar results have been presented by the other LEP
experiments (the hadronic production of jets at $p\bar p$ colliders
has also been analyzed in a similar way).
A summary of the colour-factor ratios obtained by the different
experiments is given in Fig.~\ref{fig:colour_factors_comb}.
\setcounter{equation}{0}
\section{DEEP INELASTIC SCATTERING}
\label{sec:dis}
We saw in Section~\ref{subsec:AF} how the deep inelastic scattering (DIS)
$e^- p \to e^- X$ can be used to learn about the proton structure.
Since this involves a bound hadronic state --the proton--, non-perturbative
phenomena such as confinement plays here a crucial role.
At the same time, the data obeys Bjorken scaling
which manifests the asymptotic freedom
property of the strong interactions. Thus, DIS appears to be an
interesting place where to investigate both perturbative and
non-perturbative aspects of QCD.
DIS can be visualized as a two-step process. First, the hard intermediate
photon, which is far off its mass-shell, scatters off a quark or
gluon with a large momentum transfer; this scattering can be
adequately described by perturbation theory.
Second, the outgoing partons recombine into hadrons
in a time of ${\cal O}(1/\Lambda)$.
Although this recombination is not calculable in perturbation theory,
the details of the non-perturbative hadronization can be
avoided, by considering fully inclusive rates, so that perturbative
QCD can be applied.
However, the hadronic bound-structure of the initial proton state,
still introduces a non-perturbative ingredient: the proton structure
functions.
\subsection{Free parton model}
Let us ignore any QCD interactions and let us assume that the nucleon
(either proton or neutron) constituents are free spin-$\frac{1}{2}$
partons. Within the quark model, the nucleons have three point-like
constituents ($p = u_v u_v d_v$, $n = u_v d_v d_v$), which we will call
{\it valence} quarks.
Gluons are of course there; however, they do not interact directly with
the photon probe. The photon--gluon interaction only occurs through
the virtual $q$-$\bar q$ pairs coupled to the gluon constituents.
Thus, instead of gluons, the photon feels a {\it sea} of
$q$-$\bar q$ partons within the nucleon.
Let us denote $u(x)$, $\bar u(x)$, $d(x)$, $\bar d(x)$,
$s(x)$, $\bar s(x)$, $\ldots\, $ the probability distributions for
$u$, $\bar u$, $d$, $\bar d$, $s$, $\bar s$, $\ldots\, $
quarks with momentum fraction $x$ in the proton.
We have seen in Section~\ref{subsec:AF} that, within the parton model,
the proton structure functions have a simple form
in terms of parton distributions:
\bel{eq:F2_ep}
F_2^{ep}(x)/x = 2 F_1^{ep}(x) =
\frac{4}{9}\, [u(x) + \bar u(x)] + \frac{1}{9}\, [d(x) + \bar d(x)]
+ \frac{1}{9}\, [s(x) + \bar s(x)] + \cdots
\end{equation}
The same parton distributions occur in other DIS processes such as
$\nu p\to l^- X$ or $\bar\nu p\to l^+ X$. However, since the
quark couplings of the intermediate
bosonic probe (a $W^\pm$ in that case) are not the same,
different combinations of these functions are measured:
\begin{eqnarray}\label{eq:F_nup}
F_2^{\nu p}(x)/x = 2 F_1^{\nu p}(x) &\!\!\! =&\!\!\!
2 \, [d(x) + s(x) + \bar u(x) + \bar c(x) + \cdots ] \ ,
\nonumber\\
F_3^{\nu p}(x) &\!\!\! =&\!\!\!
2\, [d(x) + s(x) - \bar u(x) - \bar c(x) + \cdots ]\ ,
\nonumber\\ &&\\
F_2^{\bar\nu p}(x)/x = 2 F_1^{\bar\nu p}(x) &\!\!\! =&\!\!\!
2 \, [u(x) + c(x) + \bar d(x) + \bar s(x) + \cdots ] \ ,
\nonumber\\
F_3^{\bar\nu p}(x) &\!\!\! =&\!\!\!
2 \, [u(x) + c(x) - \bar d(x) - \bar s(x) + \cdots ]\ . \nonumber
\end{eqnarray}
Using isospin symmetry, we can further relate the up- and down-quark
distributions in a neutron to the ones in a proton:
\bel{eq:n_dis}
u^n(x) = d^p(x) \equiv d(x) \; ;\qquad d^n(x) = u^p(x) \equiv u(x) \; ;
\end{equation}
the remaining parton distributions being obviously the same.
Thus, combining data from different DIS processes, it is possible
to obtain separate information on the individual parton distribution
functions.
The quark distributions must satisfy some constraints.
Since both the proton and the neutron have zero strangeness,
\bel{eq:s_SR}
\int_0^1 dx \, [s(x) - \bar s(x)] \, = \, 0 \ .
\end{equation}
Similar relations follow for the heavier flavours ($c$, \ldots).
The proton and neutron electric charges imply two additional sum rules,
\bel{eq:Q_SR}
\int_0^1 dx \, [u(x) - \bar u(x)] \, = \, 2 \ , \qquad
\int_0^1 dx \, [d(x) - \bar d(x)] \, = \, 1 \ ,
\end{equation}
which just give the excess of $u$ and $d$ quarks over antiquarks.
The quark-model concept of valence quarks gives further
insight into the nucleon structure. We can decompose the $u$ and $d$
distribution functions into the sum of valence and sea contributions,
and take the remaining parton distributions to be pure sea.
Since gluons are flavour singlet, one expects the sea to be flavour
independent. In this way, the number of independent distributions
is reduced to three:
\begin{eqnarray}\label{eq:V_S}
u(x) &\!\!\! =&\!\!\! u_v(x) + q_s(x) \ ,
\nonumber\\
d(x) &\!\!\! =&\!\!\! d_v(x) + q_s(x) \ ,
\\
\bar u(x) &\!\!\! =&\!\!\! \bar d(x) = s(x) = \bar s(x) = \ldots = q_s(x) \ .
\nonumber
\end{eqnarray}
Within this model, the strangeness sum rule \eqn{eq:s_SR}
is automatically satisfied, while \eqn{eq:Q_SR} imply constraints
on the valence-quark distributions alone.
In the analogous situation of quasi-elastic
electron--deuterium scattering, the
observed structure function shows a narrow peak around $x=\frac{1}{2}$.
This is to be expected, since the deuteron has two nucleon
constituents with $M_N\approx \frac{1}{2} M_d$ which share the total
momentum in equal terms.
A simple three-quark model for the nucleon would suggest the
existence of a similar peak
at $x=\frac{1}{3}$ in the proton and neutron structure functions.
However, the distribution shown in Fig.~\ref{fig:W2x} does not
show such behaviour.
The difference can be easily understood as originating from the
parton-sea contributions.
Taking the difference between the proton and neutron structure
functions, where the contribution from the sea cancels,
the data exhibits indeed a broad peak around
$x=\frac{1}{3}$.
Our isospin symmetric parton model implies the so-called
Gottfried sum rule \cite{GO:67}:
\bel{eq:gottfried}
\int_0^1 {dx\over x} \, \left[ F_2^{ep}(x)
- F_2^{en}(x) \right]\, =\,
\frac{1}{3} \,\int_0^1 dx \, \left[ u_v(x) - d_v(x) \right] \, = \,
\frac{1}{3} \, ,
\end{equation}
which is well satisfied by the data.
Another interesting quantity is the ratio
\bel{eq:F2_ratio}
{F_2^{en}(x) \over F_2^{ep}(x)} \, = \,
{4 d_v(x) + u_v(x) + \Sigma_{\!\!\mbox{\rm\scriptsize sea}} \over
4 u_v(x) + d_v(x) + \Sigma_{\!\!\mbox{\rm\scriptsize sea}}} \ ,
\end{equation}
where $\Sigma_{\!\!\mbox{\rm\scriptsize sea}}$ is the total sea contribution.
Since all probability distributions must be positive-definite,
this ratio should satisfy the bounds
$\frac{1}{4} \leq F_2^{en}(x) / F_2^{ep}(x) \leq 4$,
which are consistent with the data.
The measured ratio appears to tend to 1 at small $x$, indicating
that the sea contributions dominate in that region.
The conservation of the total proton momentum implies an
important sum rule:
\bel{eq:momentum_SR}
\int_0^1 dx\, x\, \left[u(x) + \bar u(x) + d(x) + \bar d(x)
+ s(x) + \bar s(x) + \cdots\right] \, = \, 1-\epsilon \ ,
\end{equation}
where $\epsilon$ is the fraction of momentum that is not carried by quarks.
One finds experimentally that $\epsilon\approx\frac{1}{2}$
(at $Q^2\sim 10$--40 GeV$^2$),
suggesting that about half of the momentum is carried by gluons.
This shows the important role of gluons in the proton structure.
Although the naive quark model works very well in many cases, it is
a too gross simplification as a model of hadrons, at least al large $Q^2$.
\subsection{QCD-improved parton model}
At lowest order the DIS process occurs through the hard scattering
between the virtual photon ($W$, or $Z$) and one constituent parton.
The obvious first QCD corrections will be due to real gluon emission
by either the initial or final quark. To get rid of infrared divergences,
the one-loop virtual gluon contribution should also be taken into account.
\begin{figure}[htb]
\centerline{\epsfysize = 5cm \epsfbox{DISview.ps}}
\caption{Resolution of the photon probe as function of $Q^2$.}
\label{fig:DISview}
\end{figure}
One can easily understand the main qualitative features of
gluon emission, with a few kinematical considerations.
At very low values of momentum transfer, the proton behaves as
a single object, either point-like (at $Q^2\approx 0$), or
with a finite size.
At higher energies, the photon is sensitive to
shorter distances and scatters with the constituent partons.
Increasing further the momentum transfer, the photon probe
has a greater sensitivity to smaller distances, and it is able to
resolve the scattered quark into a quark and a gluon.
Thus, a parton with momentum fraction $x$ can be resolved
into a parton and a gluon of smaller momentum fractions, $x'<x$ and
$x-x'$, respectively.
In a similar way, a gluon with momentum fraction $x$ can be resolved
into a quark and an antiquark.
This simple picture implies that increasing the $Q^2$,
the photon will notice some
qualitative changes in the parton distributions:
\begin{itemize}
\item Gluon bremsstrahlung will shift the valence and sea distributions
to smaller $x$ values.
\item The splitting of a gluon into a quark--antiquark pair will
increase the amount of sea (mostly at small $x$).
\end{itemize}
Thus, without any detailed calculation, one can expect to find
a definite $Q^2$ dependence in the parton distributions; i.e.
violations of Bjorken scaling due to the underlying QCD interactions.
\begin{figure}[htb]
\centerline{\epsfxsize = 14cm \epsfbox{DISge.ps}}
\caption{Leading gluonic correction to the basic DIS parton process.}
\label{fig:DIS_ge}
\end{figure}
Let us consider a quark with momentum fraction $y$. At lowest order,
its contribution to the proton structure function can be written as
\bel{eq:F_q(x)}
2 F_1^{(q)}(x) \, = \, e_q^2\,\int_0^1 dy\, q(y)\,\delta(x-y) \ .
\end{equation}
If the quark emits a gluon before being struck by the photon, its
momentum fraction will be degraded to $yz$ ($0\leq z\leq 1$).
Assuming that the quark remains approximately on-shell,
$(q+yzP)^2\approx m_q^2 \approx 0$, implying that
$yz = Q^2/2(P\cdot q) \equiv x$. Therefore, $F_1^{(q)}(x)$
gets contributions from quarks with initial momentum fractions
$y\geq x$.
The explicit calculation of the diagrams in Fig.~\ref{fig:DIS_ge}
gives the result:
\bel{eq:DF_1_q}
2\Delta F_1^{(q)}(x) \, = \, e_q^2 \, {\alpha_s\over 2\pi}\,
\int_0^1 dy\, q(y)\,\int_0^1\, dz\, \delta(yz-x)\,
\left\{ P^+_{qq}(z) \ln(Q^2/\nu_{\!\!\mbox{\rm\scriptsize IR}}^2) + C(z)\right\} ,
\end{equation}
where
\bel{eq:splitting_f}
P_{qq}(z) \,\equiv\, C_F \, \left( {1+z^2\over 1-z}\right)
\end{equation}
is called the quark {\it splitting function}.
The important feature in Eq.~\eqn{eq:DF_1_q} is the appearance
of a {\it scaling violation} through
the logarithmic $\alpha_s$ correction.
A careful analysis of the different Feynman diagrams shows that
ultraviolet divergences are absent in the total contribution.
Therefore,
this logarithm has a completely different origin than the
ultraviolet ones found in Section~\ref{sec:loops}
The logarithmic behaviour is now generated by infrared singularities
of the type discussed in Section~\ref{subsec:jets}.
More precisely, there is a collinear singularity associated with the
gluon emission process, which has been regulated with the infrared
cut-off $\nu_{\!\!\mbox{\rm\scriptsize IR}}$.
The general theorems on the cancellation of infrared divergences
do not protect the structure function $F_1^{(q)}(x)$, because
this quantity is not {\it inclusive enough}. The divergence
shows up when one tries to resolve the original
quark with momentum fraction $y$ into a quark with momentum fraction
$yz$ and a gluon. $P_{qq}(z)$ is just
the coefficient of the logarithmic divergence associated with
the splitting process $q\to qG$.
Physical observables should not depend on any cut-off,
however, our definition of a parton distribution obviously depends
on the power resolution of our photon probe.
While at low $Q^2$ the photon was testing a single parton with momentum
fraction $y=x$, now it {\it feels} the splitting of a quark with $y>x$
into a quark and a gluon with separate parton distributions.
The divergence should then be reabsorbed into the {\it observable}
parton distribution function:
\bel{eq:pdf}
q(x,Q^2) = q(x,\nu_{\!\!\mbox{\rm\scriptsize IR}}^2) +
{\alpha_s\over 2\pi} \,
\ln(Q^2/\nu_{\!\!\mbox{\rm\scriptsize IR}}^2)
\int_x^1 \, {dy\over y}\, q(y) \,
P^+_{qq}\left({x/ y}\right) \, .
\end{equation}
Both the {\it bare} distribution $q(x,\nu_{\!\!\mbox{\rm\scriptsize IR}}^2)$
and the $\alpha_s$ correction depend on the infrared cut-off, but
this dependence cancels out and does not show up in the {\it physical}
distribution function\footnote{\small
Notice, however, that the precise definition of $q(x,Q^2)$ is
{\it factorization-scheme dependent}, since we could always
include some arbitrary non-logarithmic $\alpha_s$ correction
into $q(x,Q^2)$, by simply shifting the
$C\left({x/ y}\right)$ correction factor in
\protect\eqn{eq:F_1_q_phys}.}
$q(x,Q^2)$. Instead, the parton distribution is now a $Q^2$-dependent
quantity, which fits with our intuitive picture that the photon probe
increases its resolution power with the scale.
In terms of $q(x,Q^2)$, the contribution of the quark $q$ to the
proton structure function is given by:
\bel{eq:F_1_q_phys}
2 F_1^{(q)}(x) \, = \, e_q^2 \,\left\{ q(x,Q^2) +
{\alpha_s\over 2\pi} \int_x^1 \, {dy\over y}\,
q(y)\, C\left(x/y\right)\right\} .
\end{equation}
The individual diagrams in Fig.~\ref{fig:DIS_ge} have also a soft-gluon
singularity, which manifests in the divergent behaviour of $P_{qq}(z)$
at $z=1$. This singularity cancels exactly
in the total sum of the gluon-emission and
virtual-gluon-exchange contributions.
The net result is a slight modification in the definition of
the splitting function:
\bel{eq:spf_qq}
P_{qq}^+(z) \,\delta(yz-x)\,\equiv\, P_{qq}(z)\,
\left[\delta(yz-x) - \delta(y-x)\right] \ .
\end{equation}
Eq.~\eqn{eq:pdf} shows an important thing: although perturbative QCD
is not able to predict the actual value of the distribution function,
it does predict how this distribution evolves in $\ln (Q^2)$. Thus,
given its value at some reference point $Q_0^2$, one can compute the
quark distribution at any other value of $Q^2$ (high-enough for perturbation
theory to be valid).
Including the leading higher-order logarithmic corrections into the
running coupling, the $Q^2$-evolution of the parton distribution is
given by \cite{LI:75,AP:77}:
\bel{eq:dQ2_pdf}
Q^2\, {d\over dQ^2} q(x,Q^2) \, = \,
{\alpha_s(Q^2)\over 2\pi} \int_x^1 {dy\over y}\,
q(y,Q^2)\, P^+_{qq}(x/y) \ .
\end{equation}
Thus, the change in the distribution for a quark with momentum fraction $x$,
which interacts with the virtual photon, is given by the integral over
$y$ of the corresponding distribution for a quark with momentum fraction
$y\geq x$ which, having radiated a gluon, is left with
a fraction $x/y$ of its original momentum.
The splitting function has then a very intuitive physical interpretation:
$(\alpha_s/2\pi) P^+_{qq}(x/y)$ is the probability associated
with the splitting process $q(y)\to q(x) G$.
This probability is high for large momentum fractions; i.e.
high-momentum quarks lose momentum by radiating gluons.
Therefore, increasing $Q^2$, the quark distribution function will
decrease at large $x$ and will increase at small $x$.
\begin{figure}[htb]
\centerline{\epsfxsize =14cm \epsfbox{split.ps}}
\caption{Basic parton-splitting processes.}
\label{fig:splitting}
\end{figure}
The evolution equation \eqn{eq:dQ2_pdf} is only correct for non-singlet
distributions such as $q_i(x)-q_j(x)$, where the (flavour-singlet) gluon
contribution cancels out. In general, one needs also to consider
the effects coming from the splitting of a gluon into a quark and an
antiquark, which interact with the photon probe.
The obvious generalization is \cite{AP:77}:
\bel{eq:evol_q_g}
Q^2 {d\over dQ^2} \left( \begin{array}{c} q(x,Q^2) \\ G(x,Q^2) \end{array} \right) =
{\alpha_s(Q^2)\over 2\pi} \int_x^1 {dy\over y}\,
\left[ \begin{array}{cc} P^+_{qq}(x/y) & P_{qG}(x/y) \\ P_{Gq}(x/y) & P_{GG}(x/y) \end{array}\right]
\left( \begin{array}{c} q(y,Q^2) \\ G(y,Q^2) \end{array} \right) ,
\end{equation}
where $P_{Gq}(z) = P_{qq}(1-z)$ determines the probability that a
quark radiates a gluon with a fraction $z$ of the
original quark momentum,
while
\begin{eqnarray}\label{eq:splitting_qg}
P_{qG}(z) &\!\! = &\!\! T_F \, \left[ z^2 + (1-z)^2\right] \ ,
\\ \label{eq:splitting_gg}
P_{GG}(z) &\!\! = &\!\! 2 C_A \,\left[ {z\over (1-z)_+}
+ {1-z\over z} + z (1-z) \right]
+ {1\over 6} (11 C_A - 4 N_f T_F)\,\delta(1-z) \ , \qquad
\end{eqnarray}
are the gluon splitting functions into $q\bar q$ and $GG$, respectively.
The subindex ``+'' in the $1/(1-z)_+$ factor indicates that the $z=1$
divergence disappears through
\bel{eq:ir_plus}
\int_0^1 dz\, f(z)\, [g(z)]_+ \,\equiv\,
\int_0^1 dz\, [f(z)-f(1)]\, g(z) \ .
\end{equation}
\subsection{Moments of the structure functions}
\label{subsec:moments}
The previous discussion has been based on rather qualitative arguments.
Nevertheless, the predicted evolution equation can be derived on a more
rigorous basis using the formal framework of the operator product
expansion \cite{WI:69}, which allows to make a full QCD analysis of the
moments
\bel{eq:moments}
M^q_N(Q^2) \equiv \int_0^1 dx\, x^{N-1}\, q(x,Q^2) \ ; \qquad
M^G_N(Q^2) \equiv \int_0^1 dx\, x^{N-1}\, G(x,Q^2) \ .
\end{equation}
Taking moments on both sides of Eq.~\eqn{eq:evol_q_g}, one finds
\bel{eq:mom_evol}
Q^2 {d\over dQ^2}
\left( \begin{array}{c} M^q_N(Q^2) \\ M^G_N(Q^2) \end{array}\right) =
{\alpha_s(Q^2)\over 2\pi} \left[
\begin{array}{cc} \gamma_{qq}^N & \gamma_{qG}^N \\ \gamma_{Gq}^N & \gamma_{GG}^N \end{array}\right]
\left( \begin{array}{c} M^q_N(Q^2) \\ M^G_N(Q^2) \end{array}\right) \ ,
\end{equation}
where
\bel{eq:anom}
\gamma_{ij}^N \,\equiv\, \int_0^1 dz \, z^{N-1}\, P_{ij}(z) \ ,
\end{equation}
are the so-called anomalous dimensions.
Performing the trivial integrals, one gets:
\begin{eqnarray}\label{eq:anom_res}
\gamma_{qq}^N &\!\!\! = &\!\!\! C_F\,\left[-\frac{1}{2} +
{1\over N(N+1)} - 2\sum_{k=2}^N {1\over k} \right] \ ,
\nonumber\\
\gamma_{qG}^N &\!\!\! = &\!\!\! T_F\, {2 +N+N^2\over N(N+1)(N+2)}\ ,
\nonumber\\
\gamma_{Gq}^N &\!\!\! = &\!\!\! C_F\, {2 +N+N^2\over N(N^2-1)}\ ,
\\
\gamma_{GG}^N &\!\!\! = &\!\!\! 2C_A \,\left[ -\frac{1}{12} +
{1\over N(N-1)} + {1\over (N+1)(N+2)} - \sum_{k=2}^N {1\over k} \right] \ .
\nonumber
\end{eqnarray}
For a non-singlet structure function, where the gluon component is absent,
the evolution differential equation leads to the solution
\bel{eq:dol_evol}
M_N^{q,\!\!\mbox{\rm\scriptsize ns}}(Q^2) = M_N^{q,\!\!\mbox{\rm\scriptsize ns}}(Q_0^2) \,
\left( {\alpha_s(Q^2)\over\alpha_s(Q_0^2)}\right)^{d_N} \ ;
\qquad\quad
d_N \equiv \gamma^N_{qq}/\beta_1 = {-6\gamma^N_{qq}\over 33 -2 N_f} \ .
\end{equation}
The first moment has $d_1=0$; therefore, the Gottfried sum rule
\eqn{eq:gottfried} does not get any QCD correction at this leading order.
For $N\geq 2$, $d_N>0$ so that
$M_N^{q,\!\!\mbox{\rm\scriptsize ns}}(Q^2)$ decreases as $Q^2$ increases, indicating
a degradation of momentum in the non-singlet quark distribution.
Let us now consider the flavour-singlet structure function
$\Sigma(x)\equiv\sum_i\left[ q_i(x) + \bar q_i(x)\right]$.
The $N=2$ moments $M_2^\Sigma(Q^2)$ and $M_2^G(Q^2)$
give the average total fraction of
momentum carried by quarks and gluons, respectively.
The corresponding coupled evolution equations can be easily solved.
The sum of both moments does not depend on $Q^2$, since the total
momentum is conserved:
\bel{eq:mom_consv}
M_2^\Sigma(Q^2) + M_2^G(Q^2) \, = \, 1 \ .
\end{equation}
The evolution of the $N=2$ singlet distribution then takes the simple form
\bel{eq:singlet_evol}
{M_2^\Sigma(Q^2) -{N_f\over 4C_F} M_2^G(Q^2) \over
M_2^\Sigma(Q_0^2) -{N_f\over 4C_F} M_2^G(Q_0^2)} \, =\,
{M_2^\Sigma(Q^2) -{3N_f\over 16+3N_f} \over
M_2^\Sigma(Q_0^2) -{3N_f\over 16+3N_f}} \, =\,
\left( {\alpha_s(Q^2)\over\alpha_s(Q_0^2)}\right)^{d_2^\Sigma} \ ;
\end{equation}
with $d_2^\Sigma = 2(4C_F +N_f)/(33-2N_f)$.
If $N_f<16$, $d_2^\Sigma>0$ and the right-hand side will decrease for
increasing $Q^2$.
Thus, one gets a prediction for the asymptotic values of the
average total momentum carried by quarks and gluons:
\bel{eq:asympt_mom}
\lim_{Q^2\to\infty} M_2^\Sigma(Q^2) \, = \, {3N_f\over 16+3N_f} \ ;
\qquad
\lim_{Q^2\to\infty} M_2^G(Q^2) \, = \, {16\over 16+3N_f} \ .
\end{equation}
For $N_f=4$, this gives $\frac{3}{7}$ and $\frac{4}{7}$, in good
agreement with the empirical observation that for $Q^2$ in the
range 10-40 GeV$^2$ each fraction is very close to $\frac{1}{2}$.
A very interesting issue is the behaviour of the parton distributions
at the end-points $x=0$ and $x=1$. The large $N$ moments probe the
$x\to 1$ region, while the low $x$ behaviour is controlled by
the $N\to 1$ limit.
As $N$ increases, $\gamma^N_{qG}$ and $\gamma^N_{Gq}$ tend to zero,
so that the evolution equations \eqn{eq:mom_evol} decouple;
i.e. the large $x$ behaviour of the quarks is independent of the
gluon evolution.
When $x\to 1$ the gluon distribution function approach zero more
rapidly than the quark ones. For large values of $x$ the quark
content of the nucleon is the relevant one.
Notice that $x=1$ means $W^2=M_p^2$, i.e. it actually corresponds
to the elastic photon--nucleon scattering.
At low $x$, $x/y\to 0$ and the splitting functions $P_{GG}(x/y)$
and $P_{Gq}(x/y)$ diverge.
The gluon distribution function becomes then dominant.
The low $x$ behaviour is controlled by the singular $N\to 1$ limit
of the gluon anomalous
dimension $\gamma^N_{GG}\sim 2 C_A/(N-1)$.
Making a saddle-point approximation, the $N\to 1$ moment can be
inverted; one finds in this way that for low $x$ the gluon distribution
function behaves as
\bel{eq:g_lx}
G(x) \, \sim\, {1\over x} \exp\sqrt{C(Q^2)\;\ln{1\over x}} \ ,
\end{equation}
with $C(Q^2)$ a calculable function.
Obviously, this behaviour cannot be true for arbitrarily small $x$;
something must stop the growing of the gluon distribution before
running into unitarity problems.
\begin{figure}[thb]
\centerline{\epsfxsize = 10cm \epsfbox{F2Q2H1.eps}}
\caption{Recent measurements
of $F^{ep}_2(x,Q^2)$ \protect\cite{H1:95,ZEUS:95,NMC:92,BCDMS:90}.
The $F^{ep}_2(x,Q^2)$ values are plotted with all but normalization errors
in a linear scale adding a term $c(x)=0.6 (i_x-0.4)$ to $F_2$,
where $i_x$ is the bin number starting at $i_x=1$ for $x=0.13$.
The curves represent a phenomenological fit to the data.
(Taken from Ref.~\protect\cite{H1:95}).}
\label{fig:F2Q2}
\end{figure}
Kinematically, low $x$ means the high-energy (high $W^2$) limit for
the virtual photon--nucleon scattering.
The $e$-$p$ HERA collider is ideally suited for studying this region.
The HERA experiments extend the previously accessible kinematic range
up to very large squared momentum transfers, $Q^2>5\times 10^4$ GeV$^2$,
and to very small values of $x<10^{-4}$.
The measurements reported so far \cite{H1:95,ZEUS:95}
observe indeed a significant rise
of the structure function $F^{ep}_2(x,Q^2)$ with decreasing $x$,
at fixed $Q^2$.
Around $x\sim 10^{-3}$ the decrease of $x$ by an order of magnitude
amounts to a rise of $F^{ep}_2(x,Q^2)$ of about a factor of two.
The observed $Q^2$ behaviour is consistent with the expected scaling
violations, i.e. a weak rise of $F^{ep}_2(x,Q^2)$ with increasing
$Q^2$ for $x<0.1$.
The most recent data \cite{H1:95,ZEUS:95,NMC:92,BCDMS:90}
on the proton structure function
$F^{ep}_2(x,Q^2)$ are shown in Figs.~\ref{fig:F2Q2} and \ref{fig:F2x}.
\begin{figure}[htb]
\centerline{\epsfxsize = 14cm \epsfbox{F2xH1.eps}} \vspace{-1cm}
\caption{$x$ dependence of the measured structure function
$F_2^{ep}(x,Q^2)$, for different $Q^2$ values
\protect\cite{H1:95,NMC:92,BCDMS:90}.
The curves represent a phenomenological fit to the data.
(Taken from Ref.~\protect\cite{H1:95}).}
\label{fig:F2x}
\end{figure}
\subsection{QCD fits to DIS data}
There is a twofold motivation for making careful analyses of DIS data.
First, the experimental measurement of the parton distributions provides
very valuable information on the non-perturbative regime of the
strong interactions (in addition, these parton distributions are
needed for making predictions of hard-scattering processes in
hadronic collisions). Second, the measured $Q^2$ evolution (the slopes
of the distributions) can be compared with perturbative QCD predictions.
Usually, one adopts some motivated parametrization of the quark and
gluon distributions at a fixed momentum-transfer $Q_0^2$. The
evolution equations are then used to get the proton (or neutron)
structure functions at arbitrary values of $Q^2$, and
a global fit to the data is performed.
In the actual analysis one needs to worry about the unavoidable presence
of additional non-perturbative contributions. The perturbative
evolution equations can only predict the leading logarithmic dependence of the
distribution functions with $Q^2$. These distributions
have in addition uncalculable non-perturbative corrections
suppressed by inverse powers of $Q^2$,
the so-called {\it higher-twist} contributions:
\bel{eq:higher-twists}
F_i(x,Q^2) = F^{\!\!\mbox{\rm\scriptsize LT}}_i(x,Q^2) +
{F^{\!\!\mbox{\rm\scriptsize HT}}_i(x,Q^2)\over Q^2} + \cdots
\end{equation}
The leading-twist term (LT) is the one predicted by perturbative QCD.
Since the additional $1/(Q^2)^n$ dependences have to be fitted from the
data, they increase the final uncertainties.
These corrections are numerically important for
$Q^2<{\cal O}(10 \;\mbox{\rm GeV}^2)$ and for $x$ close to 1.
Obviously, the
perturbative QCD predictions can be better tested at large $Q^2$,
where the higher-twist effects are smaller.
Since the singlet structure functions are sensitive to the gluon distribution,
which is badly known, they suffer from rather large errors. Good data
at low values of $x$ is needed in order to perform an accurate determination.
The HERA experiments are making
an important improvement in the knowledge of
these distributions.
The latest fits \cite{MSR:95}, including the most recent HERA data,
obtain gluon and sea-quark distributions at small $x$ which are
significantly different from those in previous standard sets of
parton distributions.
The new gluon distribution is larger for $x\leq 0.01$ and smaller
for $x\sim 0.1$.
The reduction of the gluon distribution in the interval
$x\sim 0.1-0.2$ is compensated by an increase in the fitted
value of $\alpha_s$ \cite{MSR:95}, bringing the DIS determination
\cite{VM:92,MSR:95}
\bel{alpha_s_DIS}
\alpha_s(M_Z^2) \, =\, 0.114\pm 0.005
\end{equation}
in better agreement with the
world average values, which we discuss in the next section.
\setcounter{equation}{0}
\section{DETERMINATION OF THE STRONG COUPLING}
In the massless quark limit, QCD has only one free parameter: the
strong coupling $\alpha_s$. Thus, all strong interaction
phenomena should be described in terms of this single input.
The measurements of $\alpha_s$ at different processes and at
different mass scales provide then a crucial test of QCD:
if QCD is the right theory
of the strong interactions, all measured observables should lead
to the same coupling.
\begin{figure}[hbt]
\centerline{\mbox{\epsfysize=10.0cm\epsffile{alphaold.ps}}}
\vspace{-0.3cm}
\caption{Compilation of $\alpha_s$ measurements as function of the energy scale
\protect\cite{BE:94,WE:94}.}
\label{fig:alpha_run}
\end{figure}
\begin{figure}[thb]
\centerline{\epsfysize = 13cm \epsfbox{alphatab.ps}}
\caption{Summary \protect\cite{WE:94}
of $\alpha_s$ measurements, evolved to the scale $M_Z$.
Starred items include preliminary results.}
\label{fig:alpha_Z}
\end{figure}
Obviously, the test should be restricted to those processes
where perturbative techniques are reliable. Moreover, the same
definition of $\alpha_s$
should be taken
everywhere; the $\overline{\mbox{\rm MS}}$ scheme is usually adopted as
the standard convention.
Since the running coupling is a function of energy,
one can either compare the different determinations at the
different scales where they are measured, checking in this way
the predicted $Q^2$ dependence of the coupling, or
use this prediction to bring all measurements to a common
reference scale where they are compared. Nowadays, the $Z$-mass
scale is conventionally chosen for such a comparison.
In order to assess the significance of the test, it is very important
to have a good understanding of the uncertainties associated
with the different measurements. This is not an easy question,
because small non-perturbative effects can be present in many
observables. In addition, some quantities have been computed
to a very good perturbative accuracy (next-to-next-to-leading order),
while others are only known at the leading or next-to-leading order;
the resulting values of $\alpha_s$ refer then to different
perturbative approximations.
The estimate of theoretical uncertainties is also affected by the
plausible asymptotic (i.e. not convergent) behaviour of the
perturbative series in powers of $\alpha_s$. Although this is a
common problem of Quantum Field Theories, it is probably more
severe in QCD because the coupling is rather big (at usual energies).
Fig.~\ref{fig:alpha_run} summarizes \cite{BE:94,WE:94}
the most reliable measurements
of the strong coupling as function of the energy scale. The
agreement with the predicted running of $\alpha_s$,
indicated by the curves, is indeed very good.
The value of $\alpha_s(m_\tau^2)$, extracted from the hadronic width of the
$\tau$ lepton, provides a very important low-energy measurement;
although it has a rather
large relative error, it implies a very precise prediction at the $M_Z$
scale, which is in excellent agreement with the direct determinations
of $\alpha_s(M_Z^2)$ performed at the $Z$ peak.
Fig.~\ref{fig:alpha_Z} \cite{WE:94}
compares the different measurements at the
common reference scale $M_Z$.
The average af all determinations gives \cite{BE:94,WE:94}:
\bel{eq:alpha_average}
\alpha_s(M_Z^2) \, = 0.117 \pm 0.005 .
\end{equation}
\setcounter{equation}{0}
\section{CHIRAL SYMMETRY}
\label{sec:chpt}
Up to now, we have only discussed
those aspects of QCD which can be analyzed in a perturbative way.
Thus, we have restricted ourselves to the study of scattering processes at
large momentum transfers, and inclusive transitions
which avoid the hadronization problems.
The rich variety of strong-interacting phenomena governed by the confinement
regime of QCD has been completely ignored.
There are certainly many approximate tools to investigate
particular aspects of non-perturbative physics;
however, rigorous first-principle QCD calculations seem
unfortunately out of reach for present techniques.
Nevertheless, we can still investigate some general properties of QCD
using symmetry considerations.
\subsection{Flavour symmetries}
In order to build the QCD Lagrangian,
we made extensive use of the $SU(3)_C$
colour symmetry, which is the basis of
the strong interaction dynamics. The Lagrangian \eqn{eq:L_QCD}
has additional {\it global} symmetries associated with the quark
flavour numbers:
\begin{enumerate}
\item ${\cal L}_{\!\!\mbox{\rm\scriptsize QCD}}$ is invariant under a global phase
redefinition of all quark flavours,
\begin{equation}\label{eq:baryon_number}
q_f \, \longrightarrow\, \exp(i\theta)\, q_f \ .
\end{equation}
This symmetry is associated with the conservation of the baryon number.
\item ${\cal L}_{\!\!\mbox{\rm\scriptsize QCD}}$ is also invariant
under independent phase redefinitions
of the different quark flavours,
\bel{eq:flavour_number}
q_f \, \longrightarrow\, \exp(i\theta_f)\, q_f \ .
\end{equation}
This symmetry implies the conservation of flavour.
\item For equal quark masses, there is a larger symmetry
under $SU(N_f)$ transformations in flavour space,
\bel{eq:isospin}
q_f \,\longrightarrow\, U_{ff'}\, q_{f'} \ , \qquad\qquad U\in SU(N_f) \ .
\end{equation}
This is a good symmetry of the light-flavour sector ($u$, $d$, $s$), where
quark masses can be ignored in first approximation. One has then the
well-known isospin ($N_f=2$) and $SU(3)$ symmetries.
\item
In the absence of quark masses, the QCD Lagrangian splits into
two independent quark sectors,
\bel{eq:LR_sectors}
{\cal L}_{\!\!\mbox{\rm\scriptsize QCD}}
\,\equiv\, -{1\over 4}\, G^{\mu\nu}_aG_{\mu\nu}^a
+ i\bar q_L \gamma^\mu D_\mu q_L +
i\bar q_R \gamma^\mu D_\mu q_R \ .
\end{equation}
Here, $q$ denotes the flavour (and colour) vector \
$q = \mbox{\rm column}(u,d,\ldots)$, and $L,R$ stand for the
left- and right-handed components of the quarks.
Thus, the two quark chiralities live in separate
flavour spaces which do not talk each other (gluon interactions
do not change the chirality), implying that all previous flavour
symmetries get duplicated in the two chiral sectors.
\end{enumerate}
The baryon number symmetry \eqn{eq:baryon_number} is usually called $U(1)_V$,
since both chiralities transform in the same way.
Its chiral replication is the corresponding $U(1)_A$ transformation:
\bel{eq:U1_A}
q_L \, \longrightarrow\, \exp(-i\theta)\, q_L \ ; \qquad\qquad
q_R \, \longrightarrow\, \exp(i\theta)\, q_R \ .
\end{equation}
This symmetry of the classical (massless) QCD Lagrangian gets broken by
quantum effects (triangular loops of the type shown in Fig.~\ref{fig:triangle},
with gluons instead of photons); this is the so-called $U(1)_A$ anomaly.
Although \eqn{eq:U1_A} is not a true symmetry of QCD,
it gets broken in a very
specific way, which leads to important implications.
A discussion of the phenomenological role of anomalies is beyond the
scope of these lectures. However, let me mention that this anomaly is
deeply related to interesting low-energy phenomena such as the
understanding of the $\eta'$ mass, or
the so-called {\it proton spin crisis}\footnote{\small
This is a quite unfortunate name, because:
1) the underlying QCD dynamics has little to do
with the parton-model description of the proton spin;
and 2) it is certainly not a crisis but rather
a success of QCD.
The failure of the naive quark-model
description of an observable where gluons
are predicted to play a crucial role (the anomaly), is indeed a clear
experimental confirmation of the QCD dynamics.}.
I want to concentrate here in the chiral extension of the old eightfold
$SU(3)_V$ symmetry, i.e. in the global
$G\equiv SU(3)_L\otimes SU(3)_R$ symmetry
of the QCD Lagrangian for massless $u$, $d$ and $s$ quarks.
This larger symmetry is not directly seen in the hadronic spectrum.
Although hadrons can be nicely classified in $SU(3)_V$ representations,
degenerate multiplets with opposite parity do not exist.
Moreover, the octet of pseudoscalar mesons
($\pi$,$K$,$\eta$) happens to be much lighter than all other
hadronic states.
There are two different ways in which a symmetry of the Lagrangian can
be realized. In the usual one (Wigner--Weyl), the ground state (the vacuum)
is also invariant. Then, all physical states can be classified in
irreducible representations of the symmetry group \cite{CO:66}.
Certainly, the hadronic spectrum does not look like that, in the case
of the chiral group.
There is a second (Nambu--Golstone),
more sophisticated, way to realize a symmetry. In
some cases, the vacuum is not symmetric. The hadronic spectrum
corresponds to energy excitations over the physical vacuum and, therefore,
will not manifest the original symmetry of the Lagrangian.
However, Goldstone's theorem \cite{GO:61} says that
in such a case there should appear a massless scalar for each
broken generator of the original symmetry group.
If the chiral symmetry is realized in this way, there should be
eight pseudoscalar massless states (Goldstone bosons)
in the hadronic spectrum; this is precisely the number of states
of the lightest hadronic multiplet: the $0^-$ octet.
Thus, we can identify the $\pi$, $K$ and $\eta$ with the Goldstone
modes of QCD; their small masses being generated by the
quark-mass matrix which explicitly breaks the global chiral symmetry
of the Lagrangian.
In the Standard electroweak model, the local
$SU(2)_L\otimes U(1)_Y$
symmetry is also realized in
the Nambu--Goldstone way. There, the symmetry-breaking phenomena is
assumed to be related to the existence of some scalar multiplet which gets
a vacuum expectation value. Since a {\it local} symmetry gets
(spontaneously) broken in that case, the Goldstone modes combine
with the gauge bosons giving massive spin-1 states plus the Higgs particle.
The QCD case is simpler, because it is a {\it global} symmetry the
one which gets broken. However, something should play the role of the
electroweak scalar field. Since quarks are the only fields carrying
flavour, they should be responsible for the symmetry breaking. The simplest
possibility is the appearance of a quark condensate
\bel{eq:quark_condensate}
v\equiv\langle 0| \bar u u |0\rangle =
\langle 0| \bar d d |0\rangle =
\langle 0| \bar s s |0\rangle < 0 \ ,
\end{equation}
generated by the non-perturbative QCD dynamics.
This would produce a dynamical breaking
of chiral symmetry, keeping at the same time the observed
$SU(3)_V$ symmetry.
\subsection{Effective Chiral Lagrangian}
The Goldstone nature of the pseudoscalar mesons implies strong
constraints on their interactions, which can be most easily analyzed
on the basis of an effective Lagrangian.
The Goldstone bosons correspond to the zero-energy excitations
over the quark condensate; their fields can be collected in a
$3\times 3$ unitary matrix $U(\phi)$,
\begin{equation}
\langle 0| \bar q^j_L q^i_R|0\rangle \, \longrightarrow \, {v\over 2}\,
U^{ij}(\phi) ,
\end{equation}
which parametrizes those excitations.
A convenient parametrization is given by
\begin{equation}
U(\phi) \equiv \exp{\left(i \sqrt{2} \Phi / f\right)} ,
\end{equation}
where
\begin{equation}
\begin{array}{c}
\Phi (x) \equiv
\frac{\displaystyle \vec{\lambda}}{\displaystyle \sqrt 2} \, \vec{\phi}
= \, \left( \begin{array}{ccc}
\frac{\displaystyle \pi^0}{\displaystyle \sqrt 2} \, + \, \frac{\displaystyle \eta_8}{\displaystyle \sqrt 6}
& \pi^+ & K^+ \\
\pi^- & - \frac{\displaystyle \pi^0}{\displaystyle \sqrt 2} \, + \, \frac{\displaystyle \eta_8}
{\displaystyle \sqrt 6} & K^0 \\
K^- & \bar K^0 & - \frac{\displaystyle 2 \, \eta_8}{\displaystyle \sqrt 6}
\end{array} \right) .
\end{array}
\end{equation}
The matrix
$U(\phi)$ transforms linearly under the chiral group, [$g_{L,R}\in
SU(3)_{L,R}$]
\begin{equation}\label{eq:utransf}
q_L\,\stackrel{G}{\longrightarrow}\, g_L\, q_L ,\quad
q_R\,\stackrel{G}{\longrightarrow}\, g_R\, q_R \qquad
\Longrightarrow\qquad
U(\phi) \, \stackrel{G}{\longrightarrow}\, g_R \, U(\phi) \, g_L^\dagger \; ,
\end{equation}
but the induced transformation on the Goldstone fields
$\vec{\phi}$ is highly non-linear.
Since there is a mass gap separating the pseudoscalar octet
from the rest of the hadronic spectrum,
we can build a low-energy effective field theory
containing only the Goldstone modes.
We should write the most general Lagrangian involving the matrix
$U(\phi)$, which is consistent with chiral symmetry.
Moreover, we can
organize the Lagrangian in terms of increasing powers of
momentum or, equivalently, in terms of an increasing number of
derivatives (parity conservation requires an even number of derivatives):
\begin{equation}
{\cal L}_{\!\!\hbox{\rm\scriptsize eff}}(U) \, = \, \sum_n \, {\cal L}_{2n} \ .
\end{equation}
In the low-energy domain, the
terms with a minimum number of derivatives will dominate.
Due to the unitarity of the $U$ matrix, $U U^\dagger = 1$, at least
two derivatives are required to generate a non-trivial interaction.
To lowest order, the effective chiral Lagrangian is uniquely
given by the term
\begin{equation}\label{eq:l2}
{\cal L}_2 = {f^2\over 4}\,
\mbox{\rm Tr}\left[\partial_\mu U^\dagger \partial^\mu U \right] .
\end{equation}
Expanding $U(\phi)$ in a power series in $\Phi$, one obtains the
Goldstone's kinetic terms plus a tower of interactions involving
an increasing number of pseudoscalars.
The requirement that the kinetic terms are properly normalized
fixes the global coefficient $f^2/4$ in (\ref{eq:l2}).
All interactions among the Goldstones can then be predicted in terms
of the single coupling $f$:
\begin{equation}
{\cal L}_2 \, = \, {1\over 2} \,\mbox{\rm Tr}\left[\partial_\mu\Phi
\partial^\mu\Phi\right]
\, + \, {1\over 12 f^2} \,\mbox{\rm Tr}\left[
(\Phi\stackrel{\leftrightarrow}{\partial}_{\!\mu}\Phi) \,
(\Phi\stackrel{\leftrightarrow}{\partial^\mu}\Phi)
\right] \, + \, {\cal O}(\Phi^6/f^4) .
\end{equation}
To compute the $\pi\pi$ scattering amplitude, for instance, is now
a trivial perturbative exercise. One gets the well-known \cite{WE:66}
Weinberg result [$t\equiv (p_+' - p_+)^2$]
\begin{equation}\label{eq:WE1}
T(\pi^+\pi^0\to\pi^+\pi^0) = {t/ f^2}.
\end{equation}
Similar results can be obtained for $\pi\pi\to 4\pi, 6\pi, 8\pi, \ldots$\,
The non-linearity of the effective Lagrangian relates
amplitudes with different numbers of Goldstone bosons, allowing
for absolute predictions in terms of $f$.
Notice that the Goldstone interactions are proportional to their
momenta (derivative couplings).
Thus, in the zero-momentum limit, pions become free.
In spite of confinement, QCD has a weakly-interacting regime at low
energies, where a perturbative expansion in powers of momenta can be applied.
It is straightforward to generalize the effective Lagrangian
(\ref{eq:l2}) to incorporate electromagnetic and semileptonic
weak interactions. One learns then that $f$ is in fact
the pion-decay constant $f\approx f_\pi=92.4$ MeV, measured in
$\pi\to\mu\nu_\mu$ decay \cite{PI:95}.
The corrections induced by the non-zero quark
masses are taken into account through the term
\bel{eq:L_m}
{\cal L}_m \, = \, {|v|\over 2}\, \mbox{\rm Tr}\left[{\cal M} (U + U^\dagger)\right]
\ , \qquad {\cal M}\equiv\mbox{\rm diag}(m_u,m_d,m_s) \ ,
\end{equation}
which breaks chiral symmetry in exactly the same way as
the quark-mass term in the underlying QCD Lagrangian does.
Eq.~\eqn{eq:L_m}
gives rise to a quadratic pseudoscalar-mass term plus
additional interactions proportional to the quark masses.
Expanding in powers of $\Phi$
(and dropping an irrelevant constant), one has
\begin{equation}\label{eq:massterm}
{\cal L}_m \, = \,
|v|\,\left\{ -{1\over f^2} \mbox{\rm Tr}\left[{\cal M}\Phi^2\right]
+ {1\over 6 f^4} \mbox{\rm Tr}\left[ {\cal M} \Phi^4\right]
+ {\cal O}(\Phi^6/f^6) \right\} .
\end{equation}
The explicit evaluation of the trace in the quadratic mass term provides
the relation between the physical meson masses and the quark masses:
\begin{eqnarray}\label{eq:masses}
M_{\pi^\pm}^2 & = & (m_u+m_d) {|v|\over f^2}\ , \nonumber\\
M_{\pi^0}^2 & = & (m_u+m_d) {|v|\over f^2} - \varepsilon +
{\cal O}(\varepsilon^2)\ , \nonumber\\
M_{K^\pm}^2 & = & (m_u + m_s) {|v|\over f^2}\ , \\
M_{K^0}^2 & = & (m_d + m_s) {|v|\over f^2}\ , \nonumber\\
M_{\eta_8}^2 & = & {1\over 3} (m_u+m_d + 4 m_s) {|v|\over f^2} + \varepsilon +
{\cal O}(\varepsilon^2)\ , \nonumber
\end{eqnarray}
where
\begin{equation}
\varepsilon = {|v|\over 2f^2}\ {(m_u - m_d)^2\over (2m_s - m_u-m_d)} \ .
\end{equation}
Chiral symmetry relates the magnitude of the meson and quark masses
to the size of the quark condensate.
Taking out the common $|v|/f^2$ factor, Eqs.~(\ref{eq:masses}) imply
the old Current Algebra mass ratios,
\begin{equation}\label{eq:mratios}
{M^2_{\pi^\pm}\over m_u+m_d} = {M^2_{K^+}\over (m_u+m_s)} =
{M_{K^0}\over (m_d+m_s)}
\approx {3 M^2_{\eta_8}\over (m_u+m_d + 4 m_s)} \ ,
\end{equation}
and
[up to ${\cal O}(m_u-m_d)$ corrections]
the Gell-Mann--Okubo mass relation
\begin{equation}
3 M^2_{\eta_8} = 4 M_K^2 - M_\pi^2 \ .
\end{equation}
Although chiral symmetry alone cannot fix the absolute values
of the quark masses, it gives information about quark-mass
ratios. Neglecting the tiny ${\cal O}(\varepsilon)$ effects,
one gets the relations
\bel{eq:ratio1}
{m_d - m_u \over m_d + m_u} \, =\,
{(M_{K^0}^2 - M_{K^+}^2) - (M_{\pi^0}^2 - M_{\pi^+}^2)\over M_{\pi^0}^2}
\, = \, 0.29 \ ,
\end{equation}
\bel{eq:ratio2}
{2 m_s -m_u-m_d\over 2 (m_u+m_d)} \, = \,
{M_{K^0}^2 - M_{\pi^0}^2\over M_{\pi^0}^2}
\, = \, 12.6 \ .
\end{equation}
In (\ref{eq:ratio1}) we have subtracted the pion square-mass
difference, to take into account the electromagnetic contribution
to the pseudoscalar-meson self-energies;
in the chiral limit ($m_u=m_d=m_s=0$), this contribution is proportional
to the square of the meson charge and it is the same for $K^+$ and $\pi^+$.
The mass formulae (\ref{eq:ratio1}) and (\ref{eq:ratio2})
imply the quark-mass ratios advocated by Weinberg:
\begin{equation}\label{eq:Weinbergratios}
m_u : m_d : m_s = 0.55 : 1 : 20.3 \ .
\end{equation}
Quark-mass corrections are therefore dominated by $m_s$, which is
large compared with $m_u$ and $m_d$.
Notice that the difference $m_d-m_u$ is not small compared with
the individual up- and down-quark masses; in spite of that,
isospin turns out
to be an extremely good symmetry, because
isospin-breaking effects are governed by the small ratio
$(m_d-m_u)/m_s$.
The $\Phi^4$ interactions in (\ref{eq:massterm})
introduce mass corrections to the $\pi\pi$ scattering amplitude
(\ref{eq:WE1}),
\begin{equation}\label{eq:WE2}
T(\pi^+\pi^0\to\pi^+\pi^0) = {t - M_\pi^2\over f_\pi^2} \ .
\end{equation}
Since $f\approx f_\pi$ is fixed from pion decay, this result
is now an absolute prediction of chiral symmetry.
The lowest-order chiral Lagrangian encodes
in a very compact way all the Current Algebra results obtained in
the sixties \cite{currentalgebra}.
The nice feature of the chiral approach is its elegant
simplicity, which
allows to estimate higher-order corrections in a systematic way.
A detailed summary of the chiral techniques and their
phenomenological applications can be found in
Ref.~\cite{PI:95}.
\section{SUMMARY}
Strong interactions are characterized by three basic properties:
asymptotic freedom, confinement and dynamical chiral symmetry breaking.
Owing to the gluonic self-interactions, the QCD coupling becomes
smaller at short distances, leading indeed to an asymptotically-free
quantum field theory.
Perturbation theory can then be applied at large momentum transfers.
The resulting predictions have achieved a remarkable success,
explaining a wide range of phenomena in terms of a single coupling.
The running of $\alpha_s$ has been experimentally tested at
different energy scales, confirming the predicted QCD behaviour.
The growing of the running coupling at low-energies
makes very plausible
that the QCD dynamics generates the required confinement
of quarks and gluons into colour-singlet hadronic states.
A rigorous proof of this property is, however, still lacking.
At present, the dynamical details of hadronization are completely unknown.
Non-perturbative tools, such as QCD sum rules and lattice calculations,
provide indirect evidence that QCD also implies the proper pattern
of chiral symmetry breaking.
The results obtained so far support the existence of a non-zero
$q$-$\bar q$ condensate in the QCD vacuum, which dynamically breaks
the chiral symmetry of the Lagrangian.
However, a formal understanding of this
phenomena has only been achieved in some approximate limits.
Thus, we have at present an overwhelming experimental and theoretical
evidence that the $SU(3)_C$ gauge theory correctly describes the hadronic
world.
This makes QCD
the established theory of the strong interactions.
Nevertheless,
the non-perturbative nature of its low-energy limit
is still challenging our theoretical capabilities.
\section*{ACKNOWLEDGEMENTS}
I would like to thank the organizers for the charming atmosphere of this
school, and the students for their many interesting questions and
comments. I am also grateful to
B. Gavela, J. Fuster and A. Santamar\'{\i}a
for their help with the postscript figures.
This work has been supported in part by CICYT (Spain) under grant
No. AEN-93-0234.
\newpage
\renewcommand{\theequation}{A.\arabic{equation}}
\setcounter{equation}{0}
\section*{\boldmath APPENDIX A: $SU(N)$ ALGEBRA}
$SU(N)$ is the group of $N\times N$ unitary matrices,
$U U^\dagger = U^\dagger U =1$, with $\det U=1$.
The generators of the $SU(N)$ algebra,
$T^a$ ($a=1,2,\ldots,N^2-1$), are hermitian,
traceless matrices satisfying the commutation relations
\bel{eq:T_com}
[T^a, T^b] \, = \, i f^{abc}\, T^c \, ,
\end{equation}
the structure constants $f^{abc}$ being real and totally antisymmetric.
The fundamental representation $T^a = \lambda^a/2$ is $N$-dimensional.
For $N=2$, $\lambda^a$ are the usual Pauli matrices, while
for $N=3$, they correspond to the eight Gell-Mann matrices:
\begin{eqnarray}\label{eq:GM_matrices}
\lambda^1 \! = \!\left( \begin{array}{ccc} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{array} \right) ,
\quad\,
\lambda^2 &\!\!\! \! = &\!\!\!\!
\left( \begin{array}{ccc} 0 & -i & 0 \\ i & 0 & 0 \\ 0 & 0 & 0 \end{array} \right) ,
\quad
\lambda^3 \! = \!\left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 0 \end{array} \right)
,
\quad
\lambda^4 \! = \!\left( \begin{array}{ccc} 0 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \end{array} \right) ,
\nonumber\\ && \\
\lambda^5 \! = \!
\left( \begin{array}{ccc} 0 & 0 & -i \\ 0 & 0 & 0 \\ i & 0 & 0 \end{array} \right) \! ,
\;\;
\lambda^6 &\!\!\!\! = &\!\!\!
\left( \begin{array}{ccc} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{array} \right)\! , \;\;
\lambda^7 \! = \!\left( \begin{array}{ccc} 0 & 0 & 0 \\ 0 & 0 & -i \\ 0 & i & 0 \end{array} \right)
\! , \;\;
\lambda^8 \! = \!
{1\over\sqrt{3}}\!
\left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -2 \end{array} \right) \! . \nonumber
\end{eqnarray}
They satisfy the anticommutation relation
\bel{eq:anticom}
\left\{\lambda^a,\lambda^b\right\} \, = \,
{4\over N} \,\delta^{ab} \, I_N \,
+ \, 2 d^{abc} \, \lambda^c \, ,
\end{equation}
where $I_N$ denotes the $N$-dimensional unit matrix and the constants
$d^{abc}$ are totally symmetric in the three indices.
For $SU(3)$, the only non-zero (up to permutations)
$f^{abc}$ and $d^{abc}$ constants are
\begin{eqnarray}\label{eq:constants}
&&{1\over 2} f^{123} = f^{147} = - f^{156} = f^{246} = f^{257} = f^{345}
= - f^{367} = {1\over\sqrt{3}} f^{458} = {1\over\sqrt{3}} f^{678} =
{1\over 2}\, , \hfil
\nonumber\\
&&d^{146} = d^{157} = -d^{247} = d^{256} = d^{344} =
d^{355} = -d^{366} = - d^{377} = {1\over 2}\, ,
\\
&&d^{118} = d^{228} = d^{338} = -2 d^{448} = -2 d^{558} = -2 d^{688} =
-2 d^{788} = -d^{888} = {1\over \sqrt{3}}\, . \qquad\qquad
\nonumber
\end{eqnarray}
The adjoint representation of the $SU(N)$ group is given by
the $(N^2-1)\!\times\! (N^2-1)$ matrices
$(T^a_A)_{bc} \equiv - i f^{abc}$.
The relations
\begin{eqnarray}\label{eq:invariants}
{\rm Tr}\left(\lambda^a\lambda^b\right) = 4 T_F
\, \delta_{ab}
\, , \qquad\qquad\quad && T_F = {1\over 2} \, ,
\nonumber\\
\left(\lambda^a\lambda^a\right)_{\alpha\beta} = 4
C_F \, \delta_{\alpha\beta} \, , \qquad\qquad\quad
&& C_F = {N^2-1\over 2N} \, ,
\\ \;
{\rm Tr}(T^a_A T^b_A) = f^{acd} f^{bcd} = C_A \,\delta_{ab} \, , \quad
&& C_A = N \, , \qquad\nonumber
\end{eqnarray}
define the $SU(N)$ invariants $T_F$, $C_F$ and $C_A$.
Other useful properties are:
\begin{eqnarray}
\left(\lambda^a\right)_{\alpha\beta}
\left(\lambda^a\right)_{\gamma\delta}
= 2 \delta_{\alpha\delta}\delta_{\beta\gamma}
-{2\over N} \delta_{\alpha\beta}\delta_{\gamma\delta} \, ;
\qquad &&
{\rm Tr}\left(\lambda^a\lambda^b\lambda^c\right)
= 2 (d^{abc} + i f^{abc})\, ;
\qquad\nonumber\\ \;\;
{\rm Tr}(T^a_A T^b_A T^c_A) = i \, {N\over 2} f^{abc} \, ;
\qquad \sum_b d^{abb} = 0\, ; \quad &&
d^{abc} d^{ebc} = \left( N - {4\over N}\right) \delta_{ae} \, ;
\\
f^{abe} f^{cde} + f^{ace} f^{dbe} + f^{ade} f^{bce} = 0 \, ; \qquad\qquad &&
f^{abe} d^{cde} + f^{ace} d^{dbe} + f^{ade} d^{bce} = 0 \, . \qquad\quad\nonumber
\end{eqnarray}
\newpage
\renewcommand{\theequation}{B.\arabic{equation}}
\setcounter{equation}{0}
\section*{APPENDIX B: GAUGE-FIXING AND GHOST FIELDS}
The fields $G^\mu_a$ have 4 Lorentz degrees of freedom,
while a massless spin-1 gluon has 2 physical polarizations only.
Although gauge invariance makes the additional degrees of freedom irrelevant,
they give rise to some technical complications when quantizing the gauge
fields.
The canonical momentum associated with $G^\mu_a$,
$\Pi^a_\mu(x)\equiv
\delta{\cal L}_{\!\!\mbox{\rm\scriptsize QCD}}/\delta (\partial_0G^\mu_a)
= G^a_{\mu 0}$,
vanishes identically for $\mu=0$.
The standard commutation relation
\bel{eq:quantization}
\left[ G^\mu_a(x), \Pi^\nu_b(y) \right] \delta(x^0-y^0) \, = \,
i g^{\mu\nu} \delta^{(4)}(x-y) \, ,
\end{equation}
is then meaningless for $\mu=\nu=0$. In fact, the field $G^0_a$ is just a
classical quantity, since it commutes with all the other fields.
This is not surprising, since we know that there are 2 unphysical components
of the gluon field, which should not be quantized. Thus, we could just impose
two gauge conditions, such as $G^0_a = 0$ and $\vec\nabla \vec G_a = 0$,
to eliminate the 2 redundant degrees of freedom,
and proceed working with the physical gluon polarizations only. However,
this is a (Lorentz) non-covariant procedure, which leads to a very
awkward formalism. Instead, one can impose a Lorentz-invariant gauge
condition, such as $\partial_\mu G^\mu_a = 0$. The simplest way to
implement this is to add to the Lagrangian the gauge-fixing term
\bel{eq:L_GF}
{\cal L}_{\!\!\mbox{\rm\scriptsize GF}} \, = \, -{1\over 2\xi} \, (\partial^\mu G_\mu^a)\,
(\partial_\nu G^\nu_a)
\end{equation}
where $\xi$ is the so-called gauge parameter.
The 4 Lorentz components of the canonical momentum
\bel{eq:canonical}
\Pi^a_\mu(x) \equiv {\delta{\cal L}_{\!\!\mbox{\rm\scriptsize QCD}}\over\delta
(\partial_0 G^\mu_a)}
= G^a_{\mu 0} - {1\over \xi}\, g_{\mu 0}\, (\partial^\nu G_\nu^a)
\end{equation}
are then non-zero, and one can develop a covariant quantization formalism.
Since \eqn{eq:L_GF} is a quadratic $G_a^\mu$ term, it modifies the gluon
propagator:
\bel{eq:propagator}
\langle 0 | T[G^\mu_a(x) G^\nu_b(y)]|0\rangle =
i \delta_{ab} \int {d^4k\over (2\pi)^4} {\mbox{\rm e}^{-ik(x-y)}\over k^2 + i\varepsilon}
\left\{ -g^{\mu\nu} + (1-\xi) {k^\mu k^\nu\over k^2 + i\varepsilon}\right\}
\, .
\end{equation}
Notice, that the propagator is not defined for $\xi=\infty$, i.e. in
the absence of the gauge-fixing term \eqn{eq:L_GF}.
In QED, this gauge-fixing procedure is enough for making a consistent
quantization of the theory. The initial gauge symmetry of the Lagrangian
guarantees that the redundant photon polarizations do not generate
non-physical contributions to the scattering amplitudes, and the final
results are independent of the arbitrary gauge parameter $\xi$.
In non-abelian gauge theories, like QCD, a second problem still remains.
\begin{figure}[htb]
\centerline{\epsfysize =3.5cm \epsfbox{qqGG.ps}}
\vspace{-0.2cm}
\caption{Tree-level Feynman diagrams contributing to $q\bar q\to GG$.}
\label{fig:qqGG}
\end{figure}
Let us consider the scattering process $q\bar q\to G G$, which proceeds
through the three Feynman graphs shown in Fig.~\ref{fig:qqGG}. The scattering
amplitude has the general form
$T = J^{\mu\mu'} \varepsilon_{\mu\phantom{'}}^{(\lambda)}
\varepsilon_{\mu'}^{(\lambda')}$.
The probability associated with the scattering process
\bel{eq:prob}
{\cal P} \sim {1\over 2} J^{\mu\mu'} (J^{\nu\nu'})^\dagger \,
\sum_\lambda \varepsilon_\mu^{(\lambda)}\varepsilon_\nu^{(\lambda)*}\,
\sum_{\lambda'} \varepsilon_{\mu'}^{(\lambda')}\varepsilon_{\nu'}^{(\lambda')*}
\end{equation}
involves a sum over the final gluon polarizations.
One can easily check that the physical probability ${\cal P}_T$, where only the
two transverse gluon polarizations are considered in the sum, is different
from the covariant quantity ${\cal P}_C$, which includes a sum over all
polarization components: ${\cal P}_C > {\cal P}_T$.
In principle, this is not a problem because only ${\cal P}_T$ has physical meaning;
we should just sum over the physical transverse polarizations to get the
right answer. However, the problem comes back at higher orders.
\begin{figure}[hbt]
\centerline{\epsfysize =3.5cm \epsfbox{qqqq.ps}}
\vspace{-0.2cm}
\caption{1-loop diagrams contributing to $q\bar q\to q\bar q$.}
\label{fig:loop}
\end{figure}
The covariant gluon propagator \eqn{eq:propagator} contains the 4 polarization
components; therefore higher-order graphs such as the ones in
Fig.~\ref{fig:loop} get unphysical contributions from the longitudinal and
scalar gluon polarizations propagating along the internal gluon lines.
The absorptive part of these 1-loop graphs (i.e. the imaginary part obtained
putting on-shell the two gluon lines within the loop)
is equal to $|T(q\bar q\to GG)|^2$.
Thus, these loops suffer the same probability problem than the tree-level
$q\bar q\to GG$ amplitude.
The propagation of unphysical gluon components implies then a violation
of unitarity (the two fake polarizations contribute a positive probability).
In QED this problem does not appear because the gauge-fixing condition
$\partial^\mu A_\mu=0$ still leaves a residual gauge invariance
under transformations satisfying $\Box\theta = 0$. This guarantees that
(even after adding the gauge-fixing term) the electromagnetic current
is conserved, i.e.
$\partial_\mu J^\mu_{\mbox{\rm\scriptsize em}}=\partial_\mu (eQ\bar\Psi\gamma^\mu\Psi) =
0$.
If one considers the $e^+e^-\to\gamma\gamma$ process, which proceeds through
diagrams identical to a) and b) in Fig.~\ref{fig:qqGG},
current conservation implies
$k_\mu J^{\mu\mu'} = k'_{\mu'} J^{\mu\mu'} = 0$, where $k_\mu$ and $k'_{\mu'}$
are the momenta of the photons with polarizations $\lambda$ and $\lambda'$,
respectively (remember that the interacting vertices contained in
$J^{\mu\mu'}$ are in fact the corresponding electromagnetic currents).
As a consequence, the contributions from the
scalar and longitudinal photon polarizations vanish
and, therefore, ${\cal P}_C = {\cal P}_T$.
The reason why ${\cal P}_C\not={\cal P}_T$ in QCD stems from the third diagram in
Fig.~\ref{fig:qqGG}, involving a gluon self-interaction.
Owing to the non-abelian character of the $SU(3)$ group, the gauge-fixing
condition $\partial_\mu G^\mu_a=0$ does not leave any residual
invariance\footnote{\small
To maintain $\partial_\mu (G^\mu_a)'=0$ after the gauge transformation
\eqn{eq:inf_transf}, one would need
$\Box \delta\theta_a = g_s f^{abc}\partial_\mu(\delta\theta_b) G^\mu_c$,
which is not possible because $G^\mu_c$ is a quantum field.}.
Thus, $k_\mu J^{\mu\mu'}\not= 0$.
\begin{figure}[hbt]
\centerline{\epsfysize =3cm \epsfbox{ghosts.ps}}
\caption{Feynman diagrams involving the ghosts.}
\label{fig:ghosts}
\end{figure}
Again, the problem could be solved adopting a non-covariant quantization where
only the physical transverse polarizations propagate; but the resulting
formalism would be awful and very inconvenient for performing
practical calculations.
A more clever solution
consist \cite{FE:63} in adding additional unphysical fields,
the so-called {\it ghosts}, with a coupling to the gluons
such that exactly cancels {\it all} unphysical contributions from
the scalar and longitudinal gluon polarizations.
Since a positive fake probability has to be cancelled, one needs fields
obeying the wrong statistics (i.e. of negative norm)
and thus giving negative probabilities.
The magic cancellation is achieved by adding to the Lagrangian the
Faddeev--Popov term \cite{FP:67},
\bel{eq:L_FP}
{\cal L}_{\!\!\mbox{\rm\scriptsize FP}} \, = \, -\partial_\mu\bar\phi_a D^\mu\phi^a \, ,
\qquad
\quad D^\mu\phi^a\equiv \partial^\mu\phi^a - g_s f^{abc} \phi^b G^\mu_c \, ,
\end{equation}
where $\bar\phi^a$, $\phi^a$ ($a=1,\ldots,N_C^2-1$) is a set of
anticommuting (i.e. obeying the Fermi-Dirac statistics), massless,
hermitian, scalar fields.
The covariant derivative $D^\mu\phi^a$ contains the needed coupling to the
gluon field. One can easily check that
diagrams d) and d') in Fig.~\ref{fig:ghosts} exactly cancel the unphysical
contributions from diagrams c) and c') of Figs.~\ref{fig:qqGG} and
\ref{fig:loop}, respectively; so that finally ${\cal P}_C={\cal P}_T$.
Notice, that the Lagrangian \eqn{eq:L_FP} is necessarily not Hermitian,
because one needs to introduce an explicit violation of unitarity
to cancel the unphysical probabilities and restore the unitarity of the
final scattering amplitudes.
The exact mechanism giving rise to the ${\cal L}_{\!\!\mbox{\rm\scriptsize FP}}$ term
can only be understood (in a simple way) using the more powerful
path-integral formalism, which is beyond the scope of these lectures.
The only point I would like to emphasize here, is that the addition of
the gauge-fixing and Faddeev--Popov Lagrangians is just a mathematical
trick, which allows to develop a simple covariant formalism, and
therefore a set of simple Feynman rules, making easier to perform
explicit calculations.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,793 |
fou un remer suís que va competir durant les dècades de 1930 i 1940.
El 1936 va prendre part en els Jocs Olímpics de Berlín, on disputà tres proves del programa de rem. Guanyà la medalla de plata en el quatre amb timoner, formant equip amb Hans Homberger, Alex Homberger, Karl Schmid i Rolf Spring; i la de bronze en el quatre sense timoner, formant equip amb Hans Homberger, Alex Homberger i Karl Schmid. En la prova del vuit amb timoner fou sisè.
En el seu palmarès també destaquen cinc medalles al Campionat d'Europa de rem, dues d'or, dues de plata i una de bronze entre el 1934 i 1947, sempre en la prova del quatre sense timoner.
Referències
Remadors suïssos
Medallistes suïssos als Jocs Olímpics d'estiu de 1936 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,720 |
\section{Guidelines}
At the magnificient Boston Museum of Fine Arts one can see a big stone brought
in from Northern Africa, covered with strange hieroglyphes. More than 2000
years ago it located in the Great Temple of Amun at the old City of Jebel
Barkal in the kingdom of Nubia and is assumed to describe the rulership of
king Tanyidamani. The text is written in the Meroitic language, which is still
underdeciphered. Neither the grammar of that language nor the content of the
text on the Stone of Amun is known, only the letters.
In particle physics today one is facing a similar problem, as far as the
masses of the leptons and quarks are concerned. After the discovery of the
$t$--quark the spectrum of these masses (apart from the yet unknown neutrino
masses) is known. It is a rather wild spectrum, extending over 5 orders of
magnitude, from the tiny electron mass to the huge $t$--mass, but the actual
dynamics behind this spectrum remains mysterious. Nature speaks to us in some
kind of Meroitic language. The letters of this language, i. e. the masses and
flavor mixing parameters, are known, but the grammar and the content of the
text is unknown. Of course, in my talk I cannot offer a complete solution of
the mass problem, but I shall describe what I would like to define as the
grammar of patterns and rules, which are not only very simple, but seem to
come out very well, if confronted with the experimental results.
Let me remind you, just for illustration, of the observed eigenvalues of the
quark masses. Typical numbers are, at a renormalization point of
\[
\mu = m_t (\cong 175):
\]
\begin{equation}
\begin{array}{lclllclllclll}
m_u & : & 3.3 & MeV & \, m_c & : & 0.84 & GeV & \, m_t & : & 175 & GeV \\
m_d & : & 6.3 & MeV & \, m_s & : & 0.11 & GeV & \, m_b & : & 3.2 & GeV
\end{array}
\end{equation}
These masses are, of course, just eigenvalues of the quark mass
matrices, which in the Standard Model are introduced by the coupling of the
quark fields to the scalar field.
The phenomenon of flavor mixing arises due to the observed fact that the
$W$--boson, after interacting with a mass eigenstate, produces a state, which
is a mixture of all three quark mass eigenstates of the same electric charge.
Thus a $u$--quark, for example, is transformed primarily into a $d$--quark
(with a probability of about 95\%), sometimes into a $s$--quark (probability
about 5\%), and occasionally (probability about $10^{-5}$) into a $b$--quark,
provided that the energy transfer is large enough. This mismatch between the
$U$--sector and the $D$--sector \, of \, the quarks \, is usually
\, parametrized \, by the CKM mixing matrix \cite{{Cabibbo63},{KM73}}.
The phenomenon of flavor mixing, which is intrinsically linked to
$CP$--violation, is an important ingredient of the Standard Model of Basic
Interactions. Yet unlike other features of the Standard Model, e.\ g.\ the
mixing of the neutral electroweak gauge bosons, it is a phenomenon which can
merely be described. A deeper understanding is still lacking, but most
theoreticians would agree that it is directly linked to the mass spectrum of
the quarks -- the possible mixing of lepton flavors will not be discussed
here. Furthermore there is a general consensus that a deeper dynamical
understanding would require to go beyond the physics of the Standard Model.
In this talk I shall not go thus far. Instead I shall demonstrate that the
observed properties of the flavor mixing, combined with our knowledge about
the quark mass spectrum, suggest specific symmetry properties which allow
to fix the flavor mixing parameters with high precision, thus predicting the
outcome of the experiments which will soon be performed at the $B$--meson
factories.
In the standard electroweak theory the phenomenon of flavor
mixing of the quarks is described by the $3\times 3$ unitary CKM--matrix.
This
matrix can be expressed in terms of four parameters, which are usually
taken as three rotation angles and one phase.
In the standard model the generation of quark masses
is intimately related to the phenomenon of flavor mixing. In
particular, the flavor mixing parameters do depend on the
elements of quark mass matrices. A particular structure of the
underlying mass matrices calls for a particular choice of the
parametrization of the flavor mixing matrix. For example, in
ref. (3) it was noticed that a rather special form of
the flavor mixing matrix results, if one starts from Hermitian mass
matrices in which the (1,3) and (3,1) elements vanish. This has been
subsequently observed again in a number of papers
\cite{{Hall},{FX97}}. Recently we have studied the exact form of such a
description from a general point of view and pointed out some
advantages of this type of representation in the discussion of flavor
mixing and $CP$-violating phenomena \cite{FX97}, which will be discussed
later.
In the standard model the weak charged currents are given by
\begin{equation}
\overline{(u, ~ c, ~ t)}^{~}_L \left ( \matrix{
V_{ud} & V_{us} & V_{ub} \cr
V_{cd} & V_{cs} & V_{cb} \cr
V_{td} & V_{ts} & V_{tb} \cr} \right )
\left ( \matrix{
d \cr s \cr b \cr} \right )_L \; ,
\end{equation}
where $u$, $c$, ..., $b$ are the quark mass eigenstates, $L$ denotes
the left-handed fields, and $V_{ij}$ are elements of the CKM matrix
$V$. In general $V_{ij}$ are complex numbers, but their absolute
values are measurable quantities. For example, $|V_{cb}|$ primarily
determines the lifetime of $B$ mesons. The phases of $V_{ij}$,
however, are not physical, like the phases of quark fields. A phase
transformation of the $u$ quark ($u \rightarrow u ~ e^{{\rm
i}\alpha}$), for example, leaves the quark mass term invariant but
changes the elements in the first row of $V$ (i.e., $V_{uj} \rightarrow
V_{uj} ~ e^{-{\rm i}\alpha}$). Only a common phase transformation of all
quark fields leaves all elements of $V$ invariant, thus there is a
five-fold freedom to adjust the phases of $V_{ij}$.
In general the unitary matrix $V$ depends on nine parameters.
Note that in the absence of complex phases $V$ would consist of only three
independent parameters, corresponding to three (Euler) rotation
angles. Hence one can describe the complex matrix $V$ by three
angles and six phases. Due to the freedom in redefining the quark
field phases, five of the six phases in $V$ can be absorbed and we arrive
at the well-known result that the CKM matrix $V$ can be parametrized
in terms of three rotation angles and one $CP$-violating phase.
Recently it was shown that one way to describe the mixing of three families
is particularly useful. It is given as follows \cite{FX97}:
\begin{eqnarray}
V & = & \left( \matrix{
c_{\rm u} & s_{\rm u} & 0 \cr
-s_{\rm u} & c_{\rm u} & 0 \cr
0 & 0 & 1 \cr } \right ) \left ( \matrix{
e^{-i \varphi} & 0 & 0 \cr
0 & c & s \cr
0 & -s & c \cr } \right ) \left ( \matrix{
c_{\rm d} & -s_{\rm d} & 0 \cr
s_{\rm d} & c_{\rm d} & 0 \cr
0 & 0 & 1 \cr } \right) \nonumber \\ \nonumber \\ \nonumber
\end{eqnarray}
\vspace*{-1.5cm}
\begin{eqnarray}
= \left( \matrix{
s_u s_d c + c_u c_d e^{- i \varphi} & s_u c_d c - c_u s_d e^{-i \varphi}
& s_u s \cr
c_u s_d c - s_u c_d e^{-i \varphi} & c_u c_d c + s_u s_d e^{-i \varphi}
& c_u s \cr
- s_d s & - c_d s & c \cr } \right) .
\end{eqnarray}
The three angles $\theta_{\rm u}$, $\theta_{\rm d}$ and
$\theta$ in Eq. (12) can all be arranged to lie in the first quadrant
through a suitable redefinition of quark field phases. Consequently
all $s_{\rm u}$, $s_{\rm d}$, $s$ and $c_{\rm u}$, $c_{\rm d}$, $c$
are positive. The phase $\varphi$ can in general take values from 0
to $2\pi$; and $CP$ violation is present in weak interactions
if $\varphi \neq 0, \pi$ and $2\pi$.
In comparison with all other parametrizations discussed
previously \cite{KM73,Standard}, the one given here
has a number of interesting features which in our view make it very
attractive and provide strong arguments for its use in future
discussions of flavor mixing phenomena, in particular, those in
$B$-meson physics. We shall discuss them below.
a) As shown in ref. (5), the flavor mixing matrix $V$ in Eq. (12) follows
directly from the chiral expansion of the mass
matrices. Thus it naturally takes into account the hierarchical structure of the
quark mass spectrum.
b) The complex phase describing $CP$ violation ($\varphi$) appears only in the
(1,1), (1,2), (2,1) and (2,2) elements of $V$, i.e.,
in the elements involving only the quarks of the first and second
families. This is a natural description of $CP$ violation since in our
hierarchical approach $CP$ violation is not directly linked to the third family, but
rather to the first and second ones, and in particular to the mass terms of the
$u$ and $d$ quarks.
It is instructive to consider the special case $s_{\rm u} = s_{\rm d}
= s = 0$. Then the flavor mixing matrix $V$ takes the form
\begin{equation}
V \; = \; \left ( \matrix{
e^{-{\rm i}\varphi} & 0 & 0 \cr
0 & 1 & 0 \cr
0 & 0 & 1 \cr} \right ) \; .
\end{equation}
This matrix describes a phase change in the weak transition between
$u$ and $d$, while no phase change is present in the
transitions between $c$ and $s$ as well as $t$ and $b$.
Of course, this effect can be absorbed in a phase change of the $u$-
and $d$-quark fields, and no $CP$ violation is present. Once the
angles $\theta_{\rm u}$, $\theta_{\rm d}$ and $\theta$ are introduced,
however, $CP$ violation arises. It is due to a phase change in the weak
transition between $u^{\prime}$ and $d^{\prime}$, where $u^{\prime}$
and $d^{\prime}$ are the rotated quark fields, obtained by applying
the corresponding rotation matrices given in Eq. (12) to the
quark mass eigenstates ($u^{\prime}$: mainly $u$, small admixture of
$c$; $d^{\prime}$: mainly $d$, small admixture of $s$).
c) The dynamics of flavor mixing can easily be interpreted by
considering certain limiting cases in Eq. (8). In the limit $\theta
\rightarrow 0$ (i.e., $s \rightarrow 0$ and $c\rightarrow 1$), the
flavor mixing is, of course, just a mixing between the first and
second families, described by only one mixing angle (the Cabibbo angle
$\theta_{\rm C}$).
It is a special and essential feature of the representation (8) that the Cabibbo
angle is {\it not} a basic angle, used in the parametrization.
The matrix element $V_{us}$ (or $V_{cd}$) is
indeed a superposition of two terms including a phase. This feature
arises naturally in our hierarchical approach, but it is not new. In
many models of specific textures of mass matrices, it is indeed the
case that the Cabibbo-type transition $V_{us}$ (or $V_{cd}$)
is a superposition of several
terms. At first, it was obtained by me
in the discussion of the two-family mixing, and in various studies of quark
mass matrices \cite{Fritzsch79,Dimopoulos92}.
In the limit $\theta =0$ considered here, one has $|V_{us}| = |V_{cd}|
= \sin\theta_{\rm C} \equiv s^{~}_{\rm C}$ and
\begin{equation}
s^{~}_{\rm C} \; =\; \left | s_{\rm u} c_{\rm d} ~ - ~ c_{\rm u} s_{\rm d}
e^{-{\rm i}\varphi} \right | \; .
\end{equation}
This relation describes a triangle in the complex plane which we shall denote
as the ``LQ-- triangle'' (``light quark triangle''). This triangle is a
feature of the mixing of the first two families. Explicitly one has
(for $s=0$):
\begin{equation}
\tan\theta_{\rm C} \; =\; \sqrt{\frac{\tan^2\theta_{\rm u} +
\tan^2\theta_{\rm d} - 2 \tan\theta_{\rm u} \tan\theta_{\rm d}
\cos\varphi}
{1 + \tan^2\theta_{\rm u} \tan^2\theta_{\rm d} + 2 \tan\theta_{\rm u}
\tan\theta_{\rm d} \cos\varphi}} \; .
\end{equation}
Certainly the flavor mixing matrix $V$ cannot accommodate $CP$ violation in
this limit. However, the existence of $\varphi$ seems necessary in order
to make Eq. (6) compatible with current data, as one can see below.
d) The three mixing angles $\theta$, $\theta_{\rm u}$ and
$\theta_{\rm d}$ have a precise physical meaning. The angle $\theta$
describes the mixing between the second and third families.
We shall refer to this mixing involving $t$ and $b$ as the ``heavy
quark mixing''.
The angle $\theta_{\rm u}$,
however, describes the $u$-$c$ mixing, and we shall denote this as the
``u-channel mixing''.
The angle $\theta_{\rm d}$ describes
the $d$-$s$ mixing: it will be denoted as the ``d-channel mixing''.
Thus there exists an asymmetry between the mixing of the first and
second families and that of the second and third families,
which in our view reflects interesting details of the underlying dynamics of
flavor mixing.
The heavy quark mixing is a combined effect, involving both charge
$+2/3$ and charge $-1/3$ quarks, while the u- or d-channel mixing
(described by the angle $\theta_{\rm u}$ or $\theta_{\rm d}$) proceeds
solely in the charge $+2/3$ or charge $-1/3$ sector. Therefore a precise
experimental determination of these two angles would allow to draw
interesting conclusions about the amount and perhaps the underlying
pattern of the u- or d-channel mixing.
e) The three angles $\theta$, $\theta_{\rm u}$ and $\theta_{\rm d}$
are related in a very simple way to observable quantities of $B$-meson
physics.
For example, $\theta$ is related to
the rate of the semileptonic decay $B\rightarrow D^*l\nu^{~}_l$;
$\theta_{\rm u}$ is associated with the ratio of the decay rate of
$B\rightarrow (\pi, \rho) l \nu^{~}_l$ to that of $B\rightarrow
D^* l\nu^{~}_l$; and $\theta_{\rm d}$ can be determined from the ratio of
the mass difference between two $B_d$ mass eigenstates to that between
two $B_s$ mass eigenstates. We find the following exact
relations:
\begin{equation}
\sin \theta \; = \; |V_{cb}| \sqrt{ 1 + \left |\frac{V_{ub}}{V_{cb}}
\right |^2} \; ,
\end{equation}
and
\begin{eqnarray}
\tan\theta_{\rm u} & = & \left | \frac{V_{ub}}{V_{cb}} \right | \; ,
\nonumber \\
\tan\theta_{\rm d} & = & \left | \frac{V_{td}}{V_{ts}} \right | \; .
\end{eqnarray}
These simple results makes our parametrization (8) uniquely favorable
for the study of $B$-meson physics.
By use of current data on $|V_{ub}|$ and $|V_{cb}|$, i.e., $|V_{cb}| =
0.039 \pm 0.002$ \cite{Neubert96,Forty97} and $|V_{ub}/V_{cb}| =0.08 \pm 0.02$
\cite{PDG96}, we obtain $\theta_{\rm u} = 4.57^{\circ} \pm
1.14^{\circ}$ and $\theta = 2.25^{\circ} \pm 0.12^{\circ}$. Taking
$|V_{td}| = (8.6 \pm 2.1) \times 10^{-3}$,
which was obtained from the analysis of current data on
$B^0_d$-$\bar{B}^0_d$ mixing,
we get $|V_{td}/V_{ts}| = 0.22 \pm 0.07$, i.e., $\theta_{\rm d} = 12.7^{\circ}
\pm 3.8^{\circ}$.
Both the heavy quark mixing angle $\theta$ and the u-channel mixing
angle $\theta_{\rm u}$ are relatively small. Recently a fit of these angles
was made \cite{PARO}, with rather small
uncertainties for the angles and the phase $\varphi $. One
finds:
\begin{eqnarray}
\Theta & = & (2.30 \pm 0.09)^0, \quad \Theta_u = (4.87 \pm 0.98)^0, \nonumber\\
\Theta_d & = & (11.71 \pm 1.09)^0, \quad \varphi = (91.1 \pm 11.8)^0
\end{eqnarray}
\\
These values are consistent with the ones given above, however the errors are
significantly smaller.
f) The phase $\varphi$ is
a phase difference between the contributions to $V_{us}$ (or $V_{cd}$)
from the u-channel mixing and the d-channel mixing. The phase $\varphi$ is
not likely to be $0^{\circ}$ or $180^{\circ}$, according
to the experimental values given above, even though the measurement of
$CP$ violation in $K^0$-$\bar{K}^0$ mixing is not taken
into account. For $\varphi =0^{\circ}$, one
finds $\tan\theta_{\rm C} = 0.14 \pm 0.08$; and for $\varphi =
180^{\circ}$, one gets $\tan\theta_{\rm C} = 0.30 \pm 0.08$. Both
cases are hardly consistent with the value of $\tan\theta_{\rm
C}$ obtained from experiments ($\tan\theta_{\rm C} \approx
|V_{us}/V_{ud}| \approx 0.226$).
g) The $CP$-violating phase $\varphi$ in the flavor mixing matrix $V$ can be
determined from $|V_{us}|$ ($= 0.2205 \pm 0.0018$)
through the following formula, obtained easily from Eq. (12):
\begin{equation}
\varphi \; =\; \arccos \left ( \frac{s^2_{\rm u} c^2_{\rm d} c^2 +
c^2_{\rm u} s^2_{\rm d} - |V_{us}|^2}{2 s_{\rm u} c_{\rm u} s_{\rm d}
c_{\rm d} c} \right ) \; .
\end{equation}
\\
The two-fold ambiguity associated with the value of $\varphi$, coming
from $\cos\varphi = \cos (2\pi - \varphi)$, is removed if one
takes $\sin\varphi >0$ into account.
More precise measurements of the angles $\theta_{\rm u}$ and
$\theta_{\rm d}$ in the forthcoming experiments of $B$ physics will
remarkably reduce the uncertainty of $\varphi$ to be determined from Eq.
(10). This approach is of course complementary to the direct determination of
$\varphi$ from $CP$ asymmetries in some weak $B$-meson decays into hadronic
$CP$ eigenstates \cite{Sanda80}.
Considering the presently known phenomenological constraints (see e.g.
ref. (7) that the value of $\varphi$ is most likely in the
range $40^{\circ}$ to $120^{\circ}$, the central value is
$\varphi \approx 81^{\circ}$.
Note that $\varphi$ is essentially independent of the angle $\theta$,
due to the tiny observed value of the latter.
Once $\tan\theta_{\rm d}$ is precisely measured, one shall be able to fix the
magnitude of $\varphi$ to a satisfactory degree of accuracy.\\
h) It is well--known that $CP$ violation in the flavor mixing matrix $V$ can
be described by the quantity ${\cal J}$ \cite{Jarlskog89}:
\begin{equation}
{\rm Im} \left( V_{il} V_{jm} V^*_{im} V^*_{jl} \right) = {\cal J}
\sum\limits^{3}_{k,n=1} \left( \epsilon_{ijk}\epsilon_{lmn} \right] \, .
\end{equation}
In our parametrisation ${\cal J}$ reads
\begin{equation}
{\cal J} = s_uc_us_dc_ds^2 \, \, c sin \varphi
\end{equation}
Obviously $\varphi = 90^{\circ }$ leads to the maximal value of ${\cal J}$.
Indeed $\varphi =90^{\circ}$, a particularly interesting case for $CP$
violation, is quite consistent with
current data. Since in our description of the flavor mixing the
complex phase $\varphi$ is related in a simple way to the phases of
the quark mass terms, the case $\varphi = 90^{\circ}$ is especially
interesting. It can hardly be an accident, and this case should be
studied further. The possibility that the phase $\varphi$ describing
$CP$ violation in the standard model is given by the algebraic number
$\pi/2$ should be taken seriously. It may provide a useful clue
towards a deeper understanding of the origin of $CP$ violation
and of the dynamical origin of the fermion masses, and might be a signed for
an interesting new symmetry (see also ref. (15)).
The case $\varphi =90^{\circ}$ has been
denoted as ``maximal'' $CP$ violation. It implies in our framework
that in the complex
plane the u--channel and d--channel mixings are perpendicular to each
other. In this special case (as well as $\theta\rightarrow 0$), we have
\begin{equation}
\tan^2\theta_{\rm C} \; =\; \frac{\tan^2\theta_{\rm u} ~ + ~
\tan^2\theta_{\rm d}}{1 ~ + ~ \tan^2\theta_{\rm u} \tan^2\theta_{\rm
d}} \; .
\end{equation}
To a good approximation (with the relative error $\sim 2\%$),
one finds $s^2_{\rm C} \approx s^2_{\rm u} + s^2_{\rm d}$.
h) At future $B$-meson factories, the study of $CP$ violation will
concentrate on measurements of the unitarity triangle
\begin{equation}
S_u ~ + ~ S_c ~ + ~ S_t \; = \; 0 \; ,
\end{equation}
where $S_i \equiv V_{id} V^*_{ib}$ in the complex
plane. The inner angles of this triangle
are as usual given by:
\begin{eqnarray}
\alpha & \equiv & \arg (- S_t S^*_u ) \; , \nonumber \\
\beta & \equiv & \arg (- S_c S^*_t ) \; , \nonumber \\
\gamma & \equiv & \arg (- S_u S^*_c ) \; .
\end{eqnarray}
In terms of the parameters
$\theta$, $\theta_{\rm u}$, $\theta_{\rm d}$ and $\varphi$, we obtain
\begin{eqnarray}
\sin (2\alpha) & = & \frac{2 c_{\rm u} c_{\rm d} \sin\varphi \left
( s_{\rm u} s_{\rm d} c + c_{\rm u} c_{\rm d} \cos\varphi \right )}{s^2_{\rm
u} s^2_{\rm d} c^2 + c^2_{\rm u} c^2_{\rm d} + 2 s_{\rm u} c_{\rm u} s_{\rm d} c_{\rm d} c
\cos\varphi} \; , \nonumber \\ \nonumber \\
\sin (2\beta) & = & \frac{2 s_{\rm u} c_{\rm d} \sin\varphi \left
( c_{\rm u} s_{\rm d} c - s_{\rm u} c_{\rm d} \cos\varphi \right )}{c^2_{\rm
u} s^2_{\rm d} c^2 + s^2_{\rm u} c^2_{\rm d} - 2 s_{\rm u} c_{\rm u} s_{\rm d} c_{\rm d} c
\cos\varphi} \; .
\end{eqnarray}
To an excellent degree of accuracy, one finds $\alpha \approx
\varphi$. In order to illustrate how accurate this relation is, let us
use the central values of $\theta$, $\theta_{\rm u}$ and $\theta_{\rm
d}$ (i.e., $\theta = 2.25^{\circ}$, $\theta_{\rm u} = 4.57^{\circ}$
and $\theta_{\rm d} = 12.7^{\circ}$). Then one arrives at
$\varphi - \alpha \approx 1^{\circ}$ as well as $\sin (2\alpha)
\approx 0.34$ and $\sin (2\beta) \approx 0.65$.
It is expected that $\sin (2\alpha)$ and $\sin (2\beta)$
will be directly measured from the $CP$ asymmetries in
$B_d \rightarrow \pi^+\pi^-$ and $B_d \rightarrow J /\psi K_S$ modes
at a $B$-meson factory.
Note that the three sides of the unitarity triangle
can be rescaled by $|V_{cb}|$. In a very good approximation
(with the relative error $\sim 2\%$), one arrives at
\begin{equation}
|S_u| ~ : ~ |S_c| ~ : ~ |S_t| \; \approx \; s_{\rm u} c_{\rm d} ~ : ~
s^{~}_{\rm C} ~ : ~ s_{\rm d} \; .
\end{equation}
Equivalently, one can obtain
\begin{equation}
s_{\alpha} ~ : ~ s^{~}_{\beta} ~ : ~ s_{\gamma} \; \approx \; s^{~}_{\rm C}
~ : ~ s_{\rm u} c_{\rm d} ~ : ~ s_{\rm d} \; ,
\end{equation}
where $s_{\alpha} \equiv \sin\alpha$, etc.
Comparing this triangle with the LQ--triangle we find that they are
indeed congruent with each other to a high degree of accuracy.
The congruent relation between these two triangles is particularly
interesting, since the LQ--triangle is essentially a feature of the physics
of the first two quark families, while the unitarity triangle by
defination is
linked to all three families. In this connection it is of special
interest to note that in models which specify the textures of the mass
matrices the Cabibbo triangle and hence the three angles of the unitarity
triangle can be fixed by the spectrum of the light quark masses and
the $CP$-violating phase $\varphi$.\\
j) Compared with the standard parametrization of the flavor mixing
matrix $V$ the parametrization discussed here has an additional
advantage: the renormalization-group evolution of $V$, from the weak
scale to an arbitrary high energy scale, is
to a very good approximation associated only with the angle $\theta$. This can
easily be seen if one keeps the $t$ and $b$ Yukawa couplings only
and neglects possible threshold effect in the one-loop
renormalization-group equations of the Yukawa matrices \cite{RGE}.
Thus the parameters $\theta_{\rm u}$, $\theta_{\rm d}$ and $\varphi$
are essentially independent of the energy scale, while $\theta$ does
depend on it and will change if the underlying scale is shifted, say
from the weak scale ($\sim 10^2$ GeV) to the grand unified theory
scale (of order $ 10^{16}$ GeV). In short, the heavy quark mixing is
subject to renormalization-group effects; but the u- and d-channel
mixings are not, likewise the phase $\varphi$ describing $CP$
violation and the LQ--triangle as a whole. It follows that only the angle
$\theta $, but not $\Theta _u, \Theta _d$ or $\varphi $, depends in its
behaviour on the reference energy scale and is increased on the underlying
model, e.\ g.\ on whether there is a supersymmetric extension of the Standard
Model or not.
We have presented a new description of the flavor mixing
phenomenon, which is based on the phenomenological fact that the quark
mass spectrum exhibits a clear hierarchy pattern. This leads uniquely
to the interpretation of the flavor mixing in terms of a heavy quark
mixing, followed by the u-channel and d-channel mixings. The complex
phase $\varphi$, describing the relative orientation of the u-channel
mixing and the d-channel mixing in the complex plane, signifies
$CP$ violation, which is a phenomenon primarily linked to the physics
of the first two families. The Cabibbo angle is not a basic mixing
parameter, but given by a superposition of two terms involving the
complex phase $\varphi$. The experimental data suggest that the phase
$\varphi$, which is directly linked to the phases of the quark mass
terms, is close to $90^{\circ}$. This opens the possibility to
interpret $CP$ violation as a maximal effect, in a similar way as
parity violation.
Our description of flavor mixing has many clear advantages compared
with other descriptions. We propose that it should be used in the
future description of flavor mixing and $CP$ violation, in particular,
for the studies of quark mass matrices and $B$-meson physics.
The description of the flavor mixing phenomenon given above is of special
interest if for the $U$ and $D$ channel mixing the quark mass textures
discussed first in \cite{Fritzsch77} are applied (see also \cite{FX98}).
In that case one finds \cite{RGE} (apart from small corrections)
\begin{equation}
{\rm tan} \Theta _d = \sqrt{\frac{m_d}{m_s}}
\end{equation}
\[
{\rm tan} \Theta _u = \sqrt{\frac{m_u}{m_c}} \, .
\]
The experimental value for ${\rm tan} \, \Theta _u$ given by the ratio
$V_{ub} / V_{cb} $ is in agreement with the observed value for
$\left( m_u / m_c \right) ^{1/2} \approx 0.07$, but the errors for both
$\left( m_u / m_c \right) ^{1/2}$ and $V_{ub} / V_{cb}$ are comparable
(about 25\%).
The angle $\Theta_d $ is expected to be about 12.6$^{\circ}$, if we use a
mass ratio $m_s / m_d \approx 20$, as obtained in chiral perturbation theory.
This agrees well with the experimental values discussed above.
As emphasized in ref.\ (17), the phase angle $\varphi $ is very close
to 90$^{\circ }$, implying that the LQ--triangle and the
unitarity triangle are essentially rectangular triangles. In particular the
angle $\beta $ which is likely to be measured soon in the study of the
reaction $B^{\circ } \rightarrow J / \psi K^{\circ }_s$ is expected to be close
to $20 ^{\circ }$.
It will be very interesting to see whether the angles $\Theta _d$ and
$\Theta _u$ are indeed given by the square roots of the light quark mass
ration $m_d / m_s$ and $m_u /m_c$, which imply that the phase $\varphi$
is close to or exactly $90 ^{\circ }$. This would mean that the light quarks
play the most important r$\hat{\rm o}$le in the dynamics of flavor mixing and
$CP$ violation.\\
\\
\newpage
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,426 |
Investing in the best dividend stocks is not only about buying companies with big and growing cash flows. Investors need to understand the competitive strengths in the business producing those cash flows in order to position their portfolio in companies having enough soundness to sustain capital distributions over time.
Brand power is a crucial source of competitive strength in the consumer business, and companies such as Coca-Cola (NYSE: KO), Procter & Gamble (NYSE: PG), and Colgate-Palmolive (NYSE: CL) benefit from rock-solid brand power, allowing them to deliver consistently growing capital distributions for shareholders over the long term. Dividends don't only provide income for investors; a solid trajectory of dividend growth is a strong reflection about a company´s quality and fundamental strengths. Coca-Cola, Procter & Gamble, and Colgate-Palmolive rely on powerfull brands to differentiate their products from the competition, and this says a lot about these companies and their ability to consistently increase dividends over years to come. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,562 |
Friedrich Hastenpflug (* 16. März 1812 in Nieder-Wildungen; † 14. Mai 1877 in Korbach) war ein deutscher Richter und Politiker.
Hastenpflug war der Sohn des Registrators Johann Friedrich Hastenpflug und dessen Ehefrau Maria (geborene Dietz). Er heiratete am 6. Juni 1844 in Nieder-Wildungen Mathilde Kleinschmit. Hastenpflug studierte ab 1832 in Göttingen Rechtswissenschaften. 1838 wurde er Advokat in Nieder-Wildungen wo er 1843 bis 1850 Stadtsekretär war. 1850 wurde er vertretungsweise und 1851 definitiv Kreisrichter in Pyrmont. 1860 wurde er in gleicher Funktion nach Korbach versetzt. 1869 wurde er Amtsrichter am Amtsgericht Korbach und später Amtsgerichtsrat.
Von 1853 bis 1859 war er für den Wahlkreis Pyrmont Abgeordneter im Landtag des Fürstentums Waldeck-Pyrmont. 1854 bis 1859 gehörte er auch dem Spezial-Landtag für das Fürstentum Pyrmont an. 1871 bis 1877 war er erneut (diesmal für den Kreis des Eisenberges) Mitglied des Landtags des Fürstentums Waldeck-Pyrmont.
Literatur
Reinhard König: Die Abgeordneten des Waldeckischen Landtags von 1848 bis 1929 (= Schriften des Hessischen Staatsarchivs Marburg. Bd. 3 = Vorgeschichte und Geschichte des Parlamentarismus in Hessen. Bd. 3). Hessisches Staatsarchiv, Marburg 1985, ISBN 3-88964-122-9, S. 49–50.
Jochen Lengemann: MdL Hessen. 1808–1996. Biographischer Index (= Politische und parlamentarische Geschichte des Landes Hessen. Bd. 14 = Veröffentlichungen der Historischen Kommission für Hessen. Bd. 48, 7). Elwert, Marburg 1996, ISBN 3-7708-1071-6, S. 169.
Jochen Lengemann: MdL Waldeck und Pyrmont 1814–1929. Biographisches Handbuch für die Mitglieder der Waldeckischen und Pyrmonter Landstände und Landtage (= Politische und parlamentarische Geschichte des Landes Hessen. Bd. 24 = Veröffentlichungen der Historischen Kommission für Hessen. Bd. 48, 16). Historische Kommission für Hessen, Marburg/Wiesbaden 2020, ISBN 978-3-923150-76-2, Nr. WA 115.
Weblinks
Landtagsabgeordneter (Fürstentum Waldeck-Pyrmont)
Landtagsabgeordneter (Fürstentum Pyrmont)
Richter (Amtsgericht)
Deutscher
Geboren 1812
Gestorben 1877
Mann
Richter (deutsche Geschichte) | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,130 |
\section{Introduction}
Extremely large magnetoresistance, i.e. dramatic increase in the resistance of a material upon applied magnetic fields, has recently attracted great interest~\cite{Mun12PRB, Ali14Nat, Liang15NatMat}. Materials with this type of property can be potentially very useful for applications such as magnetic field sensors, data storage and processing etc. Interestingly, some of these extremely large magnetoresistive materials are hosts for other exotic properties. Among the first few extremely large magnetoresistive materials, PtSn${}_{4}$~\cite{Mun12PRB} has been reported to host unusual Dirac node arc structure, that is the Dirac dispersion extending in momentum space in one dimension and gapped out at both ends~\cite{Wu2016Dirac}. Another material with extremely large magnetoresistance, Cd${}_{3}$As${}_{2}$~\cite{Liang15NatMat} was shown to be one of the first three-dimensional Dirac semimetals with linear dispersion along all three momentum directions~\cite{Wang13PRB, Neupane14NatCom, Liu14NatMat, Borisenko14PRL, Narayanan15PRL}. Extremely large magnetoresistive material, WTe${}_{2}$~\cite{Ali14Nat} has been reported to exhibit pressure-induced superconductivity~\cite{Kang15NatComm, Pan15NatComm}, and a pressure-induced Lifshitz phase transition was proposed to explain the emergence of the superconductivity~\cite{Kang15NatComm}. Surprisingly, a temperature-induced Lifshitz transition was recently reported in WTe${}_{2}$. The significant shift of the chemical potential with moderate temperature change is caused by the close proximity of electron and hole band extrema to the chemical potential~\cite{Wu15PRL}. More interestingly, WTe${}_{2}$ was the first material proposed to be a type-II Weyl semimetal~\cite{Soluyanov2015Type}. Unlike the type-I Weyl semimetals~\cite{Huang15NatCom, Weng15PRX, Xu15SciDis, Yang15NatPhys, Lv15NatPhys, Lv2015Experimental, Xu15NatPhys}, such materials have the Weyl points emerging at the touching points of the electron and hole pockets~\cite{Soluyanov2015Type}. Recently, multiple ARPES measurements reported the presence of the Fermi arc surface states in these compounds~\cite{Belopolski2016Fermi, Huang2016Spectroscopic, Tamai2016Fermi, Deng2016Experimental, Jiang2016Observation, Liang2016Electronic, Xu2016Discovery, Bruno2016Surface, Wang2016Observation, Wu2016Observation, Feng2016Spin}. Photon energy dependence measurements have been used to demonstrate the two-dimensionality (surface origin) of the Fermi arc in WTe${}_{2}$~\cite{Bruno2016Surface, Wu2016Observation}. However, detailed measurements of three-dimensional bulk electronic structures are still lacking.
ARPES has been known as the most direct technique for probing the electronic structures of materials~\cite{Damascelli03RMP, Campuzano04PS}. Early ARPES and density-functional based augmented spherical wave calculations have revealed the semimetallic nature of WTe${}_{2}$~\cite{Augustin00PRB}. However, no details close to the Fermi level were clearly resolved. More recent, high resolution ARPES data has revealed one pair of electron pockets and one pair of hole pockets of similar size, supporting the electron-hole carrier compensation theory as the primary origin of the extremely large magnetoresistance~\cite{Pletikosic14PRL}. By varying the incident photon energies in the 40--70~eV range, the ${k}_{z}$ dispersion of the states was mapped out with some bands showing low dispersion and some showing variations in intensity, but no solid conclusion can be drawn from these data~\cite{Pletikosic14PRL}. Another study reported presence of nine Fermi pockets. However, no significant photon energy dependence along the out of plane direction was observed~\cite{Jiang2015Signature}. On the other hand, magnetoresistance measurements with varying magnetic field applied at an angle with respect to the $c$ axis of the sample have led to the conclusion of three-dimensional electronic structure in WTe${}_{2}$~\cite{Thoutam2015Temperature}. Furthermore, the results from quantum oscillations--another technique to probe the Fermi surface structure--have come to similar conclusions. Angle resolved quantum oscillation measurements implied strong three-dimensionality of the band structure in this material~\cite{Zhu15PRL}. The analysis of quantum oscillations is a powerful technique to measure the extrema of the Fermi surface topology. However, one should be cautious when assigning oscillation frequencies to particular FS pockets, e.g. in measurements performed under applied pressure, one group assigned the peaks that survived at high pressure to a particular pair of electron and hole pockets~\cite{Cai15PRL}, however, the Hall effect measurements from another group found that only electron carriers were present under high pressure~\cite{Kang15NatComm}, a result that is consistent with our report of temperature-induced Lifshitz transition in WTe${}_{2}$~\cite{Wu15PRL}. Thus, in order to demonstrate the three-dimensionality of the electronic structure in WTe${}_{2}$, ultrahigh resolution ARPES measurements with fine tunable incident photon energies have real experimental advantage.
Here, we use temperature- and field-dependent resistivity measurements and ultrahigh resolution, tunable VUV laser-based ARPES to probe the three-dimensionality of the bulk electronic structure in WTe${}_{2}$. In the SdH oscillations, a low frequency peak was observed and can be explained by our photon energy dependent ARPES measurements. With the ability of fine tuning of the incident photon energy from 5.77 to 6.7~eV, we have determined Fermi surface and band structure with very high precision. At the incident photon energy of 6.7~eV, we can detect a bulk FS that consists of two pairs of electron pockets and two pairs of hole pockets, while the top of another band is located just below the Fermi level at the $\Gamma$ point. When decreasing the incident photon energy to 6.36~eV, another pair of tiny electron pockets is detected close to the $\Gamma$ point, which corresponds to the so far unaccounted for, low oscillation frequency observed in the quantum oscillation measurements~\cite{Cai15PRL, Wu15PRL}. Further decreasing the incident photon energy, we observe the disappearance of the tiny electron pockets, thus the bulk FS has only two pairs of electron and hole pockets left for this range of ${k}_{z}$ momenta. Detailed band dispersion along several cuts for different incident photon energies are presented, demonstrating the strong three-dimensionality of the bulk electronic structure in WTe${}_{2}$. These results are consistent with the band structure calculations and quantum oscillations~\cite{Ali14Nat, Cai15PRL, Wu15PRL}. Our photon energy dependent ARPES measurements have solved the mystery of the low frequency peak reported by several quantum oscillation measurements~\cite{Cai15PRL, Wu15PRL}.
\section{Experimental details}
Single crystals of WTe${}_{2}$ were grown by solution method~\cite{Canfield92PMPB, Canfield2016Use}, following the procedure describe in Ref.~\onlinecite{Wu15PRL}. The resulting crystals were blade or ribbon like in morphology with typical dimensions of 3 $\times$ 0.5 $\times$ 0.01~mm with the crystallographic $c$ axis being perpendicular to the crystal surface; the crystals are readily cleaved along this crystal surface.
Magnetic field dependent electrical transport measurements were carried out in a Quantum Design Physical Property Measurement System (PPMS) for $H \le 14$~T. Samples for standard four-probe resistivity measurement were prepared by attaching four Pt wires using Epotek-H20E silver epoxy. The field was applied parallel to the crystallographic $c$ axis, and the current was along the crystallographic $a$ axis. Magnetoresistance was measured at 1.8, 2.5, 4, 6, 8, and 10~K.
Samples used for ARPES measurements were cleaved \textit{in situ} at 40~K under ultrahigh vacuum (UHV). The data were acquired using a tunable VUV laser ARPES system, that consists of a Scienta R8000 electron analyzer, picosecond Ti:Sapphire oscillator and fourth harmonic generator~\cite{Jiang14RSI}. Data were collected with a tunable photon energies from 5.3 to 6.7~eV. Momentum and energy resolutions were set at $\sim$ 0.005~\AA${}^{-1}$ and 2~meV. The size of the photon beam on the sample was $\sim$30~$\mu$m.
\section{Experimental results}
\begin{figure}
\includegraphics[width = 3in]{Fig1.pdf}%
\caption{(color online) Quantum oscillation analysis on WTe$_{2}$.
(a) Magnetoresistance measured at $T=$1.8, 2.5, 4, 6, 8, and 10~K.
(b) Shubnikov-de Haas oscillation after subtracting the background.
(c) Fast Fourier transform (FFT) analysis of quantum oscillation.
(d) Temperature dependence of the oscillation amplitude as a function of temperatures for the peak, $F^{*}$. The closed circles are the data and solid line is the fitted line of Lifshitz-Kosevich formula.
\label{fig:Fig1}}
\end{figure}
\begin{figure*}[bt]
\includegraphics[width = 6in]{Fig2.pdf}%
\caption{Fermi surface plots and band dispersion measured at different photon energies.
(a)-(d) Fermi surface plots measured at photon energies of 6.70, 6.36, 6.05, and 5.77 eV, respectively. The red solid circles (from left to right) correspond to the quantum oscillation frequencies of ${F}^{3}$, ${F}^{2}$, ${F}^{4}$, and ${F}^{1}$, respectively. The red dashed circles correspond to the the quantum oscillation frequency of ${F}^{*}$.
(e)-(h) Band dispersion along the black dashed lines in (a)-(d), respectively. The red dashed lines are guide to the eye.
\label{fig:Fig2}}
\end{figure*}
\begin{figure*}[tb]
\includegraphics[width = 6.5in]{Fig3.pdf}%
\caption{Band dispersion, momentum dispersion curves, and energy dispersion curves measured at different photon energies.
(a)-(d) Band dispersion along the cut \#1 in Fig.~\ref{fig:Fig2}(a) measured at photon energies of 6.7, 6.36, 6.05, and 5.77 eV, respectively.
(e) Momentum dispersion curves at the E${}_{F}$ of (a)-(d).
(f)-(i) Band dispersion along the cut \#2 in Fig.~\ref{fig:Fig2}(a) measured at photon energies of 6.7, 6.36, 6.05, and 5.77 eV, respectively.
(j) Momentum dispersion curves at the E${}_{F}$ of (f)-(i).
(k)-(n) Band dispersion along the cut \#3 in Fig.~\ref{fig:Fig2}(a) measured at photon energies of 6.7, 6.36, 6.05, and 5.77 eV, respectively.
(o) Energy dispersion curves along the red dashed lines in (k)-(n). Black arrows point to the locations of the lower hole bands in (k)-(n).
(p) Diameters of the electron and hole pockets measured at different photon energies extracted from the momentum dispersion curves in (e) and (j).
\label{fig:Fig3}}
\end{figure*}
Magnetoresistance (MR) shows parabolic behavior without any saturation at high field as shown in Fig.~\ref{fig:Fig1}(a). In order to analyze the quantum oscillation spectra, we subtracted the background using a second order polynomial function to fit the background MR in the range of 6~$\le H \leq$~14~T for all temperatures. The oscillations show periodic behavior in 1/$H$ as shown in Fig.~\ref{fig:Fig1}(b).
The frequencies of the oscillation were obtained by FFT analysis shown in Fig.~\ref{fig:Fig1}(c). Five frequencies, including ${F}^{1} =92~\textrm{T}$, ${F}^{2} = 132~\textrm{T}$, ${F}^{3} = 152~\textrm{T}$, ${F}^{4} = 172~\textrm{T}$ and ${F}^{5} = 264~\textrm{T}$, are similar to published results~\cite{Cai15PRL, Zhu15PRL, Wu15PRL}. Interestingly, a new low frequency peak, ${F}^{*} = 10~\textrm{T}$, is also clearly observed in our data. The amplitude of the ${F}^{*}$ decreases with increasing temperature as shown in Fig.~\ref{fig:Fig1}(d). Note that for the sake of consistency the exactly same data acquisition and processing protocol was followed for all temperatures. The observed decrease of the oscillation amplitude is due to the temperature induced scattering of electrons, described by the Lifshitz-Kosevich formula~\cite{Shoenberg1984Magnetic}:
\begin{equation}
{ A }_{ t }\propto { B }^{ 1/2 }{ \left| \frac { { \partial }^{ 2 }S_{ t } }{ \partial { k }_{ H }^{ 2 } } \right| }^{ -1/2 }{ R }_{ T }{ R }_{ D }{ R }_{ S }
\end{equation}
\noindent where the factor ${R}_{T}$ is related to thermal damping, ${R}_{D}$ is related to impurities and ${R}_{S}$ is related to spin Zeeman splitting and superposition of spin-up and spin-down oscillations. The thermal damping part ${R}_{T}$ is defined as
\begin{equation}
{ R }_{ T }=\frac { \alpha { m }^{ * }T/B }{ sinh(\alpha { m }^{ * }T/B) }
\end{equation}
\noindent where $\alpha = 2 {\pi}^{2} c {k}_{B} / e \hbar$. Using this equation, we calculated the effective mass of the carriers linked to the oscillation frequency ${F}^{*}$, ${m}^{*}_{{F}^{*}} = 0.29 \pm 0.01~{m}_{e}$.
To match this small frequency observed in quantum oscillation to a specific Fermi surface, we carried out photon energy dependent ARPES measurements. By varying the incident photon energies, we are able to map out the band dispersion along the out of plane, ${k}_{z}$ direction~\cite{Damascelli03RMP,Campuzano04PS}. Synchrotron radiation based ARPES systems are often used for ${k}_{z}$ dispersion mapping due to the large tunable range of the incident photon energies. However, tuning photon energies with usually utilized coarse steps $\ge$~1~eV can result in some important details being missed along very key ${k}_{z}$ direction~\cite{Pletikosic14PRL, Jiang2015Signature}. By using tunable VUV laser ARPES with very fine energy steps, we mapped out the ${k}_{z}$ dispersion of WTe${}_{2}$ in great detail. Fig.~\ref{fig:Fig2} shows the FS and band dispersion measured using incident photon energies of 6.70, 6.36, 6.05, and 5.77~eV, as indicated at the top center of each plot. In Figs.~\ref{fig:Fig2}(a)-(d), we can see that the FS of WTe${}_{2}$ measured using different photon energies look similar, with two pairs of electron pockets and two pairs of hole pockets in the first BZ. However, a significant variation between the data sets is also observed. The hole band at the $\Gamma$ point has different intensities and curvatures, although none of them crosses the Fermi level as shown in Figs.~\ref{fig:Fig2}(e)-(h). Furthermore, the FS close to the $\Gamma$ point in Fig.~\ref{fig:Fig2}(b) shows a dumb-bell like structure, whereas the other three FSs show only a single hole band at the $\Gamma$ point. The band dispersion along the black dashed line in Fig.~\ref{fig:Fig2}(b) is shown in panel (f). On either side of the $\Gamma$ point, a tiny electron pocket is visible [marked by the red dashed lines in panel (f)], which is different from the band dispersion observed using other photon energies.
To directly compare the quantum oscillation results with the ARPES measurements, we have plotted the extremal orbits with the areas determined from quantum oscillation measurements on top of the Fermi surface plot as shown in Fig.~\ref{fig:Fig2}(b). The corresponding extremal areas of the Fermi surface were calculated using the Onsager relation, ${F}^{i} = \frac{\hbar c} {2 \pi e} {S}^{i}$~[Ref.~\onlinecite{Shoenberg1984Magnetic}] with ${S}_{{F}^{1}} = 0.00874~{{\textrm{\AA}}^{-2}}$, ${S}_{{F}^{2}} = 0.01262~{{\textrm{\AA}}^{-2}}$, ${S}_{{F}^{3}} = 0.01456~{{\textrm{\AA}}^{-2}}$, ${S}_{{F}^{4}} = 0.0165~{{\textrm{\AA}}^{-2}}$, and ${S}_{{F}^{*}} = 0.000971~{{\textrm{\AA}}^{-2}}$. For simplicity, we assume that the areas obtained from quantum oscillations are from simple circle/ellipse orbit extrema and the corresponding shapes are plotted in Fig.~\ref{fig:Fig2}(b). We can clearly see a good match between the quantum oscillation results and ARPES measurements of the Fermi surface. Furthermore, the electronic structure calculations that take into account the spin-orbit coupling in WTe${}_{2}$ bring extra tiny electron pockets close to the $\Gamma$ point~\cite{Ali14Nat}. Thus, our ARPES results have solved the mystery of this unaccounted for, low frequency quantum oscillation peaks. We should note that as the electronic structure of WTe${}_{2}$ is very sensitive to pressure/strain~\cite{Kang15NatComm, Pan15NatComm, Soluyanov2015Type, Wu2016Observation}, it is possible that these tiny electron pockets might be suppressed in some of the quantum oscillation or ARPES measurements~\cite{Zhu2015Quantum, Wu2016Observation}
Figure~\ref{fig:Fig3} shows the detailed band dispersion measured using various photon energies. Panels (a)--(d), (f)--(i), and (k)--(n) present the band dispersions measured using photon energy of 6.7, 6.36, 6.05 and 5.77~eV, respectively, and correspond to the cuts as marked \#1, 2, and 3 in Fig.~\ref{fig:Fig2}(a). In panels (a)--(d), only minor intensity differences can be seen between the four measurements. At the photon energy of 6.05 and 5.77 eV, the electron pockets are clear and symmetric. On the other hand, the electron pockets measured at the photon energy of 6.7 and 6.36 eV are not symmetric in intensity, probably due to the matrix elements effect. To quantify the electron pocket sizes in panels (a)--(d), we have plotted the momentum distribution curves (MDCs) at the Fermi level ${E}_{F}$ in Fig.~\ref{fig:Fig3}(e). The peak locations of the MDCs show clear differences across these four photon energies (peak locations of the left branches are aligned for easy comparison). Panels (f)--(i) present the band dispersion from cut \#2, which clearly shows that the hole pocket measured with 5.77 eV photons is significantly smaller than the other three. Panel (j) shows the MDCs at the ${E}_{F}$ from panels (f)--(i), illustrating different hole pocket sizes [also left aligned as in (e)]. Panels (k)--(n) show the photon energy dependence of the hole bands at the $\Gamma$ point [cut \#3 in Fig.~\ref{fig:Fig2}(a)]. Two hole bands can be clearly seen at the $\Gamma$ point with different separations between them for different photon energies. Panel (o) shows the energy distribution curves (EDCs) from panels (k)--(n), where the black arrows point to the peak locations in the lower hole bands. The upper hole bands sit at roughly the same binding energy for these photon energies, but none of them crosses the Fermi level. On the other hand, the distance between the upper and lower hole bands is very different across these photon energies, with 5.77 eV showing the maximum separation. By fitting two Lorentzian functions to the MDCs in panels (e) and (j), we calculate the electron/hole pocket sizes and summarize the results in panel (p). With the decreasing incident photon energy, the size of the electron pocket decreases and then increases. On the other hand, the size of the hole pocket increases and then decreases. This trend (strong three-dimensionality along ${k}_{z}$ direction) is consistent with the band structure calculations shown in Ref.~\onlinecite{Ali14Nat}, where the hole pockets have a concave shape and the electron pockets have a convex shape along ${k}_{z}$ direction toward the center of the zone.
\section{Conclusion}
In conclusion, we used temperature- and field-dependent resistivity measurements in tandem with ultrahigh resolution laser ARPES to investigate the detailed electronic structure of WTe${}_{2}$. The photon energy dependence measurements with relatively fine energy steps have revealed the three-dimensional character of the electron and hole pockets along the $\Gamma-Z$ direction. With the increase of the incident photon energy from 5.77 to 6.70~eV (i.e., probing along ${k}_{z}$ direction), we have observed that the hole pocket expands and then shrinks, while the electron pocket displays opposite behavior. Strong photon energy dependence is also observed in the hole bands at the $\Gamma$ point. Furthermore, at the photon energy of 6.36~eV we have revealed a pair of tiny electron pockets sitting at the opposite side of the $\Gamma$ point, providing strong support for the low quantum oscillation frequency peak that was not accounted for in the previous studies~\cite{Wu15PRL, Cai15PRL}.
\begin{acknowledgements}
Research was supported by the US Department of Energy, Office of Basic Energy Sciences, Devision of Materials Science and Engineering. Ames Laboratory is operated for the US Department of Energy by the Iowa State University under Contract No. DE-AC02-07CH11358. Y.W. (Analysis of ARPES data) was supported by Ames Laboratory's Laboratory-Directed Research and Development (LDRD) funding. N.H.J. was supported by the Gordon and Betty Moore Foundation EPiQS Initiative (Grant No. GBMF4411). L.H. was supported by CEM, a NSF MRSEC, under Grant No. DMR-1420451.
\end{acknowledgements}
Raw data for this manuscript is available at \url{http://lib.dr.iastate.edu/ameslab_datasets/}.
| {
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} | 7,937 |
{"url":"https:\/\/www.semanticscholar.org\/paper\/The-art-of-simulating-the-early-universe.-Part-I.-Figueroa-Florio\/1ffa294e157ec3c1366c2a1a2baf7f0a1c276ce8","text":"# The art of simulating the early universe. Part I. Integration techniques and canonical cases\n\n@article{Figueroa2020TheAO,\ntitle={The art of simulating the early universe. Part I. Integration techniques and canonical cases},\nauthor={Daniel G. Figueroa and Adrien Florio and Francisco Torrenti and Wessel Valkenburg},\njournal={Journal of Cosmology and Astroparticle Physics},\nyear={2020},\nvolume={2021}\n}\n\u2022 Published 26 June 2020\n\u2022 Physics\n\u2022 Journal of Cosmology and Astroparticle Physics\nWe present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and FLRW backgrounds, we introduce the basic tools for the discretization of field theories, including lattice gauge invariant techniques. Following, we discuss and classify numerical algorithms, ranging from methods of \ud835\udcaa(\u03b4 t2) accuracy like staggered leapfrog and\u2026\n\n### Electromagnetic bursts from mergers of oscillons in axion-like fields\n\n\u2022 Physics\nJournal of Cosmology and Astroparticle Physics\n\u2022 2021\nWe investigate the bursts of electromagnetic and scalar radiation resulting from the collision, and merger of oscillons made from axion-like particles using 3+1 dimensional lattice simulations of the\n\n### One $\\mu$ to rule them all: CMB spectral distortions can probe domain walls, cosmic strings and low scale phase transitions\n\n\u2022 Physics\n\u2022 2022\n: We present a new probe of purely gravitationally coupled sectors with large anisotropies. These anisotropies are damped via gravitational interactions with the baryon-photon \ufb02uid, which is heated\n\n### Dynamics of Non-minimally Coupled Scalar Fields in the Jordan Frame\n\n\u2022 Physics\n\u2022 2021\nDaniel G. Figueroa, a Adrien Florio, b Toby Opferkuch, 4, 5, c and Ben A. Stefanek d Instituto de F\u0301\u0131sica Corpuscular (IFIC), Universitat de Val\u00e8ncia-CSIC, E-46980, Valencia, Spain. Center for\n\n### Gravitational wave production from preheating with trilinear interactions\n\n\u2022 Physics\n\u2022 2022\n: We investigate the production of gravitational waves (GWs) during preheating with monomial\/polynomial in\ufb02ationary potentials, considering a trilinear coupling \u03c6\u03c7 2 between a daughter \ufb01eld \u03c7 and the\n\n### Dark matter production via a non-minimal coupling to gravity\n\n\u2022 Physics\n\u2022 2022\nWe study postin\ufb02ationary scalar dark matter production via its non-minimal coupling to gravity. During the in\ufb02aton oscillation epoch, dark matter is produced resonantly for a su\ufb03ciently large\n\n### Scalar Dark Matter Production from Preheating and Structure Formation Constraints\n\n\u2022 Physics\n\u2022 2022\nWe investigate the out-of-equilibrium production of scalar dark matter (DM) from the inflaton condensate during inflation and reheating. We assume that this scalar couples only to the inflaton via a\n\n### Characterizing the post-inflationary reheating history, Part II: Multiple interacting daughter fields\n\n\u2022 Mathematics\n\u2022 2022\nWe characterize the post-inflationary dynamics of an inflaton \u03c6 coupled to multiple interacting daughter fields Xn (n = 1, . . . Nd) through quadratic-quadratic interactions g2 n\u03c6 2X2 n. We assume a\n\n### On gravitational preheating\n\n\u2022 Physics\nJournal of Cosmology and Astroparticle Physics\n\u2022 2022\nWe consider dark matter production during the inflaton oscillation epoch. It is conceivable that renormalizable interactions between dark matter and inflaton may be negligible. In this case, the\n\n### Preheating in Palatini Higgs inflation on the lattice\n\n\u2022 Physics\nJournal of Cosmology and Astroparticle Physics\n\u2022 2022\nWe study preheating following Higgs inflation in the Palatini formulation of gravity. We numerically evolve perturbations of the radial mode of the Higgs field and that of three scalars modeling the\n\n## References\n\nSHOWING 1-10 OF 281 REFERENCES\n\n### The Art of Lattice and Gravity Waves from Preheating\n\nA new lattice code HLATTICE is presented, which differs from previous public available codes in the following three aspects: a much higher accuracy is achieved with a modified sixth-order symplectic integrator; scalar, vector, and tensor metric perturbations in synchronous gauge and their feedback to the dynamics of scalar fields are all included.\n\n### Preheating with nonminimal kinetic terms.\n\n\u2022 Physics\nPhysical review letters\n\u2022 2013\nIt is shown that parametric resonance in the matter field along with self-resonance in the inflaton repopulate the universe with matter particles as efficiently as in traditional preheating.\n\n### Non-Abelian chiral instabilities at high temperature on the lattice\n\n\u2022 Physics\n\u2022 2015\nA bstractWe report on an exploratory lattice study on the phenomenon of chiral instabilities in non-Abelian gauge theories at high temperature. It is based on a recently constructed anomalous\n\n### Gravitational waves from Abelian gauge fields and cosmic strings at preheating\n\n\u2022 Physics\n\u2022 2010\nPrimordial gravitational waves provide a very important stochastic background that could be detected soon with interferometric gravitational wave antennas or indirectly via the induced patterns in\n\n### Irreducible background of gravitational waves from a cosmic defect network: Update and comparison of numerical techniques\n\n\u2022 Physics\n\u2022 2020\nCosmological phase transitions in the early Universe may produce relics in the form of a network of cosmic defects. Independently of the order of a phase transition, topology of the defects, and","date":"2022-11-29 08:20:40","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.4205624759197235, \"perplexity\": 4907.085256267185}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-49\/segments\/1669446710690.85\/warc\/CC-MAIN-20221129064123-20221129094123-00621.warc.gz\"}"} | null | null |
var webPage = require('webpage');
var fs = require('fs');
var system = require('system')
// 'file:///users/anders/Downloads/pagedump/sentence.html'
if (system.args.length != 3) {
console.log('Usage: measure.js URL filename');
phantom.exit(1);
}
var inputUrl = system.args[1]
// Prefix of outputFile - not in URL syntax
var outputFile = system.args[2]
var page = webPage.create();
page.viewportSize = { width: 1280, height: 1024 };
//page.paperSize = { width: '1024px', height: '768px', margin: '0px' }
page.open(inputUrl, function(status) {
var boxes = page.evaluate(function() {
var info = Array()
var children = document.getElementsByClassName("char");
for (var i = 0; i < children.length; i++) {
var child = children[i];
var bb = child.getBoundingClientRect()
info.push({text: child.textContent,
id: child.getAttribute("id"),
bottom: bb.bottom,
height: bb.height,
left: bb.left,
right: bb.right,
top: bb.top,
width: bb.width})
}
return info;
});
var stream = fs.open(outputFile+".tsv", 'w');
var columns = ['id', 'text', 'height', 'width', 'top', 'bottom', 'left', 'right']
stream.write(columns.join("\t"))
stream.write("\n")
for (var i in boxes) {
var box = boxes[i]
var line = [box.id, box.text, box.height, box.width, box.top, box.bottom, box.left, box.right]
stream.write(line.join("\t"))
stream.write("\n")
// console.log(boxes[i].text, boxes[i].left);
}
stream.close()
page.render(outputFile+".png")
phantom.exit();
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"redpajama_set_name": "RedPajamaGithub"
} | 3,522 |
package record
import (
"context"
"sync"
"time"
"github.com/ipfs/go-ipfs/Godeps/_workspace/src/bazil.org/fuse"
"github.com/ipfs/go-ipfs/Godeps/_workspace/src/bazil.org/fuse/fs"
)
type nothing struct{}
// ReleaseWaiter notes whether a FUSE Release call has been seen.
//
// Releases are not guaranteed to happen synchronously with any client
// call, so they must be waited for.
type ReleaseWaiter struct {
once sync.Once
seen chan nothing
}
var _ = fs.HandleReleaser(&ReleaseWaiter{})
func (r *ReleaseWaiter) init() {
r.once.Do(func() {
r.seen = make(chan nothing, 1)
})
}
func (r *ReleaseWaiter) Release(ctx context.Context, req *fuse.ReleaseRequest) error {
r.init()
close(r.seen)
return nil
}
// WaitForRelease waits for Release to be called.
//
// With zero duration, wait forever. Otherwise, timeout early
// in a more controller way than `-test.timeout`.
//
// Returns whether a Release was seen. Always true if dur==0.
func (r *ReleaseWaiter) WaitForRelease(dur time.Duration) bool {
r.init()
var timeout <-chan time.Time
if dur > 0 {
timeout = time.After(dur)
}
select {
case <-r.seen:
return true
case <-timeout:
return false
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,060 |
Q: Changing link in UiWebView I have to write very simple application whoes open link in UiWebView but I have a little problem because I want that UiWebView download link from outside data e.g. http://www.example.com/link.txt and check link on every run of application. I tried to download data to NSStringbut I don't have any ideas how to use this with UiWebView. Thanks for help!
A: Create an NSURLRequest with the URL you downloaded. Then you can change the WebView's content with loadRequest(_ request: NSURLRequest)
Swift 2.2:
let myURLString = "the url you read from the file"
let url = NSURL(string: myURLString)
let request = NSURLRequest(url)
//assuming, the property webView is the UIWebView you want to change
webView.loadRequest(request)
Objective-C:
NSString * myURLString = @"the url you read from the file";
NSURL * url = [[NSURL alloc] initWithString:myURLString];
NSURLRequest * request = [[NSURLRequest alloc] initWithURL:url];
//assuming, the property webView ist the UIWebView you want to change
[self.webView loadRequest:request];
More information:
*
*UIWebView
*NSURLRequest
*NSURL
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,661 |
\section{INTRODUCTION}
``While there is considerable optimism that lattice gauge theory will continue to improve as a means of studying nonperturbative QCD, it is also extremely important to pursue covariant, nonperturbative approximation methods. In particular, there is a continuing need for the development of approximation techniques and models which bridge the gap between perturbative QCD and the large amount of low- and intermediate-energy phenomenology in a single covariant framework.'' Thus began Ref.\,\cite{Williams:1989tv} and although these observations remain true today, material progress has been made on all fronts. This contribution provides a glimpse of advances made with DSEs since \emph{Few Body 17}.
The DSEs are a nonperturbative tool for the study of quantum field theory in general \cite{Roberts:1994dr} and continuum strong QCD in particular. They provide a generating tool for perturbation theory and, since QCD is asymptotically free, this means that any model-dependence in the application of these methods can be restricted to the long-range domain. In this mode, the DSEs provide a tool with which strong interaction phenomena can be used to map out, e.g., the behaviour at long range of the interaction between light-quarks. This is not accessible by other means (see, e.g., Refs.\,\cite{Krein:1990sf,Bali:2005bg}). DSEs enable the study of: hadrons as composites of dressed-quarks and -gluons; the phenomena of confinement and DCSB, and therefrom an articulation of any connection between them. The solutions of the DSEs are Schwinger functions, from which all cross-sections can be constructed. Hence they can be used to make predictions for real-world experiments. One merit in this is that any assumptions employed, or guesses made, can be tested, verified and improved, or rejected in favour of more promising alternatives. The modern application of these methods is described in Refs.\,\cite{Roberts:2000aa,Alkofer:2000wg,Maris:2003vk,Fischer:2006ub} with a pedagogical overview provided in Refs.\,\cite{Holl:2006ni,BhagwatSchladming}.
\section{MESONS}
A barrier to the ready application of DSEs is the requirement of truncation, which is made necessary by the coupling between equations. Naturally, the well-known and much-applied weak-coupling expansion reproduces everything accessible in perturbation theory, but that is inadequate to meet hadron physics' nonperturbative challenges. Thus the nonperturbative, systematic, and symmetry-preserving truncation introduced in Refs.\,\cite{Munczek:1994zz,Bender:1996bb} has been a boon, enabling the proof of exact results in QCD.
For example, an exact mass formula for flavour-nonsinglet pseudoscalar mesons was derived \cite{Maris:1997hd}: $f_H m_H^2 = [m_1(\zeta)+m_2(\zeta)]\rho_H(\zeta)$, in which $m_{1,2}(\zeta)$ are the running current-quark masses of the constituents, $\zeta$ is the renormalisation mass-scale, and
\begin{eqnarray}
\label{fH}
f_{H} \, P_\mu &=& Z_2 {\rm tr} \int_q^\Lambda \! \sfrac{1}{2} (T^H)^T \gamma_5
\gamma_\mu {\cal S}(q_+)\, \Gamma_{H}(q;P)\, {\cal S}(q_-)\,,\\
i \rho_{H}\!(\zeta)\, &=& Z_4\,{\rm tr}
\int^\Lambda_q
(T^H)^T \, \gamma_5 \, {\cal S}(q_+)\, \Gamma_{H}(q;P)\, {\cal S}(q_-)\,,
\end{eqnarray}
where: $Z_{2,4}$ are the quark wave-function and Lagrangian-mass renormalisation constants; $\int^\Lambda_q := \int^\Lambda d^4 q/(2\pi)^4$ represents a \textit{Poincar\'e-invariant} regularisation of the integral, with $\Lambda$ the regularisation mass-scale; the matrices $T^H$ are constructed from the generators of $SU(N_f)$ with, e.g., \mbox{$T^{\pi^+}=\mbox{\small $\frac{1}{2}$} (\lambda^1+i\lambda^2)$} providing for the flavour content of a positively charged pion; $q_\pm = q\pm P/2$; ${\cal S}= {\rm diag}[S_u,S_d,S_s,\ldots]$; and $\Gamma_{H}(q;P)$ is the meson's Bethe-Salpeter amplitude. The Gell-Mann--Oakes--Renner relation is a corollary. In deriving these expressions, reference is not made to the magnitude of the current-quark mass. Hence they apply equally to heavy-light systems, in which case follows \cite{Ivanov:1997iu} $f_H \propto 1/\hat m_Q$ and \cite{Ivanov:1998ms}
$m_H \propto \hat m_Q \;\; \mbox{for} \;\; 1/\hat m_Q\sim 0\,,$
where $ \hat m_Q$ is the renormalisation-group-invariant current-quark mass of the meson's heaviest constituent. Moreover, the mass formula applies not just to ground states but to all mesons on the $J^{PC}=0^{-+}$ trajectory, whether they are radial excitations or hybrids. A corollary of this observation is that, as a necessary consequence of chiral symmetry and its dynamical breaking, \cite{Holl:2004fr}
\begin{equation}
\label{fpinzero}
f_{\pi_n}^{\hat m =0} \equiv 0\,, \forall \, n\geq 1\,,
\end{equation}
where $n$ labels a state on the $0^{-+}$ trajectory, with $n=0$ being the ground-state. Thus, in the presence of dynamical chiral symmetry breaking (DCSB) all pseudoscalar mesons except the ground-state decouple from the weak interaction in the chiral limit. (At the true current-quark mass $f_{\pi_1}/f_{\pi_0}=-0.02$ \cite{Holl:2004fr}.) On the other hand, in the absence of DCSB the leptonic decay constant of the ground state $0^{-+}$ also vanishes in the chiral limit, and hence all pseudoscalar mesons are blind to the weak interaction. The result in Eq.\,(\ref{fpinzero}) can be used as a benchmark to tune and validate lattice-QCD techniques that try to determine the properties of excited state mesons \cite{McNeile:2006qy}. Exact results for two-photon decays of pseudoscalar mesons are elucidated in Ref.\,\cite{Holl:2005vu}.
Statements may also be made about scalar mesons. The renormalised Ward-Takahashi identity for the vector vertex can be expressed
\begin{equation}
\label{vwti}
P_\mu i\Gamma_\mu^H(k;P;\zeta) = {\cal S}(k_+) T^H - T^H {\cal S}(k_-) - [{\cal M}^\zeta,T^H] \, i\Gamma_{\mathbf 1}^H(k;P;\zeta)\,,
\end{equation}
where ${\cal M}^\zeta= {\rm diag}[m_u(\zeta),m_d(\zeta),m_s(\zeta),\ldots]$ with, e.g., $m_u(\zeta)$ being the running $u$-quark mass at a renormalisation mass-scale $\zeta$, and $\Gamma_{\mathbf 1}^H(k;P;\zeta)$ is the scalar vertex. Both $\Gamma_\mu^H(k;P;\zeta)$ and $\Gamma_{\mathbf 1}^H(k;P;\zeta)$ can be obtained from an inhomogeneous Bethe-Salpeter equation. In the neighbourhood of a scalar bound-state pole
\begin{equation}
\left. \Gamma_{\mu,\mathbf 1}^{H}(k;P)\right|_{P^2+m_{\sigma_n^H}^2 \approx 0}= \frac{{\cal R}_{\mu,\mathbf 1}}{P^2 + m_{\sigma_n^H}^2} \Gamma_{\sigma_n^H}(k;P) + \; \Gamma_{\mu,\mathbf 1}^{H\,{\rm reg}}(k;P) \,,
\left\{\begin{array}{l}
{\cal R}_\mu = f_{\sigma_n^H} \, P_\mu\\
{\cal R}_{\mathbf 1} = \rho_{\sigma_n^H}(\zeta)
\label{genvv}
\end{array}\right.;
\end{equation}
viz., each vertex may be expressed as a simple pole plus terms regular in its neighbourhood, with $\Gamma_{\sigma_n^H}(k;P)$ representing the bound-state's normalised Bethe-Salpeter amplitude,
and
\begin{eqnarray}
\label{fsigman} f_{\sigma_n^H} \, P_\mu &=& Z_2\,{\rm tr} \int^\Lambda_q
(T^H)^T \gamma_\mu\, {\cal S}(q_+)\, \Gamma_{\sigma_n^H}(q;P)\, {\cal S}(q_-) \,, \\
\label{cpres} \rho_{\sigma_n}\!(\zeta)\, &=& Z_4\,{\rm tr}
\int^\Lambda_q (T^H)^T \, {\cal S}(q_+)\, \Gamma_{\sigma_n^H}(q;P)\, {\cal S}(q_-)\,.
\end{eqnarray}
The residues expressed in Eqs.\,(\ref{fsigman}) and (\ref{cpres}), are gauge invariant and cutoff independent.
If one substitutes Eqs.\,(\ref{genvv}) into Equation~(\ref{vwti}), it follows immediately that
\begin{equation}
\label{fsigma0}
f_{\sigma_n^H} \equiv 0\,,\; \forall H=0^{++}\, \& \,\forall n\,,
\end{equation}
because $[{\cal M}^\zeta,T^{0^{++}}]=0$; namely, for all and any states on a $0^{++}$ trajectory, whether ground-state, radial excitation or hybrid, the leptonic decay constant is zero \cite{Maris:2000ig}. Phenomenological studies that employ the truncation of Refs.\,\cite{Munczek:1994zz,Bender:1996bb} are guaranteed to preserve this result. Any study in which Eq.\,(\ref{fsigma0}) is not manifest violates current conservation.
This says nothing about the scalar residue, $\rho_{\sigma_n}\!(\zeta)$, knowledge of which can be useful, e.g., in constraining analyses of scalar meson production in $D$- and $B$-meson decays \cite{El-Bennich:2006yy}. We have estimated this residue using the renormalisation-group-improved rainbow-ladder truncation of the DSEs introduced in Ref.\,\cite{Maris:1999nt}, which represents the first term in the DSE truncation mentioned above. However, this order is not sophisticated enough to predict, e.g., the mixing angle for the $f_0$. Hence, for illustration, the results in Table~\ref{scalarresidue} are for a pure $\bar uu$ dressed-quark state and a pure $\bar ss$ dressed-quark state. We acknowledge that there are numerous phenomenological difficulties encountered in understanding the scalar states below $1.4\,$GeV (see, e.g., Ref.\,\cite{Pennington:2005am}) and an improved treatment might begin with an estimate of meson-loop effects via the manner employed in Ref.\,\cite{Holl:2005st}.
\begin{table}[t]
\caption{\label{scalarresidue}Ground-state scalar meson quantities calculated using the model of Ref.\,\protect\cite{Maris:1999nt} with $\omega=0.38\,$GeV and $\zeta=\zeta_{19}=19\,$GeV. NB.\ $\rho_{\sigma_n^H}(\zeta) =: m_{\sigma_n^H} \phi_{\sigma_n^H}$; $m_q \rho_{\sigma_n^H}$ is a renormalisation-point-invariant and hence one may use one- or two-loop evolution to define, e.g., $\phi_{\sigma_0^H}(\zeta=\zeta_1=1\,{\rm GeV})$. With one-loop evolution, $\phi_{\sigma_0^{\bar u u}}(\zeta_1)=0.281\,$GeV and $\phi_{\sigma_0^{\bar s s}}(\zeta_1)=0.245\,$GeV.}
\begin{tabular}{@{}cccccc}\hline
\rule{0ex}{3ex}$H$
& $m_q(\zeta_{19}) $ (GeV)
& $m_{\sigma_0^H} $ (GeV)
& $\rho_{\sigma_0^H}(\zeta_{19})$ (GeV$^2$)
& $\phi_{\sigma_0^H}(\zeta_{19})$ (GeV)
& $m_q \rho_{\sigma_0^H}$ (GeV$^3$) \\
$\bar u u$ & 0.0037 & 0.675 & (0.529)$^2$ & 0.415 & (0.101)$^3$ \\
$\bar s s$ & 0.0835 & 1.076 & (0.628)$^2$ & 0.366 & (0.321)$^3$\\\hline
\end{tabular}
\end{table}
There is a conjecture \cite{Glozman:2003bt} that DCSB notwithstanding, the properties of highly excited mesons exhibit a pattern that is consistent with a Wigner realisation of chiral symmetry. In the present context, this could be manifested in
\begin{equation}
\rho_{\sigma_n^H}(\zeta) \approx \rho_{\pi_n^H}(\zeta)\,,\; \mbox{for}\;n\;\mbox{large}\,.
\end{equation}
$\rho_{\pi_n^H}(\zeta)$ and $\rho_{\sigma_n^H}(\zeta)$ are gauge invariant.
Moreover these residues are different for the ground and low-lying excited $0^{-+}$ and $0^{++}$ states; e.g., $\rho_{\pi_0^{\bar uu}}(\zeta_{19})=(0.488\,{\rm GeV})^2$, $\rho_{\pi_1^{\bar uu}}(\zeta_{19})=-(0.471\,{\rm GeV})^2$ and $\rho_{\sigma_1^{\bar uu}}(\zeta_{19})=-(0.382\,{\rm GeV})^2$. Finally, when chiral symmetry is restored at nonzero temperature, one has \cite{Maris:2000ig} $\rho_{\pi_n^H}(\zeta)=\rho_{\sigma_n^H}(\zeta)$.
The broad application of DSEs to meson properties; e.g., the illustration of these and other exact results, and the model-sensitive prediction of experimental observables, is reviewed in Ref.\,\cite{Maris:2003vk}, with many more recent studies identified by reference thereto.
\section{NUCLEONS}
\emph{Few Body 17} heard no mention of DSE baryon structure and interaction studies. In the interim a tolerably realistic picture of nucleons has been composed. This is not to say the study of baryons is at a level of sophistication comparable to that of mesons. Indeed, it is at roughly the same stage as was the study of mesons more than a decade ago; namely, model-building and phenomenology constrained and informed by the best available hadron physics theory.
In quantum field theory a nucleon appears as a pole in a six-point quark Green function, with the residue proportional to the nucleon's Faddeev amplitude. That is obtained from a Poincar\'e covariant Faddeev equation which adds-up all the possible quantum field theoretical exchanges and interactions that can take place between the three dressed-quarks which constitute the nucleon. A merit of the Poincar\'e covariant Faddeev equation is that a modern understanding of the structure of dressed-quarks and -gluons (see Sect.\,5.1 of Ref.~\cite{Holl:2006ni}) is straightforwardly incorporated; viz., effects owing to and arising from the strong momentum dependence of these propagators are realised and exhibited.
The tractable treatment of the Faddeev equation requires a truncation. One is founded \cite{Cahill:1988dx} on the observation that an interaction which describes colour-singlet mesons also generates quark-quark (diquark) correlations in the colour-$\bar 3$ (antitriplet) channel \cite{Cahill:1987qr}. The dominant correlations for ground state octet and decuplet baryons are scalar and axial-vector diquarks. This can be understood on the grounds that: the associated mass-scales are smaller than the baryons' masses \cite{Burden:1996nh,Maris:2002yu}, with models typically giving (in GeV)
$m_{[ud]_{0^+}} = 0.74 - 0.82$,
$m_{(uu)_{1^+}}=m_{(ud)_{1^+}}=m_{(dd)_{1^+}}=0.95 - 1.02$;
the electromagnetic size of these correlations is less than that of the proton \cite{Maris:2004bp} -- $r_{[ud]_{0^+}} \approx 0.7\,{\rm fm}$, from which one may estimate $r_{(ud)_{1^+}} \sim 0.8\,{\rm fm}$ based on the $\rho$-meson/$\pi$-meson radius-ratio \cite{Burden:1995ve,Hawes:1998bz}; and the positive parity of the correlations matches that of the baryons. Both scalar and axial-vector diquarks provide attraction in the Faddeev equation.
\begin{figure}[t]
\centerline
\includegraphics[width=0.60\textwidth]{GEnGMnFB18.eps}}
\vspace*{-4ex}
\caption{\label{GEnGMn}\emph{Solid curve} -- $\mu_n\, G_E^n(Q^2)/G_M^n(Q^2)$ obtained from the form factors calculated in Ref.\,\protect\cite{Alkofer:2004yf,Holl:2005zi}. The band shows the response of the ratio to changes in the axial-vector diquark's electromagnetic properties; viz., variation of $\pm 1$ about the reference values: $\mu_{1^+}=2$, $\chi_{1^+}=1$ and $\kappa_{\cal T} = 2$, and also reflects Monte-Carlo-integration error. \emph{Dashed curve} -- $-(1/6) (r_n^2)^{\rm exp.} Q^2$; \emph{dash-dot curve} -- $-(1/6) (r_n^2)^{\rm calc.} Q^2$. Data from Ref.\,\protect\cite{Madey:2003av}.}
\end{figure}
The truncation of the Faddeev equation's kernel is completed by specifying that the quarks are dressed, with two of the three dressed-quarks correlated always as a colour-$\bar 3$ diquark. Binding is then effected by the iterated exchange of roles between the bystander and diquark-participant quarks. This ensures that the Faddeev amplitude exhibits the correct symmetry properties under fermion interchange. A Ward-Takahashi-identity-preserving electromagnetic current for the baryon thus constituted is subsequently derived~\cite{Oettel:1999gc}. It depends on the electromagnetic properties of the axial-vector diquark correlation: its magnetic and quadrupole moments, $\mu_{1^+}$ and $\chi_{1^+}$, respectively; and the strength of electromagnetically induced axial-vector $\leftrightarrow$ scalar diquark transitions, $\kappa_{\cal T}$.
Figure~\ref{GEnGMn} depicts the calculated ratio $\mu_n G_E^n(Q^2)/G_M^n(Q^2)$. The behaviour of the analogous proton ratio was published in Ref.\,\cite{Alkofer:2004yf,Holl:2005zi}: it passes through zero at $Q^2\approx 6.5\,$GeV$^2$. It is noteworthy that in the neighbourhood of $Q^2=0$,
\begin{equation}
\label{smallQ}
\mu_p\,\frac{ G_E^n(Q^2)}{G_M^n(Q^2)} = - \frac{r_n^2}{6}\, Q^2 ,
\end{equation}
where $r_n$ is the neutron's electric radius. Our calculation shows this to be a good approximation for $r_n^2 Q^2 \nlsim 1$. The data \cite{Madey:2003av} are consistent with this. The calculated curve omitted pion-loop effects from the current and therefore underestimated the magnitude of $r_n^2$. This is apparent in the figure. It is thus evident that, just as for the proton, the small $Q^2$ behaviour of this ratio is materially affected by the neutron's pion cloud.
Pseudoscalar mesons are not pointlike and therefore their contributions to form factors diminish in magnitude with increasing $Q^2$ (see, e.g., Refs.~\cite{Alkofer:1993gu,Sato:2000jf,Miller:2002ig,Hammer:2003qv}). It follows therefore that the evolution of $\mu_n G_E^n(Q^2)/G_M^n(Q^2)$ on $Q^2\ngsim 2\,$GeV$^2$ is primarily determined by the quark-core of the neutron. This calculation predicts that the ratio will continue to increase steadily until $Q^2\simeq 8\,$GeV$^2$.
In a Poincar\'e covariant treatment the quark core of a nucleon is necessarily described by a Faddeev amplitude with nonzero quark orbital angular momentum. This is why the Faddeev amplitude is a matrix-valued function with a rich structure that, in a baryons' rest frame, corresponds to a relativistic wave function with $s$-wave, $p$-wave and even $d$-wave components~\cite{Oettel:1998bk}. Figure~\ref{GEnGMn} illustrates that while there is some quantitative sensitivity to the electromagnetic structure of the diquark correlations, the gross features of the form factors are primarily governed by correlations expressed in the nucleon's Faddeev amplitude and, in particular, by the amount of intrinsic quark orbital angular momentum \cite{Bloch:2003vn}. The nature of the kernel in the Faddeev equation specifies just how much quark orbital angular momentum is present in a baryon's rest frame.
\section{CLOSING}
Two emergent phenomena are responsible for the observed properties of hadrons: confinement and dynamical chiral symmetry breaking. They can be viewed as an essential consequence of the presence and role of particle-antiparticle pairs in an asymptotically free theory and therefore can only be veraciously understood in relativistic quantum field theory. Quantum mechanics is inadequate and supposed successes within that framework should be viewed as a consequence of fine-tuning or good fortune.
DSEs are well suited to the study of hadron physics at and beyond the frontiers being explored by modern, high-luminosity facilities. The framework quite naturally wraps each of QCD's elementary excitations in a cloud of virtual particles that is exceedingly dense at low momentum. It admits a systematic, symmetry preserving and nonperturbative truncation scheme, and thereby gives access to continuum strong QCD. The tractability of the truncation scheme makes available a practical tool for the prediction of observables. The consequent opportunities for rapid feedback between experiment and theory brings within reach an intuitive understanding of strong interaction phenomena. Furthermore, a dialogue between DSE and lattice-QCD studies is today proving fruitful.
A pressing task is the drawing of an accurate map of the confinement force between light-quarks within hadrons. The careful and quantitative study of mesons in the mass range $1$ -- $2\,$GeV appears to us as a certain way to make progress in this direction.
\bibliographystyle{elsart-num}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,592 |
Viktor Davidovitch Koupreïtchik ou Kupreïtchik (en russe : Купрейчик, Виктор Давыдович ; transcription anglaise : Viktor Kupreichik) est un joueur d'échecs soviétique puis biélorusse né le à Minsk et mort le .
Grand maître international à partir de 1980 et double champion de Biélorussie (en 1972 et 2003), il a remporté le tournoi de Hastings en 1981-1982, devant Andersson et Smyslov. De 1994 à 2002, il a participé à cinq olympiades d'échecs avec la Biélorussie.
Biographie
Olympiades universitaires
Au début de sa carrière, Viktor Koupreïtchik participa aux olympiades universitaires (joueurs de moins de 26 ans) de 1968, 1969 et 1974 et remporta trois médailles d'or par équipe ainsi que la médaille d'or individuelle au deuxième l'échiquier de réserve en 1968 et 1969. Il était considéré comme un joueur de talent qui avait besoin de discipline pour se développer.
Résultats aux championnats d'URSS
Lors de ses trois premières participations au championnat d'URSS, il finit dernier. À Moscou (tournoi zonal), en 1969, il marqua 6,5 points sur 22 (+3 -12 =7) et annula contre Petrossian, Polougaîevski, Smyslov et Taîmanov ; en 1974, à Léningrad, il ne fit qu'une seule nulle (3,5 points sur 15 : +3 -11 =1) ; en 1976 (6 / 17, +5 -10 =2), il ne fit que deux nulles et cinq victoires.
À la fin de des années 1970, il finit - du championnat de 1979 : après une défaite lors de la première ronde, il remporta cinq parties de suite. Un ans plus tard, en 1980-1981, il commença le tournoi par cinq victoires consécutives et termina -. Dans les années 1980, il finit - en novembre-décembre 1981, puis dernier en 1985 (avec seulement quatre nulles) et - en 1987.*
Championnats de Biélorussie
Koupreïtchik remporta le championnat de la République socialiste soviétique de Biélorussie en 1972 et le championnat de la Biélorussie en 2003.
Palmarès international
Dans les tournois internationaux, Koupreitchik remporta
le tournoi de Wijk aan Zee B (tournoi de maîtres) en 1977 ;
Kirovakan en 1978 (ex æquo avec Vaganian) ;
Reykjavik (+5 =7) devant Browne et Miles ;
Plovdiv (+6 =5) et Medina del Campo (+4 =5) en 1980 ;
Hastings en 1981-1982 (+6 -1 =6).
Grâce à ces résultats, Koupreïtchik reçut le titre de grand maître international en 1980, et fut classé - joueur mondial en janvier et juillet 1981.
Après sa victoire à Hastings, il remporta la victoire à
Sverdlovsk en 1984 (ex æquo avec Psakhis, M. Gourevitch et V. Gavrikov) ;
Zenica en 1985 ;
Pinsk et Winnipeg en 1986 ;
Malmö en 1987-1988 (ex æquo avec Aleksandr Beliavski) ;
Melbourne, devant Vassili Ivantchouk, Akopian et Naum Kagan ;
Esbjerg en 1988 ;
Val-Maubuée en 1989 ;
Rimavská Sobota et Oberwart en 1990.
En 2003, Koupreïtchik a remporté le championnat d'Europe d'échecs rapides sénior.
Viktor Koupreïtchik est mort le .
Compétitions par équipe avec la Biélorussie
Koupreïtchik a disputé cinq olympiades (de 1994 à 2002) et trois championnats d'Europe par équipe (en 1992, 1999 et 2003) avec la Biélorussie. Avec Koupreïtchik au deuxième échiquier, l'équipe biélorusse finit douzième de l'olympiade d'échecs de 1994.
Notes et références
Annexes
Bibliographie
Liens externes
Naissance en juillet 1949
Naissance à Minsk
Naissance en RSS de Biélorussie
Joueur soviétique d'échecs
Joueur biélorusse d'échecs
Grand maître international
Décès à 67 ans
Décès à Minsk
Décès en mai 2017
Étudiant de l'université d'État de Biélorussie | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 103 |
Q: How to generate an SSL client certificate from a disconnected network? I have a unique situation where I need to implement client certificate authentication over HTTPS between IE browser and IIS 6. The browser and IIS are separated by a firewall that only allows the browser to connect to IIS on the SSL port.
We have an internal certificate server on the same network as IIS. I've generated an SSL server cert for IIS and that is installed. I configured IIS to only allow SSL, require client certificates.
The limitation here is the browser machine is on a disconnected network, so I can't go to the CA's http://caserver/CertSrv URL and request a client cert like you normally would.
I figured if there were a way that I could generate a CSR against the Root CA's public key, I can copy it to the CA server to generate the client cert. But, there appears to be no provision in IE or the Certificates MMC to do this. The Certificates MMC seems to require a direct connection to the CA.
Has anyone solved this before?
FYI, All servers referenced run Windows Server 2003.
Update: Thanks to Jonas Oberschweiber and Mark Sutton for pointing out the CertReq.exe command line tool. Using this, I've generated a CSR, and consequently a client certificate that installs successfully. However, IE is apparently not sending this client cert when accessing the IIS server in question; it still generates a 403.7 "Forbidden: SSL client certificate is required." I suspect that the reason is that the Subject field of the client cert does not match the user id of the account running IE, thus perhaps not sending a mismatching client cert. The Subject matches that of the user I used to submit the CSR and generate the client cert on the other end of the firewall.
Does the Subject field matter? Is there something else I need to do to enable IE to send this cert?
A: Use the certreq command on your client as follows
certreq -new -f filein c:\certrequest.req
Here is and example of the filein
[Version]
Signature="$Windows NT$"
[NewRequest]
Subject="CN=dc1.extranet.frbrikam.com"
EncipherOnly = False
Exportable = False
KeyLength = 1024
KeySpec = 1
KeyUsage = 0xA0
MachineKeySet = True
ProviderName = "Microsoft RSA SChannel Cryptographic Provider"
ProviderType = 12
RequestType = CMC
[RequestAttributes]
CertificateTemplate=TLSServer
Replace the CertificateTemplate with the name of your certificate template
Once you have your request file you need to take it to the certificate authority on a usb stick and use the web enrolment interface as usual to process the request file.
Take the output certificate back to the client open it and click install.
A: You sound like you have already tried a couple of things so my guess is that you are already aware of these, but I'm going to post them anyway, just in case: Certificate Command Line Tools. I am not sure, however, if they do what you want.
A: Go the http://caserver/CertSrv site that you mentioned using a 3rd computer that can see the CA server. Select the 3rd option, download a CA cert, cert chai, or CRL. On the next page select 'Download CA Certificate Chain', which will download the p7b file. Using a flash drive (or email, etc) transfer this to the other computer which will allow you to import it into the trusted root servers in IE.
http://technet.microsoft.com/en-us/library/cc787796.aspx
A: Suggestiong for the update, just in case - what is the trusted cert list of in the server?
Subject DN being the same as Windows username has never been a problem for me - although I don't use IIS much. However, somewhere in IIS there is sure to be a trusted certificate list. This error sounds to me like the server's trusted certs list does not include the CA or Root CA that issued the client certificate.
This is particularly true if you never get a certificate selection popup window in IE when you hit the IIS server - even though you have a certificate configured in your IE cert store. That means that the client hit the server, the server gave a list of trusted certs and the client didn't have a cert that fit the list. So the SSL session went to the Forbidden error state.
If the certificate selection window popped up, and you selected and sent the cert, there may be other configuration problems on the server side..
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,204 |
These two….I tell ya. You can see the playfulness between them from their photos!
They came to Costa Rica with a very small group of friends for a "vacation" — never telling their friends that they were getting married until the day before the planned wedding. Surprise! | {
"redpajama_set_name": "RedPajamaC4"
} | 96 |
package com.facebook.buck.parser;
import com.facebook.buck.model.BuildTarget;
import com.facebook.buck.model.BuildTargetPattern;
import com.facebook.buck.model.ImmediateDirectoryBuildTargetPattern;
import com.facebook.buck.model.SingletonBuildTargetPattern;
import com.facebook.buck.model.SubdirectoryBuildTargetPattern;
import com.facebook.buck.rules.CellPathResolver;
import com.google.common.base.Preconditions;
import com.google.common.base.Strings;
import java.nio.file.Path;
import java.util.Optional;
/**
* Context for parsing build target names. Fully-qualified target names are parsed the same
* regardless of the context.
*/
public abstract class BuildTargetPatternParser<T> {
private static final String BUILD_RULE_PREFIX = "//";
private static final String WILDCARD_BUILD_RULE_SUFFIX = "...";
private static final String BUILD_RULE_SEPARATOR = ":";
private final String baseName;
protected BuildTargetPatternParser(String baseName) {
this.baseName = Preconditions.checkNotNull(baseName);
}
public String getBaseName() {
return baseName;
}
protected boolean isWildCardAllowed() {
return false;
}
/**
* 1. //src/com/facebook/buck/cli:cli will be converted to a single build target 2.
* //src/com/facebook/buck/cli: will match all in the same directory. 3.
* //src/com/facebook/buck/cli/... will match all in or under that directory. For case 2 and 3,
* parseContext is expected to be {@link BuildTargetPatternParser#forVisibilityArgument()}.
*/
public final T parse(CellPathResolver cellNames, String buildTargetPattern) {
Preconditions.checkArgument(
buildTargetPattern.contains(BUILD_RULE_PREFIX),
String.format("'%s' must start with '//' or a cell followed by '//'", buildTargetPattern));
if (buildTargetPattern.endsWith("/" + WILDCARD_BUILD_RULE_SUFFIX)) {
return createWildCardPattern(cellNames, buildTargetPattern);
}
BuildTarget target = BuildTargetParser.INSTANCE.parse(buildTargetPattern, this, cellNames);
if (target.getShortNameAndFlavorPostfix().isEmpty()) {
return createForChildren(target.getCellPath(), target.getBasePath());
} else {
return createForSingleton(target);
}
}
private T createWildCardPattern(CellPathResolver cellNames, String buildTargetPattern) {
if (!isWildCardAllowed()) {
throw new BuildTargetParseException(
String.format("'%s' cannot end with '...'", buildTargetPattern));
}
Path cellPath;
int index = buildTargetPattern.indexOf(BUILD_RULE_PREFIX);
if (index > 0) {
cellPath = cellNames.getCellPath(Optional.of(buildTargetPattern.substring(0, index)));
buildTargetPattern = buildTargetPattern.substring(index);
} else {
cellPath = cellNames.getCellPath(Optional.empty());
}
if (buildTargetPattern.contains(BUILD_RULE_SEPARATOR)) {
throw new BuildTargetParseException(
String.format("'%s' cannot contain colon", buildTargetPattern));
}
if (!buildTargetPattern.equals(BUILD_RULE_PREFIX + WILDCARD_BUILD_RULE_SUFFIX)) {
String basePathWithPrefix =
buildTargetPattern.substring(
0, buildTargetPattern.length() - WILDCARD_BUILD_RULE_SUFFIX.length() - 1);
BuildTargetParser.checkBaseName(basePathWithPrefix, buildTargetPattern);
}
String basePathWithSlash =
buildTargetPattern.substring(
BUILD_RULE_PREFIX.length(),
buildTargetPattern.length() - WILDCARD_BUILD_RULE_SUFFIX.length());
// Make sure the basePath comes from the same underlying filesystem.
Path basePath = cellPath.getFileSystem().getPath(basePathWithSlash);
return createForDescendants(cellPath, basePath);
}
/**
* Used when parsing target names relative to another target, such as in a build file.
*
* @param baseName name such as {@code //first-party/orca}
*/
public static BuildTargetPatternParser<BuildTargetPattern> forBaseName(String baseName) {
Preconditions.checkNotNull(Strings.emptyToNull(baseName));
return new BuildFileContext(baseName);
}
/** Used when parsing target names in the {@code visibility} argument to a build rule. */
public static BuildTargetPatternParser<BuildTargetPattern> forVisibilityArgument() {
return new VisibilityContext();
}
/** Used when parsing fully-qualified target names only, such as from the command line. */
public static BuildTargetPatternParser<BuildTargetPattern> fullyQualified() {
return new FullyQualifiedContext();
}
/**
* @return description of the target name and context being parsed when an error was encountered.
* Examples are ":azzetz in build file //first-party/orca/orcaapp/BUCK" and
* "//first-party/orca/orcaapp:mezzenger in context FULLY_QUALIFIED"
*/
protected abstract T createForDescendants(Path cellPath, Path basePath);
protected abstract T createForChildren(Path cellPath, Path basePath);
protected abstract T createForSingleton(BuildTarget target);
private abstract static class BuildTargetPatternBaseParser
extends BuildTargetPatternParser<BuildTargetPattern> {
public BuildTargetPatternBaseParser(String baseName) {
super(baseName);
}
@Override
public BuildTargetPattern createForDescendants(Path cellPath, Path basePath) {
return SubdirectoryBuildTargetPattern.of(cellPath, basePath);
}
@Override
public BuildTargetPattern createForChildren(Path cellPath, Path basePath) {
return ImmediateDirectoryBuildTargetPattern.of(cellPath, basePath);
}
@Override
public BuildTargetPattern createForSingleton(BuildTarget target) {
return SingletonBuildTargetPattern.of(
target.getUnflavoredBuildTarget().getCellPath(), target.getFullyQualifiedName());
}
}
private static class BuildFileContext extends BuildTargetPatternBaseParser {
public BuildFileContext(String basePath) {
super(basePath);
}
}
/**
* When parsing a build target for the visibility argument in a build file, targets must be
* fully-qualified, but wildcards are allowed.
*/
private static class FullyQualifiedContext extends BuildTargetPatternBaseParser {
public FullyQualifiedContext() {
super("");
}
}
private static class VisibilityContext extends BuildTargetPatternBaseParser {
public VisibilityContext() {
super("");
}
@Override
protected boolean isWildCardAllowed() {
return true;
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,360 |
Bastrop City Council could vote to repeal development moratorium Tuesday after floods
by: Candy Rodriguez
Posted: May 14, 2019 / 10:45 AM CDT / Updated: May 14, 2019 / 03:57 PM CDT
BASTROP (KXAN) — For the past nine months, the City of Bastrop has been under a development moratorium. Tuesday night, the city council is expected to lift the ban.
It was enacted on August 14, 2018, after city officials noticed homes that had never flooded before started to flood last year. Then, in November, it was extended to May and the city adopted an emergency drainage ordinance.
"We weren't against development, we were against development that could have an adverse impact to drainage," said Mayor Connie Schroeder.
If the council lifts the ban, the city plans to implement an Enhanced Permit Review Ordinance and a new drainage ordinance to ensure development moving forward won't lead to more floods.
Since the city enacted the moratorium, they began working on Building Bastrop. An initiative to create new land use regulations. The Enhanced Permit Review Ordinance will be an interim process for interested developers until Building Bastrop is finalized. They expect to present the first draft next week.
Schroeder said this is all to get ready for the growth that's expected within the city.
"Projections are saying that we could double or triple our population in the next 10 to 15 years," she said. "The old adage of you either control the growth or the growth controls you."
Despite the moratorium being in place, the city still approved more than 600 permits. Schroeder said these were approved after they determined it would not impact drainage.
Here's a breakdown of the permits issued since mid-August 2018 through mid-April 2019:
A total of 617 permits were issued.
49 of those were for new single-family residences
13 commercial remodels
Four new commercial buildings
Three commercial finish-out permits
The remainder of the permits are trade permits: electric, HVAC, plumbing, etc.
Since the emergency drainage ordinance went into effect last November, Schroeder said they learned is drainage should be looked at first.
"We will look at the drainage and take drainage into account in development as one of the very first steps," she said and added this has to happen before the project is organized on the property. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 39 |
**FAST, FRESH AND FULL-ON FLAVORS
FROM STREET FOODS TO THE SPECTACULAR**
**JOHN GREGORY-SMITH**
CONTENTS
INTRODUCTION
EXPRESS FLAVOUR ESSENTIALS
MIGHTY BITES
NOT QUITE LUNCH
MIDWEEK LIFESAVERS
NICE & EASY
SOMETHING SPECTACULAR
NAUGHTY BUT NICE
**INTRODUCTION**
**Food, recipes, cooking, spices and eating are my life, so when my publisher asked me to follow up my first book, _Mighty Spice Cookbook_ , I was thrilled. I had already been working on new recipes, so it was a great time to pop the question.**
**The _Mighty Spice Cookbook_ set out to show everyone how simple it was to cook with spices. I never used more than five spices in each recipe and I kept the ingredients supermarket friendly. It made sense that the next step would be to show everyone how fast it is to cook with spices, whatever the occasion. _Mighty Spice Express_ was born, and we started putting ideas down. I always like to introduce new recipes and flavors, so I travel abroad for my research. I carefully chose the countries to visit that would give me the most inspiration for express cooking.**
**"Express" obviously meant street food, and this has been a real inspiration for the book. Street food shows the best a place has to offer and a snapshot of what's hot right now. It is always served fast and furious, and can be hot or cold, savory or sweet. But, guaranteed, it will be tasty, fresh and cooked to perfection. Quite simply, if the food doesn't cut the mustard it won't be there the following morning.**
**DUCKING AND DIVING IN FEZ**
**_Mighty Spice Express_ took me to the stunning city of Fez in Morocco, which has the oldest working _medina_ —or old part of the city—in the world. This means a vast expanse of car-free city where people live and trade. The buildings are packed so tightly together that most of the streets are actually narrow passages supported by huge wooden struts, which are best navigated by frequent ducking—Bilbo Baggins and co. would have been perfectly at home.**
**To an outsider, the city is a maze, and one that needs a guide. Luckily, I had the best in Gail Leonard. Gail organized street-food tours of fabulous Fez and we met one cold January morning by the magnificent Blue Gate. After coffee, we stopped for a sassy sweetbread sandwich—fried sweetbreads that were served in a bun with spices and finely chopped onions. It was delicious and, strangely, it worked as a great pick-me-up first thing in the morning. It was also to serve as the inspiration for my Blue Gate Fez Sandwich in the Mighty Bites chapter.**
**The natural slope of the ancient city took us south. We wound through narrow passages lit by hazy shafts of light and emerged onto one of the main market streets in Fez. Chickens clucked while waiting for someone's pot. Alongside the chickens were camel heads, spices, herbs, beautiful juicy strawberries, olives, nuts, harissa paste and a wonderful little stand that sold _bessara_. _Bessara_ is a breakfast soup made from fava beans. It's rich and thick and perfect for keeping hungry workers full until lunchtime. My bowl was seasoned heavily with chili and cumin and tasted utterly sublime.**
**SPECIALTIES FROM THE SEA AT ESSAOUIRA**
**After Fez I took the train south to the remarkable coastal town of Essaouira. There are times when my job is unbelievable, and this was one of them. I arrived at this magical place and went for a long run along the beach. Kite surfers took off in the sparkling waters around me, horses galloped along the shore and the whole time the setting sun framed the walled city like a movie. I even made some new friends of the canine variety, who followed me all the way back to my hotel. This became slightly awkward when I had to navigate through the fashionable cafés of the town, red-faced, sweating and trailed by stray dogs.**
**_Mighty Spice Express_ is about making any meal an occasion fast. Fish and shellfish cook quickly, and Essaouira fed my mind, tummy and soul with seafood. I was inspired at every turn, especially when I had dinner at Sam's—not quite the evocative Moroccan-nights' name I would have come up with for the best seafood place in town, but who am I to judge? Sam's was located at the end of the pier, past the rocking fishing boats, dried nets and slightly spooky seagulls. From the outside the restaurant looked like a blue-and-yellow lobster shack from _Family Guy_. Inside, the decor of jewel-encrusted spider crabs and black-and-white photographs of Hollywood stars was equally baffling, but the food was on the money. It was coastal Moroccan with a classic French twist—wow! Get in a taxi right now, ask for Sam's and order the monkfish skewers. You will not be disappointed.**
**COCONUT, FENUGREEK AND THE BRIGHT COLORS OF INDIA**
**The next stop for my research was India—Goa to be exact—where the coconut curries and fresh coastal food were all made in no time. Every town has its local food heroes, and in Dabolim it's Rita Shinde. From her beautiful garden, Rita taught the local women how to make the excellent, fresh food of southern India. Now, not being local or a woman, I was very lucky she took me on. We went through all the classic Goan dishes, then she taught me about the tamarind-based Hindi food and, finally, the Catholic Goan cuisine, which used the pungent local vinegar in abundance. Her _reshado_ sauce has been an utter revelation for me and I am happy to say that it has inspired several of the dishes in this book.**
**After Goa, I traveled north to Mumbai—a melting pot of all that India has to offer. This particular trip was made extra special by two people, Lizzie and Amish. With Lizzie's military organizational skills and Amish's local knowledge, I ate everything in Mumbai! They even arranged a low-key visit to Dharavi, one of the famed city slums. I don't know why, but for some reason I had been geared up for a massive bout of Western guilt. I expected to see horrific things, but the trip was one of the most amazing experiences I have ever had in my whole life.**
**The slum—wrongly named because it suggests something bleak—is a fully functioning city within a city. Hundreds of thousands of people live, work and socialize here. Working conditions are pretty terrible, but there is such life and energy! Everyone was busy working in industry—sorting plastics, building machinery, sewing clothes, making soap and producing most of Mumbai's poppadoms. There was more of a sense of community in that place than I have ever felt anywhere else before. Everyone knew one another. They chatted, they worked and they went to the main street to eat, drink, shop and even go to the movies. The residential areas were spotless. People took pride in where they lived. For every bit of dreary gray, the inhabitants' love of bright colors prevailed. For every funny odor, the wonderful smells of fenugreek and coconut oil filled the air. Even the constant noise of the traffic was drowned out by high-pitched Hindi love songs. I loved it and even now I can feel goose bumps while I'm writing about my time there. I feel honored to have been to Dharavi.**
**EATING FOR FOUR IN THE FAR EAST**
**The final area my research for _Mighty Spice Express_ took me to the Far East. Having already spent time in Thailand and Laos, I decided to expand my knowledge and go to Seoul and northeastern China to learn something new. Seoul was crazy—a vast metropolis of cool people, wicked food and technology that would have humbled the Starship Enterprise.**
**I kicked off my first night by exploring the low-level restaurants that lined the cross streets between the skyscrapers of Gangnam District. For some reason, every restaurant I went into threw me out. Tired and hungry, and feeling a bit like I hadn't been picked for the sports team, I retired to my hotel. Thankfully, the next day I was informed that it was not because I was weird and Western, but because the restaurants in question served huge sharing dishes that were way too big for one person. Armed with this invaluable local information I returned, asked for a table for four and ate everything myself.**
**The next morning, my guide took me around the north of the city. First I learned how to make precious kimchi, which is the cornerstone of every Korean meal. Next, we went on a serious street-food tour. We ate so well: _pa jun_ , a fantastic Korean pancake; giant steamed dumplings filled with pork and scallions; _bibimbap_ , a classic rice dish; grilled kebabs; noodle soup with clams; and spicy fried tofu. The choices seemed endless—and everything was delicious.**
**AIRBORNE EXERCISES AND SPECTACULAR BARBECUES**
**There are not enough superlatives in the world for me to describe China. Shanghai, for example, is the only place where you can order scorpion, dim sum, sea cucumber and foie gras all at once. Several years ago my great friends, Mike and Annie, introduced me to the food of Dongbai, an area of northeastern China where Annie was born. Since then, I have been obsessed with going to this part of the world, and luckily it fitted the bill for _Mighty Spice Express_. I found myself on a flight with Mike and Annie heading to the city of Shenyang to learn about Dongbai food and their famous barbecue. All that I love about China happened on that flight. At one point, the stoic passengers, who had sat so silently, were drawn to attention by the cabin crew who had formed a line down the middle of the plane. They proceeded to demonstrate a series of exercises intended to help combat cramp and deep vein thrombosis that wouldn't have looked out of place at a Spice Girls concert. The silence broke and everyone joined in expressively copying the moves. The routine culminated in hands that were crossed over shoulders, then flying into the air for an ecstatic double clap, and then the passengers returned to the demure silence of before. It was amazing and so random, just like the rest of the country.**
**We went straight from the airport to a restaurant called Little South Island BBQ that was owned by a friend of Annie's. It was here that I learned the secret of Dongbai food, their barbecue and the true meaning of Chinese hospitality. Lots of things in China happen behind closed doors, including "cutting loose," which is exactly what happened at lunch. While the rest of the restaurant was filled with hushed diners, we were holed up in a private room surrounded by friends, family, food and way too much alcohol. Every sublime dish was lovingly explained to me by my hosts and followed by a lethal dose of _baiju_ , a gigantically boozy Chinese liquor. We must have eaten about 40 different dishes. You can do the math for the shots! Both the food and barbecue were an eye opener, and I learned techniques and seasonings that I had never seen before—boy, are you in for a treat!**
**ABOUT THIS BOOK**
**_Mighty Spice Express_ is all about making fantastic food in no time. To achieve this, I have developed recipes using techniques, spices, cuts of meat and fish, cooking methods and ingredients that all work toward making delicious express meals and snacks for any occasion.**
**Spices are at the heart of the recipes in this book. The more I travel the more I learn new ways to use these fabulous ingredients. They are truly versatile and it's fascinating how the same spices, used in a different way, can take the food on your table from one country to another. For me, spices offer an escape and transport me somewhere else while I eat. They add the flavors, color, heat and fragrance of some of the most beautiful and exotic places in the world. With a pinch of cumin, some grated ginger or a few slices of lemongrass I can whip up something wonderful and transform my apartment in East London into the best exotic restaurant in the world.**
**As you look through the book, you'll notice that each recipe includes pictures of the spices used, so you'll be able to see at a glance which ones you will need to make it.**
**This book is packed full of exciting recipes, which all work in the times I have given. I have lovingly time-tested each one, over and over again, to make sure that they all work perfectly. The key was getting the preparation and cooking done at exactly the right time. So that you can achieve the same fast results, I have included all the preparation in the recipe method rather than in the ingredients list. While part of the dish is cooking you'll be preparing the ingredients for the next stage. The recipes are not complicated, and the way I have designed them means you'll be making the most of your time in the kitchen. As long as you don't go off piste you'll nail the recipes easily.**
**I hope you'll enjoy making and eating this collection of recipes as much as I do and that this book will help to make cooking any meal an express experience for you.**
**EXPRESS FLAVOR ESSENTIALS**
**Stuff your cupboard and stock up your fridge with some basics and you'll be able to rustle up a spicy meal at any time.**
**A LITTLE SOUTHEASTERN ASIA**
**Coconut Creamed coconut is fresh coconut formed into a solid block. The high fat content means it will melt into a sauce to thicken and enrich it. It can also be grated over salads or onto broiled meats where it will melt through the food. Coconut cream and coconut milk are made by squeezing water through the ground flesh of a fresh coconut. The milky liquid from the first press is coconut cream. It has the highest fat content, making it rich and flavorsome. The remaining pulp is mixed with more water for a second pressing, giving the slightly milder-tasting coconut milk.**
**Fish sauce This highly smelly sauce is salty and pungent. It can be used instead of salt and to add flavor to curries, soups, stir-fries and salads.**
**Hoisin sauce is a Chinese condiment that can be used in stir-fries and as a dip for roasted meats, fish and vegetables. It has a rich soy–salty taste and it doesn't need cooking.**
**Oyster sauce is a slightly sweet condiment that is used all over south-eastern Asia. The thick brown sauce is made from soybeans and oyster extract, tasting both sweet and savory. Look for the highest percentage of oyster extract when purchasing.**
**Rice wine vinegar This provides the classic southeastern Asian sour flavor. It's great for dipping sauces and salad dressings. The taste is very tart, so it always needs to be balanced by something sweet or hot.**
**Soy sauce The brilliant _umami_ taste (meaning "pleasant savory taste" in Japanese) that soy sauce gives to food is superb. Use it in stews instead of salt to create depth of flavor. I have used light and dark soy sauces here. Traditionally, light is used as a seasoning and dark to add color. I find the light salty and fresh, and the dark much richer with a more complex flavor.**
**Sweet chili sauce is the ultimate ready-made dipping sauce. It works especially well in a salad dressing with a good squeeze of lime to balance out the sweetness. It gives instant flavor with zero effort.**
**FAVE SAVORIES**
**Pitted olives Olives have a good savory taste that complements many dishes. Scatter them all over salads and tagines, or use them in a salsa or pesto where their intense saltiness works really well.**
**Preserved lemons possess a superb and unique flavor, and are now easy to buy. Just cut them into quarters, remove and discard the flesh and finely chop or slice the rind. They work in tagines, stews, soups, salads, rice dishes and kebabs, and provide an instant Moroccan flavor.**
**Sun-dried tomatoes and paste For this book I have used sun-dried tomatoes (in oil) in salsas and sauces for their intense smoky and salty flavor. The paste adds the same big flavor without chopping or blending.**
**Tahini Made with sesame seeds, tahini is a classic Middle Eastern ingredient. The flavor is rich and intense, and a little goes a long way. It works well as a dip mixed with yogurt and is one of the main ingredients in hummus. It lasts for ages, so you'll get lots of use from one jar.**
**Tomato passata and paste So many recipes are tomato-based, and if you are short of time, tomato passata (sieved tomatoes) and paste can be a quick solution for adding flavor. They are already cooked, so the tomato richness is intensified, and they just need to be reheated.**
**Worcestershire sauce This quintessentially British ingredient is bound to be lying around in one of your kitchen cupboards. It's made from vinegar, anchovies and spices, so it's not that far removed from the fishy south-eastern Asian condiments. It adds an unusual flavor, which melts into the background when used in curries, spice pastes and salad dressings.**
**VERSATILE SPICES**
**Chili powder and chili flakes Sometimes there's no time for chopping, so keep chili powder and chili flakes on hand for an instant spicy kick.**
**Chinese five-spice powder is a mixture of spices, including star anise, fennel, cinnamon, cloves, Szechuan pepper, ginger and nutmeg, and there are endless combinations. It has a strong aniseed flavor that works well with soy sauce, making it perfect to add to Chinese dishes.**
**Chipotle chilies These are wood-smoked jalapeños, which add an incredibly woody, smoky flavor to everything, including salsas, stews, spice rubs and marinades. The taste is authentically Mexican. The chilies are dried and need a little soaking in warm water or a hot sauce to soften. They also blend into a powder easily, which is perfect for salsas, rubs or marinades.**
**Chocolate , made from cacao, is a very old spice that was used by the Mayans of Central America. The cacao beans are roasted and mixed with cocoa butter and sugar. It has a rich, spicy and nutty flavor, which develops on your palate as it melts. Use it in sweet and savory dishes. Use semisweet or bittersweet chocolate with the highest cocoa content for cooking.**
**Cinnamon is a classic spice that is used the world over. It loves everything from lamb and rice to chocolate and ice cream. I use cinnamon in ground or stick form in my recipes. If you don't have cinnamon sticks in the cupboard, you can also substitute ½ teaspoon ground cinnamon for a 2-inch stick.**
**Cumin and coriander These are the two ingredients that I would recommend to anyone who is starting to use spices. They have a wonderful flavor, they work beautifully together and can be used in many types of cuisines. Keep both ground cumin and the seeds on hand, so that you can use the seeds as a base in hot oil to flavor a dish and add some texture.**
**Smoked paprika The flavor-to-effort ratio of this superb spice is off the scale, which makes it my kitchen-cupboard essential. This bright red powder is made from ground wood-smoked peppers and/or chilies, which have a massive smoky taste. You can add it to any savory dish to inject some flavor, as well as using it in salsas, marinades, rubs and salad dressings.**
**THE RIGHT OIL AND VINEGAR FOR THE JOB**
**Olive oil and extra virgin olive oil have a much stronger flavor than other oils. This is great for cooking Mediterranean-style dishes and making salad dressings. Use the olive oil for cooking and the extra virgin olive oil for dressings (it loses flavor once heated). All olive oils have a low smoke point and so are not suitable for cooking with fierce heat, such as stir-frying.**
**Peanut oil is the best oil for making stir-fries, because it has a high smoke point, which is important when frying over high heat. It also has a mild flavor so it won't interfere with the other flavors in the dish.**
**Sesame oil has a rich, roasted-sesame flavor, which is perfect in salad dressings, rubs and marinades. Excellent, too, added at the end of a stir-fry.**
**Sunflower oil has a high smoke point. It's very mild in flavor and cheap to buy. I use it for shallow-and deep-frying in this book.**
**Balsamic vinegar This classic Italian sweet vinegar is great for roasts, stir-fries and salad dressings.**
**Cider vinegar is a versatile vinegar. It is not too tart and it works well as a substitute if you can't find rice wine vinegar.**
**Red wine vinegar has a lovely flavor that is not as sharp as the other vinegars and is perfect to use in cooking and as a base for salad dressings.**
**FRESH FLAVORINGS**
**Garlic is a staple ingredient in every kitchen I have visited all over the world. It adds a sweet, mellow background flavor when cooked slowly, or a stronger fiery flavor when cooked quickly.**
**Ginger has a fresh peppery taste that is wonderful in curries, stir-fries and salad dressings. Fresh gingerroot will last in the fridge for up to a week.**
**Green and red chilies Fresh chilies last up to 10 days in the fridge and add heat and vibrancy to dishes both savory and sweet. I love to have multiple chili options at home for my cooking.**
**Lemongrass can make a curry taste fragrant and authentic, and the delicate citrus flavor will transform a stir-fry. It goes well with soy sauce, particularly in marinades. Stored in the fridge it will last for several weeks.**
**Lemons and limes All recipes need balance, and "sour" is a key flavor in southeastern Asian cooking. Lemons and limes freshen everything up and ignite other flavors to make them stronger.**
**Parsley and cilantro These two awesome herbs add color and freshness to everything. I can't live without them. Store them in the fridge.**
MIGHTY BITES
**Here is a collection of my favorite snacks, and they are bursting with different flavors from around the world. Loads of the recipes were inspired by street food, which is quite simply the best fast food there is. Many are great for parties, when you want something to munch on while standing and having a chat with your friends, holding a drink in your other hand. With recipes ranging from Los Danzantes Empanadas, made with shrimp and mozzarella, to spicy Thai Pork Sliders, all the recipes serve 2 and there is something here for everyone. My Fried Chili Corn, sprinkled with sea salt, is quite literally "TV sports and cold beers" best buddy, but the greatest part about Mighty Bites is that all the recipes can be thrown together in 15 minutes or less.**
Chicken Tenders with Sweet Chili & Basil Sauce SERVES **2** READY IN **10 MINUTES**
**I am a sucker for chicken with a dip, which is probably a hangover from my dad's obsession with chicken and mayonnaise. My cheeky chicken snack uses little chicken tenders, which cook in no time. It's served with a punchy dipping sauce that is made with sweet chili sauce, fresh green basil and wonderful fennel seeds, which liven it up with a background hint of aniseed.**
**4 mini chicken tenders (about 7 ounces total weight)**
**2½ tablespoons olive oil**
**1 handful of basil leaves**
**1 teaspoon fennel seeds**
**3 tablespoons sweet chili sauce**
**½ lime**
**sea salt and freshly ground black pepper**
**HEAT A GRILL PAN** over high heat until smoking. Meanwhile, brush the chicken with ½ tablespoon of the oil. Place it on the pan and reduce the heat to medium. Grill the chicken 3 to 4 minutes on each side, or until golden and cooked through.
**WHILE THE CHICKEN COOKS** , put the basil, the remaining oil and a good pinch of salt and pepper into a mini food processor or blender, and blend until smooth. Pour the oil mixture into a serving bowl. Gently crush the fennel seeds with the flat side of a knife blade or using a mortar and pestle, and add them to the serving bowl. Add the sweet chili sauce, then squeeze in the juice of the lime and mix well. Serve the golden chicken with the sweet chili and basil sauce.
Blue Gate Fez Sandwich SERVES **2** READY IN **15 MINUTES**
**This awesome sandwich was inspired by a street-food vendor who was parked beside the magnificent Blue Gate in Fez, Morocco. It was a freezing-cold morning, and this wicked sandwich, packed with crunchy onions, spices and fresh herbs, was the perfect way to warm up. My version uses chicken instead of offal (sorry Fez) but it shares the big flavors.**
**2 skinless chicken breasts**
**1 tablespoon olive oil**
**½ red onion**
**½ lemon**
**8 pitted green olives**
**1 handful of parsley leaves**
**2 wholewheat buns**
**2 tablespoons sun-dried tomato paste**
**3 tablespoons mayonnaise**
**½ teaspoon ground cumin**
**a pinch of chili powder**
**sea salt and freshly ground black pepper**
**LAY THE CHICKEN BREASTS** on a cutting board and, using a rolling pin, bash them out until they are ½ inch thick. Season one side with a good pinch of salt and pepper. Heat the oil in a large skillet over medium heat and fry the chicken, seasoned-side down first, 3 to 3½ minutes on each side, or until golden and cooked through.
**WHILE THE CHICKEN COOKS** , peel and slice the onion into thin strips, then add to a mixing bowl. Squeeze the juice of the lemon all over the onions and mix well. Finely chop the olives and parsley and set aside.
**CUT THE BUNS IN HALF** and spread the sun-dried tomato paste over one half of each, and the mayonnaise over the other half. Now add the cooked chicken and season with the cumin and chili powder. Scatter the chicken with the onions, olives and parsley, and set the other half of each bun on top. Serve immediately while hot.
Thai Pork Sliders SERVES **2** READY IN **10 MINUTES**
**These lovely little sliders (small hamburgers) are so tasty and quick to make. Using really good-quality pork sausages means that the meat is already the perfect consistency to incorporate all the fragrant Thai seasonings. A fresh lime hit at the end accentuates the flavors, and the sweet chili sauce is the perfect dunking partner.**
**½-inch piece fresh gingerroot**
**1 garlic clove**
**1 lemongrass stalk**
**½ red chili**
**¼ teaspoon freshly ground black pepper**
**1 small handful of basil leaves**
**1 teaspoon fish sauce**
**7 ounces best-quality pork sausages**
**1 tablespoon olive oil**
**TO SERVE**
**1 lime**
**sweet chili sauce**
**PEEL THE GINGER** and garlic, then remove the tough outer leaves from the lemongrass and cut off the ends of the stalks. Put the ginger and garlic into a mini food processor, and add the lemongrass, chili, black pepper, basil and fish sauce. Blend to a smooth paste. Scoop the paste into a mixing bowl and set aside.
**CUT OPEN THE SAUSAGES** , peel off the skins and add the meat to the mixing bowl with the spice paste. Combine together well and divide the pork into 6 portions. Flatten each portion into the shape of a mini burger patty— _voilà_ sliders!
**PLACE THE OIL** in a large skillet over medium heat and fry the sliders 1½ to 2 minutes on each side, or until golden and crispy.
**WHILE THE PORK COOKS** , cut the lime in half and pour the sweet chili sauce into a serving bowl. Serve the sliders with the lime halves and sweet chili sauce.
Hummus Beiruti SERVES **2** READY IN **10 MINUTES**
**To me, hummus rocks! My Hummus Beiruti is a slightly dressed-up version of the awesome dip. I make a deliciously light hummus, then top it with lovely sweet lamb that has been fried, super-fast, with allspice, cumin and cinnamon. The hit of spiced lamb melts through the hummus and makes it even more unbelievably tasty. This is ready in less than 10 minutes, so there's always time for a bit of happy hummus eating.**
**¼ cup olive oil**
**4 ounces ground lamb**
**¼ teaspoon ground allspice**
**¼ teaspoon ground cumin**
**a pinch of ground cinnamon**
**1½ lemons**
**2 pieces of pita bread**
**14-ounce can chickpeas**
**1 garlic clove**
**2 tablespoons tahini**
**sea salt**
**HEAT 1 TABLESPOON OF THE OIL** in a skillet over high heat and add the lamb. Stir-fry 2 minutes, then reduce the heat to medium. Add the allspice, cumin and cinnamon, and squeeze in the juice of ½ lemon. Cook 2 to 3 minutes, stirring occasionally, until the lamb is cooked through.
**WHILE THE LAMB COOKS** , put the pita bread into a toaster and toast until crunchy. Add the chickpeas to a colander and give them a good rinse. Drain off any excess water and put them into a blender or food processor with the remaining olive oil. Peel the garlic and add it to the blender with the tahini and a scant ¼ cup water. Season with salt. Squeeze in the juice of the remaining lemon and blend until smooth. Serve the hummus with the lamb on top, and toasted pita on the side.
Korean Kebabs SERVES **2** READY IN **10 MINUTES**
**As I roamed the high-tech streets of Seoul in Korea, I found little food stands nestled in the side streets offering the tastiest snacks. My favorites were these beef kebabs, which were barbecued over hot coals and served with sticky marinade and scattered with crunchy sesame seeds. What is great about them is that they are so quick and easy to make yet they taste out of this world.**
**6-ounce sirloin steak**
**1 garlic clove**
**1½ tablespoons soy sauce**
**2 teaspoons honey**
**½ teaspoon freshly ground black pepper**
**1 teaspoon sesame oil**
**½ teaspoon peanut oil**
**1 teaspoon sesame seeds**
**CUT THE STEAK** into long, thin strips, about inch thick, and add them to a mixing bowl.
**HEAT A GRILL PAN** over high heat until smoking. Meanwhile, peel and crush the garlic. Add it to the bowl with the steak, followed by the soy sauce, honey, black pepper, sesame oil and peanut oil. Mix well to coat, then thread the strips of steak onto six metal skewers.
**GRILL THE KEBABS** 1 to 1½ minutes on each side, or until charred on the outside but still pink and juicy in the center. Transfer the kebabs to a serving dish, scatter with the sesame seeds and serve.
Moroccan Paper Bag Sardines SERVES **2** READY IN **15 MINUTES**
**I first ate this fabulous snack in Fez. After a hard day's eating, I stopped at a tiny hole-in-the-wall where I was served crisp sardines in a paper bag with a wedge of lemon. What I loved was the texture of the batter. It was an even mixture of flour and semolina, which gave even more crunch to the fish. The subtle spicing, which was mixed into the batter, really brought it to life. Just a little cumin and chili powder, and you're good to go.**
**sunflower oil, for shallow-frying**
**heaped ⅓ cup all-purpose flour**
**heaped ⅓ cup semolina**
**2 teaspoons ground cumin**
**1 teaspoon chili powder**
**8 small sardines, cleaned**
**scant ⅔ cup yogurt**
**1 teaspoon harissa or chili paste**
**1 lemon**
**sea salt**
**POUR THE OIL** into a large frying pan to a depth of ½ inch and place over medium-high heat. Meanwhile, sift the flour into a large mixing bowl and add the semolina, cumin and chili powder, then season with salt. Pour in a scant ⅔ cup cold water and beat to a thick batter. Add the sardines and gently mix to coat completely in batter.
**SHAKE ANY EXCESS BATTER** off the sardines and shallow-fry them in the hot oil 3 to 4 minutes on each side, or until beautifully golden and cooked through. Carefully remove the sardines from the oil using a slotted spoon and place them on a dish lined with paper towels to drain.
**WHILE THE SARDINES DRAIN** , add the yogurt to a serving bowl and stir in the harissa. Lightly season with salt and mix well. Cut the lemon into wedges. Serve the sardines with the harissa yogurt and lemon wedges on the side.
Crab & Scallion Pancakes SERVES **2** READY IN **15 MINUTES**
**This is a classic Korean snack and one that I know you'll love. It's actually called _pa-jun_ and is an egg-based pancake flavored with soy and chili, then stuffed with beautifully sweet crabmeat, fresh herbs and oyster sauce. Typically, it would be served with a spicy kimchi. If you can get hold of some, give it a try. But it really is just so good on its own.**
**⅓ cup all-purpose flour**
**1 egg**
**¼ teaspoon crushed chili flakes**
**1 teaspoon light soy sauce**
**3 scallions**
**1 handful of cilantro leaves**
**scant ⅔ cup cooked white crabmeat**
**½-inch piece fresh gingerroot**
**1 tablespoon peanut oil**
**2 tablespoons oyster sauce**
**ADD THE FLOUR** to a large mixing bowl, pour in ¼ cup water and crack in the egg. Season with the chili flakes and soy sauce, and beat everything together to form a smooth batter.
**TRIM THE SCALLIONS** , then finely chop the scallions and cilantro leaves, and add half to the batter. Mix well. Put the other half into a separate mixing bowl and add the crab. Peel the ginger, then grate it onto the crab and mix it in well.
**HEAT HALF THE OIL** in a large skillet over medium heat and pour in half the egg batter. Cook 1 minute on each side, then transfer to a serving plate. Keep the pancake warm while you cook a second pancake in the same way.
**BRUSH THE TOP OF EACH PANCAKE** with one-quarter of the oyster sauce. Divide the crab mixture into 2 portions and arrange 1 portion in a line down the center of each pancake. Fold the pancakes in half and transfer them to serving plates. Drizzle each portion with the remaining oyster sauce to serve.
Jonny's Dumplings SERVES **2** READY IN **15 MINUTES**
**Dim sum is somewhat of an obsession of mine. From the super-slimy rice rolls to the dry, delicate, steamed parcels of a high-brow Hong Kong hotel, I can't get enough of them. The ritual of ticking the little boxes on the menu, waiting for the steamer trolley and then dipping the glory into various soy, chili and vinegar condiments is a complete pleasure to me. To make, though, it's not such fun. However, I really wanted to get something into this book, and after eating cabbage-leaf dim sum at a restaurant called Jonny's in Korea, I thought, "bring it on," and I came up with this quick version.**
**2 large green savoy cabbage leaves**
**¼ red chili**
**1 scallion**
**1 small handful of cilantro leaves**
**5½ ounces raw shelled jumbo shrimp**
**¼ teaspoon chinese five-spice powder**
**1 teaspoon light soy sauce, plus extra to serve**
**1 tablespoon peanut oil**
**PUT THE CABBAGE LEAVES** in a heatproof bowl, cover with boiling water and let soften 2 to 3 minutes. Meanwhile, seed the chili and trim the scallion. Place them both in a blender or food processor and add the cilantro leaves, shrimp, Chinese five-spice powder and soy sauce. Blend until smooth.
**DRAIN THE CABBAGE LEAVES** in a colander and refresh under cold water a few seconds until they are cool enough to handle. Gently squeeze out any excess water and place them on a cutting board. Cut out the stems and cut the leaves into 2 halves. Put one-quarter of the shrimp mixture onto each piece of cabbage leaf and roll them up, tucking in the sides. They should look like roundish egg rolls.
**HEAT THE OIL** in a skillet over high heat and add the dumplings, fold-side down. Cook 2 minutes, then pour boiling water into the side of the skillet to a depth of inch. Cover, reduce the heat to medium and steam 4 minutes. Remove the lid and cook 2 to 3 minutes, or until most of the water has evaporated and the dumplings are cooked through. Serve with light soy sauce on the side for dipping.
Los Danzantes Empanadas SERVES **2** READY IN **10 MINUTES**
**Traditionally, _empanadas_ are deep-fried Mexican snacks that look like little cornish pasties. They are crunchy and delicious, but quite time-consuming to make. These _empanadas_ are an express version. I use a soft flour tortilla for the shell, stuff it with shrimp, mozzarella, smoky sun-dried tomatoes, chili, scallions and cilantro leaves, then pan-fry it to get a crisp outside and an oozing filling. They take only 10 minutes to make, so I am sure you'll forgive me for not being an _empanada_ purist.**
**2 scallions**
**¼ red chili**
**heaped ⅓ cup drained sun-dried tomatoes in oil**
**1 small handful of cilantro leaves**
**1 flour tortilla**
**1 tablespoon olive oil**
**2¼ ounces mozzarella cheese**
**3½ ounces cooked shelled shrimp**
**¼ lime**
**TRIM THE SCALLIONS** , then place them into a mini food processor. Add the chili, sun-dried tomatoes and cilantro, and blend to a rough paste. Place the tortilla on a cutting board and spread with the paste, leaving a ½-inch gap around the edge.
**HEAT THE OIL** in a nonstick skillet over high heat. Meanwhile, tear the mozzarella into bite-size pieces and scatter it, with the shrimp, all over one half of the tortilla. Wet your finger with cold water and then rub it around the border of the tortilla. Fold the tortilla in half and press the edges together to seal.
**CAREFULLY PUT THE EMPANADA** in the hot pan, reduce the heat to medium and cook 1½ to 2 minutes on each side, or until warmed through and golden. Cut the empanada in half and transfer to serving plates. Cut the lime quarter in half and serve with each empanada.
Dosa Rosti SERVES **2** READY IN **15 MINUTES**
**My _dosa rosti_ is a super-quick southern Indian-inspired snack. The grated potato and onion cook down fast and take on all the flavor of the spices. I love the added layer of heat from the hot lime pickle slathered over the roti. This is fast food, Indian style.**
**1 large potato (about 7 ounces in weight)**
**½ red onion**
**1 teaspoon ground cumin**
**1 teaspoon ground coriander**
**¼ teaspoon chili powder**
**¼ teaspoon turmeric**
**2 tablespoons peanut oil**
**1 teaspoon mustard seeds**
**1 tomato**
**1 handful of cilantro leaves**
**2 plain roti**
**1 tablespoon hot lime pickle**
**½ lime**
**sea salt**
**PEEL THE POTATO** and onion, then grate both into a mixing bowl. Add the cumin, coriander, chili powder and turmeric, and season with salt, then mix everything together well.
**HEAT THE OIL** in a large skillet over high heat and add the mustard seeds. Allow them to crackle a couple of seconds, then add the potatoes and onion, and stir-fry 3 minutes. Add a scant ½ cup water, stir well, then cover and reduce the heat to medium. Cook 4 to 5 minutes, stirring occasionally, until soft.
**WHILE THE POTATO COOKS** , cut the tomato in half, squeeze out the seeds, finely chop the flesh and set aside. Finely chop the cilantro leaves and reserve.
**PUT THE ROTI** onto a cutting board and spread each one evenly with the lime pickle. To serve the dish, squeeze the juice of the lime into the cooked potatoes and stir well. Divide the potato mixture between each roti, scatter with the chopped tomato and cilantro leaves, and serve.
MUMBAI MAGIC, HOLY COWS & PANEER
**The city of Mumbai thrives on street food. It feeds the masses. If you are looking for a quick lunch, a tasty snack or a refreshing drink, Mumbai has it all. The people are fiercely loyal to their favorite vendors, some of whom have been around for generations. In fact, my friends Lizzie and Amish had a _chai_ -off, both taking me to their favorite _chai wallahs_ and tutting at the thought of me drinking and enjoying the other's brew. Just for the record, guys, I enjoyed the Indian Stock Exchange _chai_ the most!**
**I sped through the city on the back of my friend's motorbike, weaving between the blacked-out Mercs, rickshaws, carts and sleeping cows to get to the finest street-food vendors. We ate _chaats_ and _pakoras_ at chhatrapati Shivaji terminus, and Parsi sweets on Marine drive, we sampled the various _puris_ and _kulfi_ from Chowpatty Beach and drank salted _lassis_ from clay mugs in the backstreets of Dharavi.**
**One smoky stand grilled up chunks of paneer and doused them in a super-spicy green chutney. It was fantastic. The slightly chewy, bland paneer was the perfect vehicle for the explosive chutney, absorbing all the flavor and some of the heat. The dish was simple to prepare, overwhelmingly tasty and only took minutes to make.**
Grilled Paneer with Mint Chutney SERVES **2** READY IN **10 MINUTES**
**For my version of the classic Indian snack, grilled paneer, I have added a little coconut to the chutney, as it works so well with the mint, chili and ground coriander. It also seems to bring all those fresh ingredients together so that their flavors combine into something new. Mr. Paneer Wallah on Uah Kham Murg in sunny Mumbai, I hope I have made you proud.**
**1 green chili**
**¼ red onion**
**2 large handfuls of mint leaves**
**½ teaspoon ground coriander**
**1 tomato**
**1 ounce creamed coconut**
**½ lemon**
**5½ ounces paneer**
**1 tablespoon olive oil**
**sea salt**
**CUT THE TOP OFF THE CHILI** and roll the chili between your hands to remove the seeds, then put the chili into a mini food processor. Peel the onion and add it to the food processor. Add the mint leaves, followed by the coriander, tomato, coconut and 3 tablespoons water. Season with salt, squeeze in the juice of the lemon and blend until smooth. Pour into a serving bowl, cover and set aside.
**HEAT A GRILL PAN** over high heat until smoking. Meanwhile, cut the paneer into ½-inch thick pieces and brush each piece with a little oil. Grill 1 to 1½ minutes on each side, or until charred with perfect grill lines. Transfer to a serving plate and serve with the madly green mint chutney.
Fried Chili Corn SERVES **2** READY IN **10 MINUTES**
**A few years ago I was in Thailand for new Year's Eve with all the family. We stayed in a beautiful house on Phuket where we were completely spoiled by the fantastic chef, Jitty. Jitty could cook like an angel sent from cooking heaven, and every meal was a complete pleasure to eat. She realized that she had a bunch of very greedy Brits, which opened up the floodgates to snacks throughout the day. Her awesome corn was served with an ice-cold beer by the pool as the sun went down. I can't give you Thai sunsets or a swimming pool, but make this corn, grab a beer and you'll be just as happy.**
**3¼ cups sunflower oil**
**9-ounce can whole kernel corn**
**¼ cup corn starch**
**1 teaspoon chili powder**
**1 teaspoon chinese five-spice powder**
**sea salt**
**HEAT THE OIL** in a deep pan over high heat. Meanwhile, drain the corn thoroughly in a colander. Pour it into a mixing bowl and add the corn starch, chili powder, Chinese five-spice powder and 1½ tablespoons cold water. Stir everything together well so the corn is completely coated with the corn starch and spices.
**USING A SLOTTED SPOON** , carefully transfer the corn to the hot oil. Stir, then deep-fry 3 minutes, or until golden and crunchy. Remove from the oil and drain very well on a plate lined with paper towels. Add the corn to serving bowls and season with salt. Serve with ice-cold beer.
NOT QUITE LUNCH
**Here are my favorite recipes for a lazy breakfast, early lunch or brunch. They remind me of being on vacation, which is only ever a good thing, when you can get up at your own pace and eat a long, leisurely meal in the early morning. My Baked Eggs with Lentils & Goat Cheese take only 15 minutes to make and are a winner every time. Fantastic Cochin Crab Cakes, flavored with curry leaves and chili, will transport you to the hot, breezy shores of southern India. And my beautifully sweet Villa Dinari Apricots, swollen in orange juice, cinnamon and honey, and served warm with yogurt, can be put together in just 10 minutes. The most time a recipe in this chapter will take to prepare and cook is 25 minutes.**
Chorizo & Chili Focaccia SERVES **2** READY IN **10 MINUTES**
**This super-fast dish is basically an open sandwich. The chorizo filling does most of the work and the fennel seeds, chili and garlic make it taste even better. Juicy cherry tomatoes, peppery arugula and salty pecorino add all the extra flavors you need to make one heck of a sandwich—and it only takes 10 minutes to prepare and cook.**
**7-ounce piece of focaccia**
**1½ tablespoons olive oil, plus extra to serve**
**5½-ounce piece of chorizo**
**2 garlic cloves**
**1 teaspoon fennel seeds**
**¼ teaspoon crushed chili flakes**
**heaped ⅔ cup cherry tomatoes**
**1 lemon**
**2 handfuls of arugula**
**1 ounce pecorino cheese**
**PREHEAT THE BROILER** to high. Meanwhile, cut the focaccia in half horizontally and carefully scoop out a little of the center from each half using your fingers. Drizzle ½ tablespoon of the oil over both halves and broil 2½ to 3 minutes, or until golden.
**WHILE THE FOCACCIA BROILS** , slice the chorizo into bite-size pieces. Peel and slice the garlic into thin slivers. Add the remaining oil to a skillet over medium heat and add the chorizo, garlic, fennel seeds and chili flakes. Stir everything together well and cook 3 to 4 minutes, stirring occasionally, until the chorizo starts turning golden at the edges.
**CUT THE CHERRY TOMATOES** into quarters while the chorizo cooks, then put them into the center of each broiled focaccia half.
**PUT THE FOCACCIA** onto a cutting board. Cut the lemon in half and squeeze the juice of 1 half into the pan with the chorizo, then stir well. Tip the delicious golden chorizo onto the focaccia, along with all the pan juices. Scatter the focaccia with the arugula and shavings of the cheese. Cut the remaining half lemon into wedges and serve it, along with a bottle of olive oil, at the table alongside the focaccia.
MIGHTY MOSQUES, BRIGHT BLUE BOSPORUS & TURKISH PIZZAS
**Istanbul is such a stunning city. It spans both sides of the mighty Bosporus, a strait that marks the divide between Europe and Asia. The European side is home to the beautiful Blue Mosque, the huge minarets of which dwarf the surrounding buildings, and the amazing Grand Bazaar, which is filled with stands selling spices, dried fruits and snacks. A quick boat trip across the sparkling turquoise waters takes you to the Asian side of the city, which has a much more laid-back feel than the majestic European side.**
**When I took the boat across the river to the Asian side of the city it was the day of a soccer game between Istanbul Buyuk and Ankaraspor. I am pleased to say that Istanbul thrashed them 3 to 0! Food was available everywhere. It was awesome. We wandered around soaking up the atmosphere, sipping ice-cold beer and munching on delicious snacks, such as _kasarli_ , a Turkish cheese sandwich, and yummy _simit_ , a chewy ring of bread covered in crunchy sesame seeds, as well as tangy fish and onion kebabs.**
**All the street food was accompanied by little glass shakers filled with blood-red Turkish chili flakes. The chili flakes have a mild, smoky flavor, like a combination of a sun-dried tomato and dried red chili. The rich flavor worked beautifully with all the charcoal-grilled food.**
**The street food that did it for me the most was _lahmacun_ , or Turkish pizza. This fabulous snack, which could thankfully be found all over the city, had a crispy, chewy base that was covered in ground beef or lamb, spices, tomato and herbs. It was always served with those wonderful chili flakes and with wedges of lemon to freshen it up and enhance all those flavors. I fell in love with this snack and am pleased to say that I have made a super-fast version—my Lahmacun Turkish Pizza can be made in just 10 minutes.**
Lahmacun — Turkish Pizza SERVES **2** READY IN **10 MINUTES**
**1½ tablespoons olive oil**
**7 ounces ground lamb**
**2 garlic cloves**
**½ teaspoon sweet paprika**
**½ teaspoon ground cumin**
**¼ teaspoon ground cinnamon**
**1 lemon**
**½ tomato**
**1 tablespoon sun-dried tomato paste**
**2 flour tortillas**
**1 small handful of mint leaves**
**1 small handful of parsley leaves**
**a pinch of crushed chili flakes**
**sea salt**
**PREHEAT THE BROILER** to high. Meanwhile, place 1 tablespoon of the oil in a large skillet over high heat. Add the lamb and stir well. Peel and crush in the garlic, and add the paprika, cumin and cinnamon to the pan, then season with salt. Squeeze in the juice of ½ lemon and stir-fry 3 to 4 minutes, or until the lamb is cooked through and golden. Remove from the heat and set aside.
**SQUEEZE THE SEEDS** out of the tomato half, then finely chop the flesh. Add the tomato to the cooked lamb followed by the sun-dried tomato paste. Stir well.
**PUT THE TORTILLAS** onto a broiler rack and brush with the remaining oil. Spoon the spicy lamb onto the tortillas and broil 1 to 2 minutes, or until the tortillas start to get crisp at the edges.
**WHILE THE LAHMACUN COOKS** , finely chop the herbs and cut the remaining lemon half into quarters. Scatter the herbs and chili flakes onto the cooked lahmacun and serve with the lemon wedges on the side.
Scrambled Eggs with Lime & Ginger Smoked Salmon SERVES **2** READY IN **10 MINUTES**
**Smoked salmon is a great express ingredient. It's bursting with flavor and you don't have to do anything to it. I have simply jazzed up the salmon with a lovely dressing made from soy sauce, sesame oil, chili powder, lime juice and ginger, all of which complement the oily fish. The addition of a bagel and some creamy eggs takes it into a breakfast place, and the pumpkin seeds add some texture.**
**1½ teaspoons soy sauce**
**½ teaspoon sesame oil**
**a pinch of chili powder**
**1 lime**
**¼-inch piece fresh gingerroot**
**5 ounces sliced smoked salmon**
**1 bagel**
**2 teaspoons butter**
**4 eggs**
**6 chives**
**1 handful of baby spinach leaves**
**1 tablespoon pumpkin seeds**
**sea salt and freshly ground black pepper**
**POUR THE SOY SAUCE** and sesame oil into a shallow dish. Add the chili powder and squeeze in the juice of the lime. Then peel the ginger and grate it into the dish. Stir with a fork, then add the salmon and gently stir again. Cover and set aside.
**CUT THE BAGEL IN HALF** and put it in the toaster to toast. Meanwhile, melt the butter in a skillet over medium heat. Crack the eggs into a mixing bowl, season with salt and pepper and beat well. Pour the eggs into the skillet with the melted butter and leave 45 seconds to let them begin to set. Stir well, then cook another 1 to 2 minutes, stirring frequently, until they are 80 percent set, then remove from the heat—the eggs will continue to cook a little.
**PUT EACH TOASTED BAGEL HALF** onto a serving plate. Spoon the eggs onto the bagel halves and use scissors to snip the chives all over the top. Add the spinach and pumpkin seeds to the dish with the salmon and toss together. Divide the salmon and spinach among the two plates to serve.
Smoked Haddock & Chumula Kedgeree SERVES **2** READY IN **20 MINUTES**
**FOR THE KEDGEREE**
**1 cup uncooked basmati rice**
**2 eggs**
**1 tablespoon olive oil**
**5 ounces undyed smoked haddock heaped ½ cup frozen peas**
**3 cardamom pods**
**2 tablespoons heavy cream (optional)**
**freshly ground black pepper**
**FOR THE CHUMULA**
**1 garlic clove**
**½ green chili**
**2 handfuls of cilantro leaves**
**1 handful of parsley leaves**
**1 teaspoon paprika**
**1 teaspoon ground cumin**
**2 teaspoons sugar**
**¼ cup olive oil**
**1 lemon**
**sea salt**
**COOK THE RICE** in boiling water 10 to 12 minutes, or until soft, or following directions on the package. Drain in a strainer and set aside.
**WHILE THE RICE COOKS** , boil the eggs in a saucepan of boiling water 7½ minutes until perfectly medium-soft. Remove with a slotted spoon and put them in a bowl of iced water to cool.
**MEANWHILE, PEEL THE GARLIC** for the chumula, then add all the ingredients for the chumula, except the lemon, to a mini food processor or blender. Squeeze in the juice of the lemon, then season with salt. Blend to a coarse paste then set aside to let the flavors develop.
**HEAT THE OIL** for the kedgeree in a large skillet over low heat. Flake in the smoked haddock and add the peas and cardamom pods. Cook gently 3 to 4 minutes, stirring occasionally, until the fish is cooked and the peas have warmed through. Pour in the chumula, the cooked rice and cream, if using, and season with black pepper. Carefully stir everything together to combine. Continue to cook another 2 to 3 minutes to allow all the flavors to come together.
**PEEL THE EGGS** and cut them in half while the kedgeree cooks. Serve the kedgeree with the eggs on the side.
Cochin Crab Cakes SERVES **2** READY IN **15 MINUTES**
**My cochin crab cakes make the perfect light meal. They are packed with juicy crabmeat, and with tomatoes, cilantro and scallions to freshen things up. Finally, mustard seeds, curry leaves, turmeric and chili add the flavors of southern India. The hit of lime at the end accentuates all the spices even more, so in only 15 minutes you get something amazing.**
**2 tablespoons peanut oil**
**1 teaspoon mustard seeds**
**a large pinch of dried curry leaves**
**¼ teaspoon turmeric**
**½ teaspoon chili powder**
**3 scallions**
**5 cherry tomatoes**
**1 handful of cilantro leaves**
**1½ cups cooked white crabmeat**
**¾ cup fresh breadcrumbs**
**1 small egg**
**1 lime**
**sea salt**
**ADD 1 TABLESPOON OF THE OIL** to a small skillet over medium heat and then add the mustard seeds. Fry 30 seconds, shaking the pan continuously, or until the mustard seeds start popping. Rub the curry leaves between your hands to break them up and let them drop into the pan. Remove the pan from the heat and add the turmeric and chili powder, and set aside.
**TRIM THE SCALLIONS** , then finely chop them with the cherry tomatoes and cilantro, and add them all to a mixing bowl. Pour in the crabmeat and breadcrumbs, and season with salt. Add the cooked spices and oil from the skillet, then crack in the egg and stir everything together well to combine. Divide the mixture into 4 and flatten each one into a crab cake about ½ inch thick.
**ADD THE REMAINING OIL** to a large skillet over medium heat and fry the crab cakes 2 minutes on each side, or until beautifully golden and warmed through. Cut the lime into wedges and serve with the hot crab cakes.
Shrimp Tortas with Salsa Mexicana SERVES **2** READY IN **20 MINUTES**
**FOR THE SHRIMP TORTAS**
**7 ounces potatoes**
**1 garlic clove**
**4 scallions**
**1 handful of cilantro leaves**
**6 ounces raw shelled jumbo shrimp**
**1 ounce feta cheese**
**½ egg**
**scant ⅔ cup all-purpose flour**
**1 tablespoon olive oil, plus extra for greasing**
**sea salt and freshly ground black pepper**
**FOR THE SALSA MEXICANA**
**1 garlic clove**
**⅔ cup drained sun-dried tomatoes in oil**
**1 dried chipotle chili**
**1 tablespoon olive oil**
**½ lime**
**CHOP THE UNPEELED POTATOES** into ½-inch cubes and cook them in a saucepan of boiling water 8 minutes, or until tender. Drain in a colander and refresh under cold water, then drain again. Return the potatoes to the saucepan and lightly mash them so they start to break down. Set aside.
**WHILE THE POTATOES COOK** , peel the garlic and trim the scallions, then put them into a food processor with the cilantro and blend to roughly chop. Add the shrimp and feta cheese, and blend to a rough paste. Pour the paste into a large mixing bowl, add the egg and flour, then season with salt and pepper. Transfer the mashed potatoes to the bowl and stir everything together well until it has a doughlike consistency.
**ADD THE OIL** to a small skillet over high heat. Scoop the potato mixture into the pan and spread it out to cover the base. Reduce the heat to medium and cook 1½ to 2 minutes, shaking the pan occasionally, until golden on one side.
**MEANWHILE, TO MAKE THE SALSA** , peel the garlic, then put it into a mini food processor or blender along with the sun-dried tomatoes, chili and oil. Squeeze in the juice of the lime, season with salt and blend to a smooth paste. Pour the smoky salsa into a serving bowl and set aside.
**WHEN THE TORTAS HAS COOKED** on one side, rub a little oil onto a side plate and carefully place it, oil-side down, over the pan with the half-cooked tortas. Holding the plate and the skillet handle, carefully flip the skillet over so that the tortas rests on the plate. Slip it back into the skillet and cook another 1½ to 2 minutes, or until golden. Serve with the hot, smoky salsa on the side.
Baked Eggs with Lentils & Goat Cheese SERVES **2** READY IN **15 MINUTES**
**At the moment, baked eggs are very trendy, and for good reason—they are delicious and require little effort. My baked eggs sit on a bed of lentils, sage, chili and scallions. I have added sun-dried tomato paste and paprika to introduce even more flavor without taking up any extra time. A final crumble of salty goat cheese, which melts into the eggs while they finish cooking, finishes everything off perfectly.**
**1 garlic clove**
**3 scallions**
**½ red chili**
**8 sage leaves**
**2 tablespoons olive oil**
**15-ounce can green lentils**
**scant ⅔ cup tomato passata**
**1 tablespoon sun-dried tomato paste**
**2 eggs**
**2 ounces goat cheese**
**¼ teaspoon paprika**
**2 slices of fantastic bread**
**sea salt and freshly ground black pepper**
**PREHEAT THE BROILER** to high. Meanwhile, peel the garlic and trim the scallions, then finely chop the garlic, scallions, chili and sage. Place 1 tablespoon of the oil in a large ovenproof skillet over medium heat and add the chopped ingredients. Cook 3 to 4 minutes, stirring occasionally, until the scallions have started to soften.
**DRAIN AND RINSE THE LENTILS** , then pour them into the pan. Add the passata and sun-dried tomato paste, then season with a good pinch of salt and pepper. Stir everything together really well to combine.
**MAKE TWO SHALLOW WELLS** in the lentil mixture and crack in the eggs. Crumble the goat cheese over the top and put a small pinch of paprika and salt onto each egg. Broil 4 to 5 minutes, or until the egg whites have just set but the yolks are still runny.
**PUT THE BREAD INTO THE TOASTER** to toast while the eggs cook. Drizzle the remaining oil over the cooked eggs and serve with the toast.
Parsi Eggs SERVES **2** READY IN **15 MINUTES**
**This was my breakfast in a little Parsi café in Mumbai after a long overnight train journey from Goa. The eggs were Indianed up with loads of spices and mixed with vegetables and fresh cilantro. It was the perfect start to the day in that magnificent city.**
**4 eggs**
**¼ teaspoon chili powder**
**½ teaspoon ground coriander**
**¼ teaspoon garam masala**
**1 garlic clove**
**3 scallions**
**1 tomato**
**1 handful of cilantro leaves**
**2 slices of brown bread**
**1 tablespoon olive oil**
**heaped ⅓ cup frozen peas**
**heaped ⅓ cup canned kernel corn**
**sea salt**
**CRACK THE EGGS** into a mixing bowl and add the chili powder, ground coriander and garam masala. Season with a good pinch of salt and beat together. Set aside.
**PEEL THE GARLIC** and trim the scallions, then finely chop the garlic, scallions, tomato and cilantro leaves. Set aside with the cilantro in a separate pile. Put the bread in the toaster to toast while you cook the eggs.
**ADD THE OIL** to a large skillet over high heat, then add the garlic, scallions and tomato. Stir-fry the mixture 2 minutes, or until the tomato starts to break down and become a little dry.
**POUR IN THE PEAS** and kernel corn, then mix well. Reduce the heat to medium and add the egg mixture. Stir everything together really well and let sit 1 minute to set. Add the cilantro and cook 1 to 2 minutes, stirring continuously, until set. Serve with the toast.
Blue Mosque Goat Cheese Tart SERVES **2** READY IN **25 MINUTES**
**My goat cheese tart is a twist on the classic turkish snack _borek_. I have made one large tart instead of fiddly individual portions, and stuffed it with chili, scallions, olives, walnuts, tarragon, goat cheese and paprika.**
**1 green chili**
**3 scallions**
**scant ⅓ cup pitted green olives**
**scant ½ cup walnuts**
**1 large handful of tarragon leaves**
**4½ ounces soft goat cheese**
**¼ teaspoon paprika**
**1 lemon**
**2 tablespoons olive oil**
**3 sheets of filo pastry, defrosted if frozen**
**heaped ⅓ cup yogurt**
**sea salt and freshly ground black pepper**
**PREHEAT THE OVEN** to 350°F. Cut the top off the chili and roll the chili between your hands to remove the seeds. Trim the scallions. Put the chili and scallions into a food processor, and add the olives, walnuts and tarragon. Blend until coarsely chopped, then add the goat cheese and paprika. Squeeze in the juice of ½ lemon and season with salt and pepper. Give it a quick blast to mix it all together.
**TAKE A PIECE OF PARCHMENT PAPER** large enough to fit in a baking pan, and crumple it up using your hands (this stops the sides from curling up). Flatten the parchment paper onto a cutting board and brush with olive oil. Lay a piece of the filo pastry on top of the parchment paper and brush it all over with oil (cover the unused filo with a damp dish towel to prevent it from drying out). Put another piece of filo pastry on top of the first layer and brush it with oil.
**SCOOP THE FILLING** into the center of the pastry and spread it out into a rectangular shape about ⅝ inch thick. Cover with the final sheet of filo pastry and fold in the sides to form a neat rectangle. Brush the top of the tart with oil and season with salt and pepper.
**TRANSFER THE TART** to the baking pan by lifting up the sides of the parchment paper, then bake 15 to 18 minutes, or until golden on top. Meanwhile, put the yogurt into a serving bowl, squeeze in the juice of the remaining ½ lemon and season with salt and pepper. Mix well. Serve the hot tart with the lemony yogurt on the side.
Za'atar Halloumi with Couscous Salad SERVES **2** READY IN **15 MINUTES**
**FOR THE ZA'ATAR HALLOUMI**
**1 tablespoon sumac**
**1 tablespoon dried oregano**
**3 teaspoons sesame seeds**
**7 ounces halloumi**
**2 tablespoons olive oil**
**FOR THE COUSCOUS**
**⅓ cup couscous**
**1 red chili**
**1 handful of parsley leaves**
**1 tablespoon capers**
**1 tablespoon olive oil**
**½ lemon**
**sea salt and freshly ground black pepper**
**TO MAKE THE ZA'ATAR** , mix the sumac, oregano, sesame seeds and a good pinch of salt in a bowl.
**PUT HALF THE ZA'ATAR** into a large mixing bowl, add the couscous and stir with a fork to combine. Pour in a generous ⅓ cup warm water, cover with plastic wrap and set aside to allow the couscous to absorb the water. This will take about 10 minutes.
**MEANWHILE, CUT THE TOP** off the chili and roll the chili between your hands to remove the seeds, then finely chop the chili and parsley. Drain and finely chop the capers. Set aside.
**CUT THE HALLOUMI** into ¼-inch slices and press each piece into the za'atar spices to cover with a thin layer on one side. Heat the oil in large skillet over medium heat. Add the halloumi, spice-side down, and fry 2 to 3 minutes on each side until golden. Remove the pan from the heat and set it aside while you finish making the salad.
**WHEN THE COUSCOUS** has absorbed all the water, fluff it up with a fork, then add the olive oil and squeeze in the juice of the lemon. Stir in the chopped chili, parsley and capers, and add a pinch of salt, if needed, and pepper. Serve the couscous with the delicious fried halloumi.
Orange & Cardamom French Toast SERVES **2** READY IN **15 MINUTES**
**For those with a sweet tooth, my orange & cardamom French toast won't disappoint. The toast is cooked until crisp in a mixture of butter, cardamom, golden raisins and orange. The cardamom flavors everything, and the golden raisins swell up in the perfumed juices. I use maple syrup as the crowning glory, because I love the slightly smoky sweetness it gives to the overall flavour of the dish.**
**2 eggs**
**scant ½ cup milk**
**1 orange**
**1 tablespoon powdered sugar**
**4 thick slices of white bread**
**(about ½ inch thick)**
**2 heaped tablespoons butter scant ½ cup golden raisins**
**6 cardamom pods**
**3 tablespoons maple syrup**
**CRACK THE EGGS** into a mixing bowl and pour in the milk. Add the zest of the orange to the bowl followed by the powdered sugar and beat together. Place the bread in a shallow dish and pour the egg mixture over it. Ensure that both sides of each slice of bread are well soaked so that nearly all the liquid is absorbed. Set aside.
**PUT THE BUTTER** and golden raisins into a large skillet over medium heat. Gently crush the cardamom pods by pressing down on them with the flat side of a knife blade, then add them to the butter. Quarter the orange and squeeze the juice of one quarter into the skillet. Stir well and cook gently 1 minute, or until the butter melts.
**ADD THE BREAD** to the skillet and fry 2½ to 3 minutes on each side until beautifully golden, shaking the pan occasionally. Divide between two serving plates and squeeze the juice of the remaining orange quarters onto each piece of toast. Drizzle with the maple syrup and serve with the yummy golden raisins.
Villa Dinari Apricots with Yogurt SERVES **2** READY IN **10 MINUTES**
**During my time in Morocco I cooked dinner with the chefs at the beautiful Villa Dinari. We made a feast that included a particularly wonderful lamb and pear tagine, which was finished off with dried apricots that had been cooked slowly in sugar and cinnamon. They were fantastic. I thought that the apricots, with a little twist, would be excellent added to a big fat bowl of creamy yogurt. For my fast breakfast version I cook the apricots for a couple of minutes in butter, orange, cinnamon and honey. Once they have swollen to capacity they go straight into bowls to be topped with some yogurt and a scattering of crunchy walnuts.**
**2 tablespoons butter**
**generous ¾ cup ready-to-eat**
**dried apricots**
**½ teaspoon ground cinnamon**
**2 tablespoons honey**
**½ orange**
**1 cup yogurt**
**scant ½ cup walnuts**
**PLACE THE BUTTER** in a skillet over medium heat and add the apricots, cinnamon and honey.
**SQUEEZE IN THE JUICE** of the orange and stir well. Cook 5 to 6 minutes, stirring occasionally, until the apricots have swollen and the sauce has thickened. Spoon the apricots and the lovely sticky sauce into two serving bowls. Divide the yogurt among the two bowls and scatter each with walnuts to serve.
MIDWEEK LIFESAVERS
**My midweek lifesavers are all you need to know for those crucial moments in life when you get in late from work and want to eat immediately. With no messing around required, these recipes are fast, fresh and furious. Try my heavenly Cambodian Seafood Amok, a coconut curry that can be made in just 15 minutes, or my Little South Island Pork Salad, which is made with juicy orange pieces and crunchy fennel, flavored with Chinese five-spice powder and chili flakes. This chapter is also home to the mighty Bosporus Burger, a succulent beef burger flavored with spices and served with blue cheese. This epic creation takes only 15 minutes to make, so you'll never be caught out hungry again. Most recipes in this chapter take 20 minutes or less to prepare and the longest takes only 25 minutes.**
Goan Cinnamon & Mint Chicken Curry SERVES **2** READY IN **20 MINUTES**
**This classic Goan dish is one of my favorite curries ever. It's vibrant in color and fresh tasting, but the best thing is that it's so simple to make. Add everything to a blender to make a killer sauce, fry the chicken, pour in the sauce and cook for a few minutes. What could be simpler?**
**scant ⅔ cup basmati rice**
**2 green chilies**
**3 garlic cloves**
**2 large handfuls of cilantro leaves and stalks**
**1 large handful of mint leaves**
**½ teaspoon ground cinnamon**
**½ teaspoon freshly ground black pepper**
**1 teaspoon sugar**
**1½ teaspoons Worcestershire sauce**
**½-inch piece fresh gingerroot**
**1 lime**
**10½ ounces boneless, skinless chicken thighs**
**1 tablespoon peanut oil**
**sea salt**
**COOK THE RICE** in boiling water 10 to 12 minutes, or until soft, or following directions on the package. Drain in a strainer, then cover the rice with a clean dish towel while still in the strainer, and set aside.
**MEANWHILE, CUT THE TOP** off each chili and roll the chili between your hands to remove the seeds, then add the chilies to a blender or food processor. Peel the garlic and add it to the blender with the cilantro leaves and stalks, mint, cinnamon, black pepper, sugar, Worcestershire sauce and a good pinch of salt. Peel and add the ginger, then squeeze in the juice of the lime and add a scant ½ cup water. Blend until smooth.
**SLICE THE CHICKEN** into thin strips. Add the oil to a skillet over high heat. Then add the chicken and stir-fry 5 to 6 minutes, or until it starts to turn golden brown. Pour in the green sauce and reduce the heat to medium. Add a scant ½ cup water to the blender, swill it around and add it to the pan to get every last drop of sauce into the dish. Stir everything together really well and simmer 5 to 6 minutes, stirring occasionally, until the chicken is cooked through and tender. Serve with the rice.
Phipp Street Stir-Fry SERVES **2** READY IN **15 MINUTES**
**I live on Phipp Street, in London, and this stir-fry was invented after a long day working in my kitchen. I mine-swept my almost empty fridge, chopped everything up and stir-fried it with some noodles. The result was this awesome dish. I hope it brings you as much satisfaction as it did me when you need a good feed after a long day and have little time for cooking.**
**5 ounces vermicelli rice noodles**
**2 tablespoons peanut oil**
**2 lemongrass stalks**
**2 garlic cloves**
**1 red chili**
**1 baby gem lettuce**
**2 boneless, skinless chicken thighs (7 ounces total weight)**
**2 teaspoons fish sauce**
**1 tablespoon light soy sauce**
**½ lime**
**COOK THE NOODLES** in boiling water 2 to 3 minutes, or until soft, or following directions on the package. Drain in a strainer and drizzle with 1 tablespoon of the oil to prevent the noodles from sticking together, then set aside.
**MEANWHILE, GET EVERYTHING READY** to stir-fry. Remove the tough outer leaves from the lemongrass and cut off the ends of the stalks. Peel the garlic and cut the top off the chili, then add the lemongrass, garlic and chili to a mini food processor, and blend to a paste. Cut the stalk off the lettuce, separate the leaves and set aside. Slice the chicken into very thin strips and reserve.
**HEAT THE REMAINING OIL** in a wok over high heat until smoking. Add the chicken and stir-fry 5 to 6 minutes, or until golden at the edges. Scoop the spice paste into the wok and stir-fry another 30 seconds, or until fragrant. Add the lettuce leaves, fish sauce and soy sauce, then squeeze in the juice of the lime. Stir-fry 1 to 2 minutes, or until the lettuce leaves have wilted and the chicken is cooked through. Finally, add the noodles, toss everything together and serve.
Chicken Morita with Avocado Sauce SERVES **2** READY IN **20 MINUTES**
**FOR THE CHICKEN MORITA**
**scant ⅔ cup basmati rice**
**2 garlic cloves**
**1 teaspoon smoked paprika**
**½ teaspoon chili powder**
**2 tablespoons sun-dried tomato paste**
**1 teaspoon tamarind paste**
**¼ teaspoon sugar**
**2 tablespoons olive oil**
**2 skinless chicken breasts**
**sea salt**
**FOR THE AVOCADO SAUCE**
**1 avocado**
**1 lime**
**heaped ⅓ cup yogurt**
**1 small handful of cilantro leaves**
**PREHEAT THE BROILER** to high. Cook the rice in boiling water 10 to 12 minutes, or until soft, or following directions on the package. Drain in a strainer, cover the rice with a clean dish towel while still in the strainer and set aside.
**MEANWHILE, PEEL THE GARLIC** , then put it into a mini food processor, and add the paprika, chili powder, sun-dried tomato paste, tamarind paste, sugar, 1 tablespoon of the olive oil and a good pinch of salt, and blend until smooth.
**LAY THE CHICKEN BREASTS** on a cutting board and, using a rolling pin, bash them out until they are about ⅝ inch thick. Prick the chicken all over with a fork, then rub the paste all over both sides. Put the chicken onto a broiler rack and broil 7 to 8 minutes, or until golden on one side.
**WHILE THE CHICKEN BROILS** , cut the avocado in half and remove the seed using a knife. Scoop the flesh out with a spoon and put it into a blender or food processor. Squeeze in the juice of ½ lime and add the yogurt, cilantro, the remaining oil and a good pinch of salt. Blend until smooth, then pour into a serving bowl. Cover and set aside. Cut the remaining lime half into 2 wedges.
**TURN THE HALF-COOKED CHICKEN** over and broil another 7 to 8 minutes, or until cooked through and tender. Serve the chicken with a wedge of lime and the cooked rice, and add the avocado sauce at the table.
Great Eastern Duck Salad SERVES **2** READY IN **25 MINUTES**
**1 tablespoon olive oil**
**2 duck breasts**
**(about 5¾ ounces each)**
**¾-pound watermelon**
**½ red chili**
**½ lime**
**2 tablespoons hoisin sauce**
**1 teaspoon light soy sauce**
**¼ teaspoon chinese five-spice powder**
**2½ cups watercress**
**1 handful of mint leaves**
**heaped ⅓ cup cashews**
**sea salt**
**HEAT THE OIL** in a skillet over high heat. Meanwhile, score the fat on the duck breasts and season both sides with salt. Carefully put the duck in the hot pan, skin-side down, and reduce the heat to medium. Cook 8 to 10 minutes, or until the skin is really crisp.
**WHILE THE DUCK COOKS** , scoop the watermelon out of the shell and cut the flesh into bite-size pieces, removing any large seeds. Add the watermelon pieces to a large mixing bowl and set aside.
**TURN THE CRISPY DUCK** over and cook another 8 to 10 minutes, or until beautifully tender and pink in the center, then remove from the heat.
**SEED AND FINELY SLICE THE CHILI** while the duck finishes cooking. Add it to the mixing bowl with the watermelon and squeeze in the juice of the lime.
**POUR AWAY ANY EXCESS FAT** from the cooked duck. Add the hoisin sauce, soy sauce and Chinese five-spice powder to the pan, and mix well. Remove the duck breasts from the pan, slice them into thick pieces and set aside. Add the watercress, mint and cashews to the bowl with the watermelon and toss everything together. Serve the salad with the beautiful duck slices, with the pan juices spooned on top.
Oaxaca Tostadas SERVES **2** READY IN **15 MINUTES**
**My _tostadas_ were inspired by the wonderful giant _tostadas_ of the Central Market in the city of Oaxaca in Mexico. They are completely delicious—you taste hot and cold, crunchy and smooth, spicy and mild, salty and sour in every bite. And, because they only take 15 minutes to make, they are a real midweek lifesaver.**
**2 tablespoons olive oil**
**2 large tortillas**
**1 red onion**
**2 garlic cloves**
**7-ounce piece of chorizo**
**2 ripe avocados**
**1 green chili**
**8 scallions**
**1 handful of cilantro leaves**
**1½ limes**
**1 tomato**
**2 ounces Gruyère cheese**
**a pinch of smoked paprika**
**sea salt**
**PREHEAT THE BROILER TO HIGH**. Meanwhile, brush 1 tablespoon of the oil all over both sides of each tortilla. Put them onto a broiler rack and broil 30 seconds to 1 minute on each side, or until crisp and golden at the edges. Remove from the broiler and place on serving plates.
**PEEL THE RED ONION AND GARLIC** , then slice the onion and roughly chop the garlic and chorizo. Heat the remaining oil in a skillet over medium heat and add the sliced and chopped ingredients. Stir well and cook 5 to 6 minutes, stirring occasionally, until golden.
**MEANWHILE, CUT THE AVOCADOS** in half and remove the seeds using a knife. Scoop the flesh out with a spoon and put it into a mini food processor or blender. Cut the top off the chili and trim the scallions, then add both ingredients to the food processor with the cilantro and a pinch of salt. Squeeze in the juice of ½ lime and blend to a rough paste.
**FINELY SLICE THE TOMATO** , grate the cheese and quarter the remaining lime. Divide the avocado mixture among the 2 tortillas and spread it evenly over them, using a knife. Arrange the tomato slices, hot chorizo and onion on top, and scatter with the cheese. Dust both tostadas with smoked paprika and serve with the lime quarters.
TINY TABLES, MOTORBIKES & BUN CHA
**When I arrived in Hanoi I was struck by the madness of the place. The air was sticky, people actually wore conical hats, smoky food stands lined the streets and an army of predatory motorbikes circled the roads like angry bulls at Pamplona.**
**Once I had plucked up the courage to cross a road (which was only after watching an old lady fearlessly stride to the other side), I was able to sample the many culinary delights of the city. Perfectly barbecued meats, grilled fish, peppered stir-fries and fragrant soups—Hanoi had it all, with fishy, hot, salty and sour flavors beautifully balanced in every bite.**
**Eating in Hanoi means eating street food—and it was everywhere. A few stands had evolved into restaurants, but on the whole you eat out on the curb, crouched at tiny tables. One lunchtime, I visited a packed street stand and squeezed onto a tiny chair, literally in the road, to slurp the lunchtime soup special, _bun cha_. It was amazing! The wonderfully salty soup was spiked with black pepper and served with tender grilled pork. The table came laden with little dishes of rice noodles, herbs and chilies to add to your bowl. This fast-food glory summed up all that was triumphant about Vietnamese food.**
Vietnamese Bun Cha SERVES **2** READY IN **20 MINUTES**
**FOR THE SOUP**
**2 cups chicken stock**
**6 black peppercorns**
**2 star anise**
**1-inch stick of cinnamon**
**2 teaspoons sugar**
**3 tablespoons fish sauce**
**2 lemongrass stalks**
**½ lime**
**5 ounces vermicelli rice noodles**
**FOR THE PORK PATTIES**
**1 small handful of cilantro leaves**
**1 small handful of mint leaves**
**4¼ ounces ground pork**
**1 teaspoon fish sauce**
**1 teaspoon peanut oil**
**TO SERVE**
**4 scallions**
**½ red chili**
**½ lime**
**1½ cups bean sprouts**
**1 large handful of cilantro leaves**
**1 large handful of mint leaves**
**POUR THE STOCK** and 2 cups water into a saucepan and add the peppercorns, star anise, cinnamon stick, sugar and fish sauce. Bash the fat ends of the lemongrass stalks with a spoon, snap them in half and add them to the pan. Squeeze in the juice of the lime, stir well and bring to a boil over medium heat.
**MEANWHILE, ADD THE NOODLES** to a pan of boiling water and let stand 3 minutes, or following the directions on the package. Drain in a strainer and refresh under cold water, then drain again. Set aside to continue draining in the strainer.
**CHOP THE HERBS** for the pork patties and put them into a large bowl. Add the pork and fish sauce and stir well to combine. Heat the oil in a skillet over medium heat. Meanwhile, divide the pork into 4 and flatten into mini burger patties. Fry the patties 3 minutes on each side, or until golden and cooked through.
**WHILE THE PORK IS COOKING** , trim the scallions, then cut each in half and then into thin strips. Seed the chili, then slice it finely. Cut the lime in half.
**DIVIDE THE NOODLES** and bean sprouts among two large serving bowls, and put 2 pork patties into each bowl. Scatter each bowl with half the scallions and the chili, then top with the lime and the herbs. Remove the spices from the stock and divide the hot, fragrant soup among the two bowls. Serve immediately.
Little South Island Pork Salad SERVES **2** READY IN **20 MINUTES**
**This dish sums up why eating real Chinese food is such a pleasure. No radioactive-red gloopy sauce, not a canned pineapple chunk in sight—just simple, fresh, clean flavors that all work superbly together in a dish that takes minutes to make. The crunchy fennel and sweet carrot soak up all the richness of the stir-fried pork and the delicious flavors of the tart dressing. This is how Chinese food should be!**
**FOR THE PORK SALAD**
**1 tablespoon peanut oil**
**¾ pound ground pork**
**½ teaspoon chinese five-spice powder**
**½ teaspoon crushed chili flakes**
**1 tablespoon light soy sauce**
**1 orange**
**1 fennel bulb**
**1 carrot**
**3½ ounces frisée lettuce leaves**
**FOR THE GINGER DRESSING**
**1½ tablespoons cider vinegar**
**2 teaspoons light soy sauce**
**½-inch piece fresh gingerroot**
**HEAT A WOK** over high heat until smoking. Pour in the oil, swirl it around and then add the pork. Stir-fry 5 to 6 minutes, or until the edges of the pork start to catch and become golden.
**SPRINKLE THE CHINESE FIVE-SPICE POWDER** and chili flakes onto the pork and add the soy sauce. Continue to stir-fry 30 seconds, then remove from the heat and set aside.
**USING A SHARP KNIFE** , cut the top and bottom off the orange, and stand it up on your cutting board. Carefully slice the skin off in sections, cutting from top to bottom. Remove any remaining pith, then cut the juicy pieces of orange away from the membrane and put them in a mixing bowl. Squeeze in any juices from the membrane.
**FINELY SLICE THE FENNEL** and add it to the bowl with the orange. Peel the carrot and grate it, using the coarse setting on a grater, into the bowl. Pour in the cider vinegar and soy sauce for the dressing, then peel and finely grate in the ginger. Add the lettuce leaves and cooked pork, along with all the lovely juices, into the mixing bowl and toss everything together to serve.
Mr. Wong's Hunan Lamb SERVES **2** READY IN **20 MINUTES**
**This dish is all about the big spices of Hunanese cooking. A fiery paste made from dried chilies, Szechuan pepper, ginger and scallions is used to coat the delicate lamb cutlets and turns them into something fierce. The sweetness of the lamb handles all the big flavors, and the delicate bok choy, soy and orange stir-fry absorbs some of the heat.**
**FOR THE LAMB**
**2 dried red chilies**
**1 teaspoon Szechuan pepper**
**½-inch piece fresh gingerroot**
**5 scallions**
**2 tablespoons peanut oil**
**6 lamb cutlets (about**
**1 pound 2 ounces total weight)**
**sea salt**
**FOR THE BOK CHOY AND ORANGE STIR-FRY**
**7 ounces bok choy**
**1 tablespoon peanut oil**
**1 tablespoon soy sauce**
**½ orange**
**PREHEAT THE BROILER** to high. Meanwhile, put the chilies, Szechuan pepper and a pinch of salt into a mini food processor, and blend to a coarse powder. Peel the ginger and trim the scallions, then add them to the food processor, followed by the oil. Blend to a rough paste.
**LIGHTLY SCORE** both sides of the lamb cutlets in a criss-cross pattern and put them in a mixing bowl. Pour in the spice paste and mix everything together well so the paste completely covers the lamb. Put the lamb on a broiler rack and broil 5 to 6 minutes on each side, or until golden outside and pink and juicy in the center.
**WHILE THE LAMB COOKS** , cut the bok choy lengthwise into quarters. Place a wok over high heat until smoking and pour in the oil. Add the bok choy and stir-fry 2 minutes, then add the soy sauce and squeeze in the juice of the orange. Continue to stir-fry 30 seconds, then reduce the heat to low and cook 3 to 4 minutes, or until tender. Serve the stir-fry with the lamb.
Grilled Eggplant with Lamb, Mint & Feta SERVES **2** READY IN **15 MINUTES**
**This is my express version of a classic Eastern Mediterranean stuffed-eggplant dish. I grill the eggplant, which is the fastest way to cook it, and top it with stir-fried lamb. The final addition of mint and feta completes the dish with the fresh and salty flavors it needs.**
**1 large eggplant**
**3 tablespoons olive oil**
**2 bay leaves**
**10½ ounces ground lamb**
**1¼ teaspoons ground allspice**
**½ teaspoon ground cinnamon**
**2 garlic cloves**
**scant 1¼ cups tomato passata**
**2¼ ounces feta cheese**
**1 small handful of mint leaves**
**sea salt and freshly ground black pepper**
**TO SERVE**
**green salad**
**HEAT A GRILL PAN** over high heat until smoking. Meanwhile, cut the eggplant lengthwise into ½-inch slices and add them to a mixing bowl. Add 2 tablespoons of the oil and a good pinch of salt and pepper. Mix everything together really well so that both sides of the eggplant slices are coated in the oil. Cook 2½ to 3 minutes on each side, or until charred and tender. Divide between two serving plates and set aside.
**WHILE THE EGGPLANT COOKS** , add the remaining oil to a skillet over medium heat. Add the bay leaves and cook 5 seconds until fragrant. Add the lamb, allspice, cinnamon and a good pinch of salt and pepper. Peel and crush in the garlic, turn the heat up to high and stir-fry 3 to 4 minutes, or until the lamb is golden.
**POUR IN THE PASSATA** and mix well. Reduce the heat to medium and cook 3 to 4 minutes, stirring occasionally, until the lamb is cooked through and the sauce has thickened. To serve the dish, spoon the lamb onto the grilled eggplant slices. Scatter with crumbled feta cheese and the mint leaves and serve with a green salad.
Taiwanese Beef Noodle Stir-Fry SERVES **2** READY IN **15 MINUTES**
**5 ounces medium egg noodles**
**2½ tablespoons peanut oil**
**8-ounce sirloin steak**
**1 red chili**
**4 scallions**
**4 garlic cloves**
**¼-inch piece fresh gingerroot**
**1 heaped cup snow peas**
**½ teaspoon freshly ground black pepper**
**½ teaspoon sugar**
**2 tablespoons soy sauce**
**COOK THE NOODLES** in boiling water 4 to 5 minutes until soft, or following directions on the package. Drain in a strainer and drizzle with 1 tablespoon of the oil to prevent the noodles from sticking together. Using a pair of scissors, cut the noodles a few at a time to shorten them (this will help them mix quicker in the wok). Set aside.
**MEANWHILE, PREPARE ALL THE INGREDIENTS** for the stir-fry. Finely slice the beef into very thin strips. Cut the top off the chili, then finely slice the chili. Trim the scallions and cut into 1-inch pieces. Peel and cut the garlic cloves in half lengthwise. Peel the ginger, then slice it into thin strips.
**HEAT A WOK** over high heat until smoking. Pour in the remaining oil and add the chili, scallions, garlic and ginger, then stir-fry 30 seconds until beautifully aromatic. Add the beef and continue to stir-fry 2 minutes, then add the snow peas, black pepper and sugar.
**CONTINUE TO STIR-FRY** 1 to 2 minutes, or until everything has taken on a lovely golden color and the beef is cooked through. Transfer the cooked noodles to the hot wok and pour in the soy sauce. Toss everything well and serve.
Beef Chili & Mint Stir-Fry SERVES **2** READY IN **15 MINUTES**
**Never one to miss a meal, I ordered my lunch to go as I was leaving my hotel in Laos to head to the airport and back to Blighty. I was eating my food as I walked to the taxi. Boy, am I glad that I am greedy. Lunch was superb—a simple beef stir-fry with chili, garlic and a few peanuts, which was lifted somewhere new with a handful of mint leaves. The mint was a superb addition to a classic southeastern Asian stir-fry and probably even worth missing a flight for.**
**5 ounces fine egg noodles**
**2½ tablespoons peanut oil**
**2 garlic cloves**
**1-inch piece fresh gingerroot**
**1 red chili**
**2 sirloin steaks (about 4¼ ounces each)**
**heaped ⅓ cup peanuts**
**1 teaspoon rice wine vinegar**
**1 tablespoon light soy sauce**
**3 tablespoons oyster sauce**
**1⅔ cups bean sprouts**
**1 handful of small mint leaves**
**COOK THE NOODLES** in boiling water 4 to 5 minutes, or until soft, or following directions on the package. Drain in a strainer and drizzle with ½ tablespoon of the oil to prevent the noodles from sticking together, then set aside. Meanwhile, peel and finely slice the garlic and ginger. Cut the top off the chili, then slice the chili. Trim and discard any fat off the steak and slice the meat into strips about inch thick.
**HEAT A WOK** over high heat and add 1 tablespoon of the oil. Add the peanuts and stir-fry 1 minute, or until golden. Remove with a slotted spoon and transfer to a plate lined with paper towels to drain. Pour away and discard the oil remaining in the wok. Return the wok to high heat and, when smoking hot, add the remaining oil and the sliced steak. Let sear 40 seconds, then stir-fry 30 seconds to take on some color. Add the garlic, ginger and chili, and continue to stir-fry 2 to 3 minutes, or until the garlic is golden.
**POUR IN THE RICE WINE VINEGAR** , soy sauce and oyster sauce, and stir well. Add the bean sprouts and continue to stir-fry 1 to 2 minutes, or until the bean sprouts are just tender but still have a little bite. Turn off the heat, then add the peanuts and the mint. Give it a final stir, then add the noodles, toss to combine and serve.
The Bosporus Burger SERVES **2** READY IN **15 MINUTES**
**1 small handful of parsley leaves**
**1 teaspoon paprika**
**2 teaspoons ground cumin**
**½ teaspoon ground ginger**
**½ teaspoon chili powder**
**10½ ounces ground beef**
**1 tablespoon olive oil**
**2 ounces blue cheese**
**¼ cup mayonnaise**
**¼ lemon**
**2 hamburger buns**
**a few large lettuce leaves**
**sea salt**
**FINELY CHOP THE PARSLEY** and add it to a large mixing bowl. Add the paprika, cumin, ground ginger, chili powder, ground beef and a really good pinch of salt. Mix everything together really well—I find that squeezing the mixture together using your hands works best.
**DIVIDE THE BEEF MIXTURE** into 2 portions and flatten each one into a patty. Push your thumb into the top of each patty to create a little indentation, which will help them cook evenly.
**HEAT THE OIL** in a skillet over high heat and add the patties, indented-side facing up. Cook 4 minutes, then turn the patties over, reduce the heat to medium-low and cook another 3 minutes. Place half of the blue cheese on each patty and cook 1 minute, or until the patties have cooked through and are wonderfully juicy and the cheese has just melted.
**WHILE THE PATTIES COOK** , put the mayonnaise in a mixing bowl and squeeze in the juice of the lemon. Add a pinch of salt and mix well. Split the hamburger buns in half and spread each evenly with the mayonnaise. Divide the lettuce leaves among the buns. Place the cooked beef patties on top of the lettuce, put the lid of the buns on top and tuck in immediately.
Salmon Bibimbap SERVES **2** READY IN **20 MINUTES**
**_Bibimbap_ is a classic Korean rice dish. Cooked rice is put into a boiling-hot stone bowl where it forms a crunchy crust. Different toppings—salmon, eggs, vegetables or pork—are added, and the dish is served with kimchi and a soy-based sauce. When you cook my salmon version ensure that the pan is really hot before you add the cooked rice so you get a good crispy crust.**
**FOR THE RICE**
**scant ⅔ cup jasmine rice**
**½-inch piece fresh gingerroot**
**3 scallions**
**1 tablespoon light soy sauce**
**1 tablespoon cider vinegar**
**FOR THE SALMON AND EGGS**
**2 tablespoons olive oil**
**2 boneless, skinless salmon fillets**
**2 eggs**
**1 teaspoon sesame seeds**
**FOR THE CHILI DRESSING**
**1 garlic clove**
**¼ cup chili sauce**
**1 tablespoon soy sauce**
**1 tablespoon cider vinegar**
**1 teaspoon sesame oil**
**COOK THE RICE** in boiling water 10 to 12 minutes, or until soft, or following directions on the package. Drain in a strainer, return to the pan, then cover and set aside. Meanwhile, heat 1 tablespoon of the oil for the salmon in a skillet over medium heat and add the salmon. Cook 2 minutes, then turn, reduce the heat to low and cook 1½ to 2 minutes, or until cooked on the outside and pink in the center. Set aside.
**WHILE THE SALMON COOKS** , peel the garlic for the dressing. Put all the dressing ingredients into a mini food processor and blend until smooth. Set aside.
**PEEL THE GINGER** for the rice and trim the scallions, then finely chop them both and add them to the pan with the cooked rice. Add the soy sauce and cider vinegar, then stir together to combine using a fork. Cover and set aside.
**HEAT THE REMAINING OIL** in a large skillet over high heat and add the rice, spreading it evenly. Then, using a spoon, create two wells and crack in the eggs. Cover and cook 2 to 3 minutes, or until the whites have set, the yolks are runny and the rice has started to brown underneath. Divide the rice and eggs among two plates. Flake the salmon over the top and scatter with the sesame seeds. Drizzle with dressing to serve.
Cambodian Seafood Amok SERVES **2** READY IN **15 MINUTES**
**FOR THE RICE NOODLES**
**3½ ounces medium rice noodles**
**1 tablespoon peanut oil**
**FOR THE AMOK CURRY PASTE**
**½-inch piece fresh gingerroot**
**2 lemongrass stalks**
**3 garlic cloves**
**½ teaspoon turmeric**
**2 dried red chilies**
**½ teaspoon freshly ground black pepper**
**½ teaspoon sugar scant ¼ cup peanuts**
**2 tablespoons peanut oil**
**FOR THE SEAFOOD CURRY**
**1 cup coconut cream**
**1 tablespoon fish sauce**
**½ lime**
**2 haddock fillets (about**
**5½ ounces each)**
**4 ounces prepared raw mixed seafood, such as mussels, jumbo shrimp and squid rings**
**1 small handful of cilantro leaves**
**COOK THE RICE NOODLES** in boiling water 4 to 5 minutes, or until soft, or following directions on the package. Drain in a strainer and drizzle with the oil to prevent the noodles from sticking together. Cover and set aside.
**MEANWHILE, TO MAKE THE CURRY PASTE** , peel the ginger, then remove the tough outer leaves from the lemongrass and cut off the ends of the stalks. Peel the garlic. Put all the curry paste ingredients into a mini food processor, and blend into a smooth paste, adding a little water if necessary.
**HEAT A LARGE WOK** over medium heat and add the curry paste. Stir-fry 30 seconds, or until fragrant. Pour in the coconut cream and fish sauce for the seafood curry, squeeze in the juice of the lime and mix everything together really well. Bring the amok sauce to a boil while you prepare the fish.
**CHOP THE HADDOCK** into bite-size pieces. Add them to the hot amok sauce followed by the mixed seafood. Gently mix everything together, reduce the heat to low and simmer gently 5 to 6 minutes, stirring occasionally, until the fish starts to flake and the seafood is cooked through.
**WHILE THE AMOK COOKS** , roughly tear the cilantro. Serve the curry with the rice noodles, scattered with the cilantro.
Crawfish, Pink Grapefruit & Glass Noodle Salad SERVES **2** READY IN **15 MINUTES**
**FOR THE GLASS NOODLE SALAD**
**5 ounces vermicelli rice noodles**
**1 pink grapefruit**
**2 scallions**
**1 ounce pea shoots or 1 handful of watercress**
**5½ ounces cooked shelled crawfish tails**
**1 small handful of basil leaves**
**1 small handful of mint leaves**
**2 tablespoons pumpkin seeds**
**FOR THE LEMONGRASS DRESSING**
**2 lemongrass stalks**
**2 limes**
**¼ teaspoon chili powder**
**2 teaspoons sugar**
**1 tablespoon olive oil**
**PUT THE NOODLES** into a heatproof bowl and cover with boiling water. Cover the bowl and set aside 2 to 3 minutes to soften. Once soft, drain in a strainer and rinse with cold water. Drain again and squeeze out any excess water with your hands so that the noodles are really dry. Set aside.
**MAKE THE DRESSING** while the noodles soften. Remove the tough outer leaves from the lemongrass and cut off the ends of the stalks. Starting at the fatter end, roughly slice each lemongrass stalk into rings. You should see a purple band in the rings. Stop slicing when there are no more purple bands, then discard the rest of the lemongrass, because it will be too tough to eat.
**GIVE THE LEMONGRASS SLICES** a quick blast in a mini food processor until they are very finely chopped, then add them to a large mixing bowl. Squeeze the juice of the limes into the bowl with the lemongrass and add the chili powder, sugar and oil. Beat everything together to get the flavors going.
**USING A SHARP KNIFE** , cut the top and bottom off of the grapefruit, then stand it up on your cutting board. Carefully slice the skin off in sections, cutting from top to bottom. Remove any remaining pith, then cut the juicy pieces of grapefruit away from the membrane and put them into the bowl with the dressing. Squeeze in the juices remaining in the membrane. Trim and finely slice the scallions, then add them to the bowl. Add the pea shoots, crawfish, basil, mint and cooked noodles. Toss everything together well. Scatter the salad with the pumpkin seeds to serve.
Warm East-Med Eggplant & Tomato Salad SERVES **2** READY IN **15 MINUTES**
**5 tablespoons olive oil**
**2 teaspoons dried mint**
**2 eggplants**
**½ red onion**
**1½ lemons**
**½ red chili**
**heaped ⅔ cup cherry tomatoes**
**scant ⅔ cup pitted black olives**
**2 large handfuls of parsley leaves**
**½ teaspoon sumac**
**1 teaspoon ground cumin**
**2 tablespoons pine nuts (optional)**
**sea salt and freshly ground black pepper**
**PREHEAT THE BROILER** to high. Meanwhile, put 3 tablespoons of the oil, 1½ teaspoons of the mint and a good pinch of salt in a mixing bowl, and stir well. Slice the eggplants into ¼-inch rings and brush both sides with the seasoned oil. Put the slices onto a broiler rack and broil 5 to 6 minutes, or until golden on one side.
**WHILE THE EGGPLANT BROILS** , peel and finely slice the onion and add it to a large mixing bowl. Squeeze in the juice of the lemons, add a pinch of salt and stir well. Finely chop the chili and halve the cherry tomatoes and stir them into the onion slices.
**WHEN THE EGGPLANT HAS COOKED** on one side, turn it over and broil another 5 to 6 minutes, or until golden on the other side and tender in the center.
**TEAR THE OLIVES** and rip the parsley leaves into the mixing bowl with the salad. Add the remaining oil and mint, and the sumac, cumin and a good pinch of black pepper. Toss everything together. Put the cooked eggplant slices into the bowl with the salad and gently stir everything together to combine. Serve the salad scattered with the pine nuts (if using).
Heather's Moroccan Paprika & Garlic Lentils SERVES **2** READY IN **20 MINUTES**
**I stayed with Heather in her beautiful home just outside Marrakesh for a few days of sunshine and cooking. She taught me how to make many amazing dishes, including the classic cold Moroccan lentil salad. It was delicious, and I loved it hot straight out of the pan. She used a beautiful expression to describe when the dish was ready: "When the lentils have 'drunk all the water' it's done." Although my version is a little different, when the lentils have "drunk all the water" and the sauce is beautifully thick, you can add the lemon and herbs and then tuck in.**
**1 onion**
**4 garlic cloves**
**2 tablespoons olive oil**
**2 bay leaves**
**2 × 14-ounce cans green lentils**
**3 tablespoons tomato paste**
**1¼ teaspoons paprika**
**2 teaspoons ground cumin**
**1½ teaspoons freshly ground black pepper**
**1 teaspoon sugar**
**1 large handful of parsley leaves**
**½ lemon**
**sea salt**
**TO SERVE**
**extra virgin olive oil**
**PEEL AND FINELY CHOP** the onion and garlic, then put them in a large saucepan, along with the olive oil and bay leaves. Cook over medium heat 5 to 6 minutes, stirring occasionally, until soft.
**MEANWHILE, DRAIN AND RINSE** the lentils, and set aside. Once the onion is soft, add the tomato paste, paprika, cumin, black pepper, sugar, lentils and a good pinch of salt. Pour in a generous 1¼ cups hot water and stir well. Bring to a boil and cook 5 to 6 minutes, stirring frequently, until the lentils have warmed through and the sauce is really thick.
**WHILE THE LENTILS COOK** , finely chop the parsley and add it to the pan with the lentils. Squeeze in the juice of the lemon and stir well, then drizzle with your fanciest extra virgin olive oil to serve.
Indian Cauliflower Soup SERVES **2** READY IN **15 MINUTES**
**This is such an awesome soup. It's rich, thick and packed with flavor. The ground spices provide a background layer of warmth, but it's the "temper" that really packs a punch. Tempering a dish means simply frying some spices in hot oil and pouring them into the dish at the end of cooking. It adds an extra layer of flavor, and it really brings the food to life.**
**For the Soup**
**1 small cauliflower**
**¾ cup vegetable stock**
**1¾ cups coconut milk**
**2 teaspoons garam masala**
**½ teaspoon turmeric**
**¼ teaspoon chili powder**
**14-ounce can lima beans**
**½ lime**
**sea salt**
**FOR THE TEMPER**
**1 onion**
**2 garlic cloves**
**2 tablespoons peanut oil**
**2 large pinches of dried curry leaves**
**USING YOUR HANDS** , break up the cauliflower into very small florets and place them straight into a saucepan. Cover with boiling water and cook over high heat 6 to 8 minutes, or until tender.
**MEANWHILE, POUR THE STOCK** and coconut milk into a saucepan, and add the garam masala, turmeric, chili powder and a good pinch of salt. Stir well and bring to a boil over high heat. Reduce the heat to low and simmer gently. While the soup simmers, peel and finely chop the onion and garlic for the temper. Drain the lima beans in a colander and rinse with cold water.
**ONCE THE CAULIFLOWER IS TENDER** , drain, using the colander containing the beans. Add both to the saucepan with the soup. Remove from the heat and blend until smooth, using an immersion hand blender or adding it to a food processor. Return the soup to low heat and simmer gently, stirring occasionally, while you make the temper.
**TO MAKE THE TEMPER** , heat the oil in a skillet over high heat and add the onion and garlic. Stir-fry 2 to 3 minutes, or until golden. Remove from the heat. Rub the curry leaves between your hands to break them up and drop directly into the skillet. Pour the temper into the soup and squeeze in the juice of the lime. Stir well and serve.
NICE & EASY
**In this chapter all the recipes are based on a really chilled-out approach to cooking for friends and family. I am talking about great food that is, quite simply, nice and easy to make. You can prepare any of these recipes armed with a glass of wine and not miss out on any of the fun, because they are all ready in 45 minutes or less. My Sumac Chicken with Black Gremolata & Tomato Salad is effortless and ready in 45 minutes. Amish's Gujarati Vegetable Curry, enriched with cashews and served with rice and chickpeas, is utterly sublime and takes only 35 minutes to make. or my Mexican Sea Bream with Roasted Lemon Zucchini & Spicy Lime Seasoning has all the flavors to blow you away, but it only takes a cool 40 minutes to cook from start to finish.**
Korean Braised Chicken with Rice Noodles SERVES **4** READY IN **35 MINUTES**
**All Korean food should have a balance of five colors—black, white, yellow, green and red. Here, the black is from the soy, the white from the chicken, yellow from the noodles, green from the cilantro and red from the chilies.**
**1¼ pounds boneless, skinless chicken thighs**
**generous ¼ cup soy sauce**
**1 tablespoon oyster sauce**
**3 tablespoons rice wine or dry white wine**
**½ tablespoon sesame oil**
**2 tablespoons brown sugar**
**½ teaspoon ground ginger**
**½ teaspoon freshly ground black pepper**
**2 dried red chilies**
**4 garlic cloves**
**1 onion**
**1 carrot**
**1 zucchini**
**7 ounces vermicelli rice noodles**
**scant ½ cup chicken stock**
**2 scallions**
**½ red chili**
**1 small handful of cilantro leaves**
**ADD THE CHICKEN** to a large, shallow flameproof casserole dish and pour in the soy sauce, oyster sauce, rice wine, sesame oil, brown sugar, ground ginger and black pepper. Crack open the dried chilies and add them to the dish, then peel and crush in the garlic. Stir everything together really well and place over medium heat.
**PEEL AND ROUGHLY SLICE** the onion, then peel the carrot. Chop the carrot and zucchini into matchsticks. Put the vegetables in the casserole dish with the chicken and stir to combine. It will look a little dry at this stage, but don't worry—the chicken and vegetables will produce lots of lovely juices. Bring to a boil, cover and reduce the heat to low. Simmer gently 15 minutes, or until the chicken is just cooked through.
**MEANWHILE, PUT THE NOODLES** in a large mixing bowl, cover with boiling water and let stand about 10 minutes to soften. Pour the stock into a small saucepan and heat gently over medium-low heat. Once the chicken is cooked, drain the noodles in a strainer and add them to the casserole dish in four little piles. Pour in the stock, then cover and cook another 10 minutes to allow the noodles to soak up the sauce. Trim and finely slice the scallions and red chili, then roughly tear the cilantro. Scatter the dish with the scallions, chili and cilantro to serve.
Roast Spatchcocked Chicken with Chimichurri & Rice & Black Bean Salad SERVES **4** READY IN **45 MINUTES**
**FOR THE CHICKEN**
**1 chicken (about**
**3 pounds 2 ounces)**
**1 tablespoon olive oil**
**sea salt and freshly ground black pepper**
**FOR THE RICE AND BLACK BEAN SALAD**
**1 cup brown rice**
**1 cup canned black beans**
**½ red onion**
**1 large handful of mint leaves**
**1 large handful of parsley leaves**
**2 tablespoons sherry vinegar**
**⅔ cup cashews**
**FOR THE CHIMICHURRI**
**1 red chili**
**½ red onion**
**2 garlic cloves**
**1 large handful of parsley leaves**
**1 tomato**
**2 teaspoons dried oregano**
**2 teaspoons ground cumin**
**1 teaspoon smoked paprika**
**¼ cup olive oil**
**¼ cup sherry vinegar**
**FOR THE LEAF SALAD**
**4¼ ounces mixed salad leaves**
**½ lemon**
**1 tablespoon olive oil**
**PREHEAT THE OVEN** to 425°F. Put the chicken onto a cutting board breast-side down. Using a pair of poultry shears, cut along either side of the spine from the neck to the rear cavity and remove it. Pull the two sides apart so that the chicken starts to open out, turn it over, breast-side up, and press down hard on each side so that the chicken flattens out. This will allow it to roast quickly and evenly.
**LAY THE SPATCHCOCKED CHICKEN** on a rack in a roasting pan and rub it all over with the oil. Season with salt and pepper. Roast 35 minutes, or until the chicken is cooked through and the juices run clear when the thickest part of the thigh is pierced with the tip of a sharp knife.
**MEANWHILE, COOK THE RICE** for the rice and black bean salad in boiling water 20 to 25 minutes, or until soft, or following directions on the package.
**TO MAKE THE CHIMICHURRI** , cut the top off the chili and roll the chili between your hands to remove the seeds. Peel the onion and garlic. Put all the ingredients for the chimichurri into a food processor or blender with a scant ½ cup water and a little salt, and blend to a coarse paste. Pour into a serving bowl, then cover with plastic wrap and set aside to allow the flavors to develop.
**DRAIN AND RINSE THE BEANS** for the rice and black bean salad, and add to a large serving bowl. Peel the red onion, then add it to a blender or mini food processor, followed by the mint and parsley. Process until finely chopped, then add to the bowl with the beans. Spoon in one-third of the chimichurri, add the sherry vinegar, season with salt and stir to combine.
**HEAT A SMALL SKILLET** over medium heat and add the cashews. Toast them 5 to 6 minutes, or until lightly golden, shaking the pan frequently to stop them from burning. Remove from the heat and set aside to cool.
**PLACE THE SALAD LEAVES** in a plastic food bag. Squeeze the juice of the lemon into the bag and add the oil. Seal the bag securely and shake it well until the salad leaves are coated in dressing. Pour the contents of the bag into a serving bowl.
**PUT THE ROASTED CHICKEN** onto a carving board. Drain the rice in a strainer and immediately refresh under cold water. Drain well and shake the strainer to remove as much water as possible. Add the rice to the bowl with the beans. Add the cashews and toss everything together until the grains of rice are completely coated with dressing. Serve slices of the lovely hot chicken with the rice and bean salad, the leafy salad and the chimichurri.
Sumac Chicken with Black Gremolata & Tomato Salad SERVES **4** READY IN **45 MINUTES**
**FOR THE SUMAC CHICKEN**
**3 tablespoons olive oil**
**3¼ pounds chicken thighs and drumsticks on the bone**
**1 pound 2 ounces small new potatoes**
**1 red onion**
**1 garlic bulb**
**1 tablespoon sumac**
**2 teaspoons dried thyme**
**sea salt and freshly ground black pepper**
**FOR THE BLACK GREMOLATA**
**⅔ cup pitted black olives**
**1 dried red chili**
**¼ teaspoon sumac**
**1 large handful of parsley leaves**
**1 large handful of dill**
**3 tablespoons olive oil**
**2 teaspoons best sticky sweet balsamic vinegar**
**½ lemon**
**scant ½ cup walnut pieces**
**FOR THE TOMATO SALAD**
**10½ ounces mixed tomatoes, such as cherry, vine, baby, plum**
**2 tablespoons best sticky sweet balsamic vinegar**
**2 tablespoons olive oil**
**a pinch of sugar**
**PREHEAT THE OVEN** to 400°F. Rub a little of the oil all over the bottom of a roasting pan and add the chicken pieces and new potatoes. Peel the onion, cut it into quarters and add it to the roasting pan. Break open the garlic bulb and remove 1 clove for the black gremolata, then scatter the rest of the cloves into the pan.
**SEASON THE CHICKEN** with the sumac and thyme, and a good pinch of salt and pepper. Drizzle everything with the remaining oil and mix all the ingredients in the pan together really well. Roast 35 to 40 minutes, or until all the chicken pieces are cooked through and tender, and everything is golden brown.
**MEANWHILE, TO MAKE THE GREMOLATA** , peel the reserved garlic clove, then add it to a mini food processor or blender, followed by the olives, chili, sumac, parsley, dill, oil, balsamic vinegar and a pinch of salt and pepper. Squeeze in the juice of the lemon and grind to a coarse paste. Add to a serving bowl and stir in the walnut pieces. Cover and set aside to allow those fantastic flavors to intensify.
**TO MAKE THE SALAD** , cut the tomatoes into different shapes and sizes, and put them in a serving bowl. Pour in the vinegar and olive oil, then season with the sugar, salt and pepper. Toss together gently, cover and set aside to allow the tomatoes to soak up the seasonings. Serve the chicken with the potatoes, gremolata and the salad.
Five-Spice Pork Belly SERVES **4** READY IN **40 MINUTES**
**Mustard is the classic accompaniment to crispy pork belly in Hong Kong— it works well and cuts through the richness of the meat. Get your butcher or supermarket meat-counter assistant to score the fat of the pork belly to help save you loads of preparation time.**
**FOR THE FIVE-SPICE PORK**
**2¾-pound piece of pork belly, skin scored**
**4 teaspoons chinese five-spice powder**
**1 teaspoon ground Szechuan pepper**
**sea salt**
**FOR THE DIPPING SAUCE**
**3 tablespoons soy sauce**
**1 tablespoon rice wine vinegar**
**2 tablespoons honey**
**¼ teaspoon chili powder**
**1 garlic clove**
**FOR THE RICE AND BOK CHOY**
**1¼ cups jasmine rice**
**7 ounces bok choy**
**TO SERVE**
**scant ⅓ cup French mustard**
**PREHEAT THE OVEN** to 500°F. Cut the pork belly into 2 pieces to help it cook more quickly, and put both pieces, skin-side up, in a roasting pan. Rub the skin with the Chinese five-spice powder, ground Szechuan pepper and a good pinch of salt. Put it into the oven, reduce the heat to 425°F and cook 30 to 35 minutes, or until the pork is cooked through and the skin is really crisp.
**MEANWHILE, MAKE THE DIPPING SAUCE**. Pour the soy sauce into a serving bowl and add 2 tablespoons water, the rice wine vinegar and honey. Add the chili powder, then peel and crush in the garlic. Whisk together, then cover and let stand to allow the flavors to develop.
**COOK THE RICE** in boiling water 10 to 12 minutes, or until soft, or following directions on the package, then drain in a strainer. Add boiling water to the saucepan to a depth of 1 inch and place over low heat. Put the strainer with the rice over the pan, cover loosely with a lid and let steam gently until you are ready to eat.
**WHEN THE PORK HAS COOKED** 25 minutes, cut the bok choy into quarters, then put it into a steamer and steam over high heat 5 minutes, or until just tender. Divide the sticky rice into four serving bowls and add the mustard to a serving dish. Carve the pork and serve with the rice, bok choy, dipping sauce and mustard.
Thai Pork with Noodles & Lemongrass & Lime Dipping Sauce SERVES **4** READY IN **40 MINUTES**
**FOR THE ROAST PORK**
**1 pork loin (about 1¼ pounds in weight)**
**4 garlic cloves**
**1 teaspoon freshly ground black pepper**
**½ teaspoon sugar**
**1 tablespoon rice wine**
**2 teaspoons fish sauce**
**1 tablespoon peanut oil**
**FOR THE LEMONGRASS AND LIME DIPPING SAUCE**
**2 lemongrass stalks**
**½-inch piece fresh gingerroot**
**1 handful of cilantro leaves and stalks**
**½ teaspoon chili powder**
**2 teaspoons sugar**
**1 tablespoon fish sauce**
**1½ limes**
**FOR THE NOODLES**
**5½ ounces green beans**
**7 ounces medium egg noodles**
**2 tablespoons peanut oil**
**1 tablespoon fish sauce**
**½ lime**
**PREHEAT THE OVEN** to 400°F. Trim the pork and cut it into 4-inch pieces and pierce all over with a fork. Put the pieces of pork into an ovenproof dish, then peel and crush in the garlic. Add the black pepper, sugar, rice wine, fish sauce and oil. Mix everything together well and roast 30 to 35 minutes, or until the pork is just cooked through and tender.
**MEANWHILE, TO MAKE THE DIPPING SAUCE** , remove the tough outer leaves from the lemongrass and cut off the ends of the stalks. Peel the ginger. Put the lemongrass and ginger into a mini food processor, and add the cilantro leaves and stalks, chili powder, sugar and fish sauce. Squeeze in the juice of the limes and add ¼ cup water. Blend to a smooth sauce and pour into a serving bowl. Cover and set aside to allow all the amazing savory flavors to come together.
**CUT THE BEANS** for the noodles in half. Cook with the noodles in boiling water 4 to 5 minutes, or until the noodles are soft, or following the directions on the package. Drain and return to the saucepan. Pour in the oil and fish sauce, then squeeze in the juice of the lime. Stir well, cover and set aside until the pork is ready. Carve the pork into thick slices and serve it on a bed of noodles and beans with the dipping sauce on the side.
Rana's Keema Shepherd's Pie SERVES **4** READY IN **45 MINUTES**
**FOR THE SPICY MASHED POTATOES**
**1 pound 10 ounces new potatoes**
**2 tablespoons butter**
**1 teaspoon garam masala**
**3 scallions**
**1 tablespoon olive oil**
**FOR THE LAMB**
**1 red onion**
**2 tablespoons peanut oil**
**3 cardamom pods**
**3 large blades of mace**
**1 pound 2 ounces ground lamb**
**1 handful of cilantro leaves**
**FOR THE TOMATO SAUCE**
**1-inch piece fresh gingerroot**
**4 garlic cloves**
**heaped ⅓ cup tomato paste**
**1½ teaspoons garam masala**
**1 teaspoon chili powder**
**½ teaspoon ground cinnamon**
**scant 1 cup frozen peas**
**sea salt**
**COOK THE UNPEELED POTATOES** in a large pan of boiling water 15 minutes, or until tender. Meanwhile, prepare the lamb. Peel and finely chop the red onion. Heat the peanut oil in a large skillet over medium heat and add the onion, cardamom pods and mace. Stir well, then add the lamb. Increase the heat to high and stir-fry 3 to 4 minutes, or until the lamb is just cooked through. Reduce the heat to medium and cook a few minutes, stirring occasionally, while you make the sauce.
**TO MAKE THE SAUCE** , peel the ginger and garlic, then add both to a mini food processor or blender, followed by the tomato paste, garam masala, chili powder, cinnamon and a good pinch of salt. Blend until smooth. Scoop the sauce into the pan with the lamb and add a scant ⅔ cup hot water and the peas. Stir well, cover, then reduce the heat to low and simmer gently 15 minutes, stirring occasionally.
**DRAIN THE COOKED POTATOES** , then return them to the pan. Mash lightly, so that they start to break up, then add the butter, garam masala and a good pinch of salt. Put the lid on the saucepan. Trim and finely chop the scallions, then add them to the pan and mix everything together well. Cover and set aside.
**PREHEAT THE BROILER** to high and finely chop the cilantro for the lamb. When the ground lamb is thick and rich, scatter with the cilantro and stir. Carefully pour the lamb mixture into an ovenproof dish and spoon the spiced potatoes evenly on top. Drizzle with olive oil and broil 5 minutes, or until crisp and golden and serve.
Lamb with Tarator Sauce, Mashed Potatoes & Tomato & Radish Salad SERVES **4** READY IN **40 MINUTES**
**Tarator sauce is a bread sauce with attitude and, served with lamb, is a classic Middle Eastern combination. It's packed with lemon juice, garlic, pine nuts, cumin and olive oil and it works beautifully with sweet and juicy lamb chops, gently flavored with allspice and oregano. The rich flavors of the lamb and sauce benefit from the contrasting fresh and simple tomato and radish salad, which was inspired by countless trips to the Eastern Mediterranean.**
**You may be thinking that mashed potatoes don't exactly sound like an exotic accompaniment for such a traditional, spiced dish—and they aren't. It is, however, my dad's favorite starch and, I agree, sometimes it's the only thing in the world that will do. In this case, the delicious simple mashed potatoes provide a bland creaminess that is the perfect vehicle to soak up all the yummy juices, so that nothing is wasted, and it goes surprisingly well with the spiciness of the roasted chops.**
**FOR THE MASHED POTATOES**
**1 pound 10 ounces new potatoes**
**3 tablespoons butter**
**sea salt and freshly ground black pepper**
**FOR THE TARATOR SAUCE**
**1 slice of white bread**
**1 garlic clove**
**1 lemon**
**heaped ⅓ cup pine nuts**
**1½ teaspoons ground cumin**
**scant ¼ cup olive oil**
**FOR THE LAMB CHOPS**
**8 small lamb chops (about 3¼ ounces each)**
**2 teaspoons ground allspice**
**2 teaspoons dried oregano**
**1 tablespoon olive oil**
**FOR THE TOMATO AND RADISH SALAD**
**heaped 1¾ cups cherry tomatoes**
**7 ounces radishes**
**2 scallions**
**1 handful of mint leaves**
**1 handful of parsley leaves**
**1 lemon**
**2 tablespoons olive oil**
**PREHEAT THE OVEN** to 400°F. To make the mashed potatoes, cook the unpeeled potatoes in a large saucepan of boiling water 15 minutes, or until tender. Drain, return them to the pan, then add the butter and a good pinch of salt and pepper. Mash together until fairly smooth, then cover and keep warm.
**MEANWHILE, MAKE THE TARATOR SAUCE**. Tear the bread into small pieces and put them into a food processor. Peel the garlic and add it to the food processor. Squeeze in the juice of the lemon and add the pine nuts, cumin and a good pinch of salt and pepper. Add 3 tablespoons water and the oil, then blend to a coarse sauce. Scoop the tarator sauce into a serving bowl, add a grinding of black pepper, if you like, then cover and set aside.
**PLACE THE LAMB CHOPS** on a cutting board and gently score both sides with a sharp knife. Put the lamb in a mixing bowl and add the allspice, oregano, oil and a good pinch of salt and pepper. Mix well so that the lamb is completely coated. Set the lamb on a rack in a roasting pan and roast 8 to 10 minutes, or until tender and juicy.
**MAKE THE SALAD** while the lamb cooks. Halve the cherry tomatoes and radishes and put them in a serving bowl. Trim and finely chop the scallions with the mint leaves, if large, and add them, with the parsley leaves, to the tomatoes. Squeeze in the juice of the lemon, then pour in the oil and season with a good pinch of salt and pepper. Toss together well to combine and set aside. Serve the cooked lamb and mashed potatoes with the salad and tarator sauce.
Four Brothers Beef Curry SERVES **4** READY IN **30 MINUTES**
**1 pound 10 ounces new potatoes**
**3 lemongrass stalks**
**3 garlic cloves**
**1 red chili**
**2 tablespoons peanut oil**
**4 cardamom pods**
**2 star anise**
**2-inch stick cinnamon**
**4 cloves**
**1¾ cups coconut cream**
**2 tablespoons tomato paste**
**2 tablespoons fish sauce**
**1 teaspoon sugar**
**4 sirloin steaks (about 4½ ounces each)**
**1 lime**
**CUT THE UNPEELED POTATOES** in half, then cook them in a large saucepan of boiling water 10 to 12 minutes, or until tender. Drain in a colander and set aside.
**MEANWHILE** , **REMOVE THE TOUGH** outer leaves from the lemongrass and cut off the ends of the stalks. Peel the garlic and cut the top off the chili. Add the lemongrass, garlic and chili to a mini food processor, and blend to a paste.
**HEAT THE OIL** in a large, shallow saucepan over medium heat and add the cardamom, star anise, cinnamon and cloves. Stir-fry 30 seconds until fragrant, then pour in the spice paste and stir-fry 10 seconds until it also releases its fragrance. Add the coconut cream followed by the tomato paste, fish sauce and sugar. Stir everything together to combine and simmer gently.
**SLICE THE STEAKS** into strips 2 inches wide and add them to the pan with the sauce. Carefully add the potatoes and mix well. Bring to a boil, then cover, reduce the heat to low and simmer gently 5 minutes. Remove the lid and cook another 10 minutes, stirring occasionally, until the beef is just cooked through and the sauce is nice and thick.
**WHILE THE STEAK COOKS** , cut the lime into quarters. Serve the beef curry with the wedges of lime on the side.
SOUKS, SAND & BERBER BEEF STEW
**Morocco is an enchanting country. I love all it has to offer, from the art and architecture to the people, dramatic landscapes and wonderful food. My research for _Mighty Spice Express_ took me there for several weeks, which included eating my way around Fez, the fabulous coastal town of Essaouira and several trips to Marrakesh.**
**I spent a very happy day in the sunny capital wandering through the _medina_ , avoiding the rugsellers and drinking lots of mint tea. I love a rooftop, and I found a good one with a picture-postcard view of the city sprawled beneath the mighty Atlas Mountains, which were dusted with snow and gleaming under the vivid blue sky.**
**As the sun went down, the city came to life. The dusty souks were lit up by a thousand lightbulbs, and hungry diners were lured out into the cool evening by the delicious smells that were cast into the air from the food stands of the infamous Jamaa el-Fna square.**
**The vendors of Jamaa el-Fna sold everything. It was advanced street-food eating. I made several laps around the stands and decided on a rich stew that was cooked in an earthenware pot called a _tangier_. The stew was simply made from meat, spices and butter, which had been left to cook for hours so that the flavor gods could work their magic and turn it into something sublime. All good things come to those who wait, but thankfully not in this book, because with a few clever changes I have recreated a rather special version of this sublime Berber beef stew that's ready in only 45 minutes. You must give it a try!**
Berber Beef Stew SERVES **4** READY IN **45 MINUTES**
**1 red onion**
**4 garlic cloves**
**1 carrot**
**2 zucchini**
**2 tablespoons olive oil**
**1 pound 5 ounces beef tenderloin or fillet**
**2 tablespoons tomato paste**
**2 teaspoons ground cumin**
**2 teaspoons ground ginger**
**1 teaspoon paprika**
**1 teaspoon freshly ground black pepper**
**½ teaspoon ground cinnamon**
**1 teaspoon flour**
**1 tablespoon honey**
**heaped ¾ cup couscous**
**1 large handful of parsley leaves**
**1 preserved lemon**
**heaped ¾ cup yogurt**
**2 tablespoons harissa paste**
**2 tablespoons toasted sliced almonds**
**sea salt**
**PEEL AND FINELY CHOP** the onion and garlic, then peel the carrot. Chop the carrot and zucchini into ½-inch half-moons. Add the oil to a large saucepan over high heat and add the carrots and zucchini. Cook 4 minutes, stirring frequently, to soften.
**MEANWHILE, CUT THE BEEF** into ¾–1¼-inch cubes and add to the cooked vegetables. Add the onion and garlic, and stir well. Reduce the heat to medium, add the tomato paste, cumin, ground ginger, paprika, black pepper, cinnamon, flour, honey and 1 cup boiling water. Stir well, bring to a boil, then cover and simmer 10 minutes, or until the beef is just cooked through.
**WHILE THE BEEF COOKS** , put the couscous in a large mixing bowl and add ¾ cup warm water. Cover with plastic wrap and let stand 10 minutes, or until ready to serve.
**FINELY CHOP THE PARSLEY** while the couscous absorbs the water. Remove the flesh from the preserved lemon, finely chop the skin and set it aside. Discard the flesh. Pour the yogurt into a serving bowl, then stir in the harissa, cover and set aside.
**REMOVE THE LID** from the cooked stew, turn the heat up to medium and cook another 5 minutes, stirring occasionally, to allow the sauce to become lovely and thick. Add the parsley and preserved lemon skin to the cooked stew, and stir well. Fluff up the couscous with a fork and divide among four serving bowls. Divide the stew among the four bowls, scatter with the almonds and serve with the harissa yogurt on the side.
Mexican Sea Bream with roasted Lemon Zucchini & Spicy Lime Seasoning SERVES **4** READY IN **40 MINUTES**
**This meal tastes awesome and is so quick to make. The beauty of the dish comes from the flavor of the sauce, which has a pronounced smoky edge. I have taken a tip from Mexican cooking and charred the onion, garlic and tomatoes before adding them to a blender with spices to make the sauce. This might sound a bit fussy, but it only takes a few extra minutes and it adds so much to the overall flavor—and the smokiness is exaggerated even more by using chipotle chilies. cinnamon and paprika create a sweeter background note to the sauce, which works so well with the fish. The flavors marry together as the sauce gently cooks for a few minutes before the fish fillets are added.**
**The dish is completed with zucchini roasted until they become soft and melt into creaminess when you eat them, and the whole thing is fired up with a wicked little chili, lime and salt seasoning, served at the table.**
**FOR THE LEMON ZUCCHINI**
**1 pound 5 ounces zucchini**
**3 large thyme sprigs**
**2 tablespoons olive oil**
**½ lemon**
**sea salt and freshly ground black pepper**
**FOR THE SEA BREAM AND SAUCE**
**2 chipotle chilies**
**1 red onion**
**4 garlic cloves**
**4 tomatoes**
**1 teaspoon ground cinnamon**
**½ teaspoon paprika**
**1 teaspoon brown sugar**
**leaves from 1 large thyme sprig**
**4 sea bream fillets (about 4½ ounces each)**
**1 handful of cilantro leaves**
**2 tablespoons best-quality extra virgin olive oil**
**FOR THE SPICY LIME SEASONING**
**2 limes**
**1 teaspoon crushed chili flakes**
**1 teaspoon sea salt**
**TO SERVE**
**4 large flour tortillas**
**PREHEAT THE OVEN** to 400°F. To make the lemon zucchini, cut the zucchini into generous ½-inch chunks and put them in a roasting pan. Add the thyme, olive oil and a good pinch of salt and pepper. Squeeze in the juice of the lemon and stir everything together well. Roast the zucchini 30 to 35 minutes, or until tender and creamy.
**MEANWHILE, SOAK THE CHIPOTLE CHILIES** for the sea bream sauce in 2 tablespoons hot water and set aside. Heat a nonstick skillet over high heat. While the pan heats, peel the onion and cut it into quarters, then peel the garlic. Carefully put them into the hot pan and toast 2 minutes. Add the tomatoes and turn the garlic. Cook another 2 to 3 minutes, or until the tomatoes and onion are charred on the cooked side and the garlic is charred on both sides.
**WHILE THE TOMATOES ARE CHARRING** , grate the zest of the limes for the spicy seasoning into a serving bowl and add the chili flakes and salt. Stir and set aside.
**TRANSFER THE CHARRED INGREDIENTS** and the chipotle chilies with their soaking liquid to a blender or food processor, and add the cinnamon, paprika, brown sugar, thyme and a good pinch of salt. Squeeze in the juice of 1½ of the limes used for the seasoning and blend to a smooth sauce.
**POUR THE SAUCE** into a large, shallow saucepan and bring to a boil over medium heat. Cook 10 minutes, stirring occasionally, then add the fish fillets, skin-side down, to the hot sauce. Cover and cook 4 to 5 minutes, or until the fish is beautifully tender and flaky.
**PINCH THE SPICY SEASONING** mixture between your fingers to release all the flavors while the fish cooks. Cut the remaining lime half into 4 segments.
**SCATTER THE COOKED FISH** with the cilantro and then drizzle with the extra virgin olive oil. Serve the fish with the cooked zucchini, tortillas, lime segments and the spicy lime seasoning on the side.
Dongbai Roast Cod with Stir-Fried Spinach & Peanuts SERVES **4** READY IN **25 MINUTES**
**This meal is a nod to my time in dongbai, china. Fish was always served as part of any meal, along with, frankly, everything—meat, shellfish, vegetables, soups, stews and dumplings. The tables groaned with food, and that's definitely one of my favorite sights. Preparing multiple dishes is hard work, so I have stripped things back for this simple but mouthwatering version.**
**The combination of chili flakes, sesame seeds and cumin seeds was my favorite discovery from this region of northern china. The three flavors work perfectly together. I grind one-half of the mixture to a powder and leave the rest whole to create a spicy coating with a crunchy texture for the fish. The spices are enhanced by the rich flavors of oyster sauce, soy sauce and honey, giving the coating a salty–sweet base. These are big flavors, and the cod loves them all.**
**The simple spinach and peanut stir-fry is slightly tart to complement the sticky roast cod. Traditionally, this would be made with chinese black vinegar, but this is hard to find and I actually really like the flavor of the red wine vinegar and soy sauce used here instead.**
**FOR THE RICE**
**1¼ cups jasmine rice**
**FOR THE ROAST COD**
**2 teaspoons crushed chili flakes**
**2 tablespoons sesame seeds**
**2 teaspoons cumin seeds**
**6 tablespoons oyster sauce**
**2 tablespoons soy sauce**
**1 tablespoon honey**
**1½ tablespoons peanut oil**
**4 skinless cod fillets (about 6 ounces each)**
**FOR THE SPINACH AND PEANUTS**
**1 tablespoon chili oil**
**heaped ⅓ cup peanuts**
**14 ounces spinach**
**1 tablespoon light soy sauce**
**2 teaspoons red wine vinegar**
**PREHEAT THE OVEN** to 400°F. Cook the rice in boiling water 10 to 12 minutes, or until soft, or following directions on the package, then drain in a strainer. Add boiling water to the saucepan to a depth of 1 inch and place on low heat. Put the strainer with the rice over the pan, partially cover and let steam gently until you are ready to eat.
**MEANWHILE, PUT HALF THE CHILI FLAKES** , sesame seeds and cumin seeds for the roast cod into a spice grinder and grind to a fine powder. Pour into a mixing bowl and add the oyster sauce, soy sauce, honey and 1 tablespoon of the oil, and stir well. Add the fish and mix well to coat completely.
**ARRANGE THE FISH** in a small roasting pan in a single layer and spoon the remaining marinade all over the fish. Scatter the fish with most of the remaining chili flakes, sesame seeds and cumin seeds, and drizzle with the remaining oil. Roast 12 to 15 minutes, or until the fish is cooked through, tender and flaky.
**MAKE THE SPINACH AND PEANUTS** while the fish cooks. Heat a wok over high heat and add the chili oil and peanuts. Stir-fry 1 minute, or until just turning golden. Add the spinach and continue to stir-fry 2 to 3 minutes, or until wilted. Drain off any excess liquid and return the wok to high heat. Pour in the soy sauce and red wine vinegar, and continue to stir-fry another minute. Scatter with the remaining chili flakes, sesame seeds and cumin seeds. Serve the fish with the sticky rice and the spinach. Remember to spoon all the lovely juices from the roasting pan onto the fish— they are too good to waste.
Shrimp & Herb Brewat with Vermicelli Rice Noodles SERVES **4** READY IN **30 MINUTES**
**FOR THE SHRIMP AND HERB BREWAT**
**1 red onion**
**4 garlic cloves**
**2 tablespoons olive oil**
**heaped 1⅓ cups cherry tomatoes**
**1 cup tomato passata**
**1 teaspoon honey**
**2 teaspoons ground cumin**
**1 teaspoon paprika**
**½ teaspoon chili powder**
**½ teaspoon freshly ground black pepper**
**½ lemon**
**scant ½ cup vegetable stock**
**1 large handful of cilantro leaves and stalks**
**1 pound 2 ounces raw shelled jumbo shrimp (with or without tails)**
**FOR THE RICE NOODLES**
**1 large handful of cilantro leaves**
**7 ounces vermicelli rice noodles**
**2 tablespoons olive oil**
**½ teaspoon ground cumin**
**¼ teaspoon chili powder**
**½ lemon**
**sea salt and freshly ground black pepper**
**PEEL AND FINELY CHOP** the onion and garlic. Place the oil in a large saucepan over medium heat. Add the onion and garlic. Stir-fry 4 to 5 minutes, or until golden.
**MEANWHILE, CUT THE CHERRY TOMATOES** in half, then add them to the cooked onion. Add the passata, honey, cumin, paprika, chili powder, black pepper and a good pinch of salt. Squeeze in the juice of the lemon and add the stock. Stir everything together really well, then bring to a boil. Cover and reduce the heat to low. Cook 10 minutes, stirring occasionally, to allow the sauce to develop in flavor.
**ROUGHLY CHOP THE CILANTRO** for both the brewat and the noodles, but keep them in separate piles. When the sauce has cooked, turn the heat up to medium. Add the shrimp and the pile of chopped cilantro leaves and stalks. Cook 5 to 6 minutes, stirring occasionally, until the shrimp have cooked through and turned pink.
**WHILE THE SHRIMP COOKS** , cook the noodles in boiling water 2 to 3 minutes, or until soft, or following directions on the package. Drain and return the noodles to the pan. Add the oil, the chopped cilantro leaves, the cumin, chili powder and a good pinch of salt and pepper. Squeeze in the juice of the lemon and stir everything together well so that all the spices and dressing completely coat the yummy noodles. Serve with the cooked shrimp and herb brewat.
Rita's Tamarind & Coconut Shrimp Curry SERVES **4** READY IN **20 MINUTES**
**This is a super-quick shrimp curry, which is hot, sweet and sour all at once. If you can't find tamarind, just squeeze in the juice of a lime. And chili powder and freshly ground black pepper are fine if you don't have the whole spices.**
**1¼ cups basmati rice**
**2 onions**
**2 tablespoons peanut oil**
**3 dried red chilies**
**10 peppercorns**
**1 teaspoon paprika**
**½ teaspoon turmeric**
**1¾ cups coconut milk**
**3 teaspoons tamarind paste**
**1 pound 2 ounces raw shelled jumbo shrimp (with or without tails)**
**1 handful of cilantro leaves**
**sea salt**
**COOK THE RICE** in boiling water 10 to 12 minutes, or until soft, or following package directions. Drain in a strainer and return to the pan. Cover the pan with a clean dish towel and then the lid. Set aside so that the rice can fluff up ready to eat.
**MEANWHILE, PEEL AND FINELY SLICE** the onions. Heat the oil in a large saucepan over medium heat and add the onions. Cook 4 to 5 minutes, stirring occasionally, or until just turning golden.
**WHILE THE ONIONS COOK** , add the chilies and peppercorns to a spice grinder, and grind to a fine powder. Pour the ground spices into the pan with the cooked onions and add the paprika, turmeric and a good pinch of salt. Stir well.
**POUR IN THE COCONUT MILK** and add the tamarind paste. Stir everything together really well so that the sauce takes on a rich red color. Bring to a boil and add the shrimp. Give them a good stir in the hot sauce, then cover and cook 5 to 6 minutes, stirring occasionally, until the shrimp are cooked through and beautifully pink. Meanwhile, roughly chop the cilantro. Scatter the cooked curry with the chopped cilantro and serve with the rice.
Condesa Smoky Beans with Green Salsa SERVES **4** READY IN **30 MINUTES**
**FOR THE RICE**
**1¼ cups long-grain rice**
**FOR THE SMOKY BEANS**
**1 chipotle chili**
**2 × 15-ounce cans pinto beans**
**1 red bell pepper**
**1 red onion**
**2 tablespoons olive oil**
**2 bay leaves**
**4 garlic cloves**
**1 teaspoon ground cinnamon**
**2 teaspoons ground cumin**
**14.5-ounce can diced tomatoes**
**1½ tablespoons honey**
**2 ounces Gruyère cheese**
**sea salt**
**FOR THE GREEN SALSA**
**1 avocado**
**3 scallions**
**1 green chili**
**2 large handfuls of cilantro leaves and stalks**
**2 tablespoons olive oil**
**1 lime**
**COOK THE RICE** in boiling water 10 to 12 minutes, or until soft, or following directions on the package. Drain in a strainer, then cover the rice with a clean dish towel while still in the strainer and set aside. Meanwhile, cut the chipotle chili for the beans in half and put both halves in a small bowl. Cover with 2 to 3 tablespoons boiling water and let stand to soften a couple of minutes.
**DRAIN AND RINSE THE BEANS** and set aside. Seed the pepper and peel the onion, then finely chop both. Place the oil in a large saucepan over high heat and add the pepper and onion. Stir-fry 3 minutes to soften, then reduce the heat to medium and add the bay leaves. Peel and crush in the garlic, and stir well.
**ADD THE CINNAMON** , cumin, tomatoes, honey and beans to the onion mixture and season with salt. Pour in the chipotle chili and its water. Stir well, cover and cook 15 minutes, stirring occasionally, or until the beans are hot and the sauce is thick.
**MAKE THE GREEN SALSA**. Cut the avocado in half and remove the seed with a knife. Scoop out the flesh into a blender or food processor. Trim the scallions and discard the top of the chili, then add them to the blender with the cilantro, oil and some salt. Squeeze in the lime juice and blend to a coarse salsa. Add to a serving bowl. Grate the cheese and scatter it onto the rice and beans. Serve with the salsa on the side.
Amish's Gujarati Vegetable Curry SERVES **4** READY IN **35 MINUTES**
**This magnificent curry can be made well in advance by making the sauce and cooking it without any of the vegetables. cook the vegetables, then refresh them under cold water. When you want to eat, reheat the sauce and add the vegetables. Cook until the vegetables have warmed through to serve.**
**1¼ cups basmati rice**
**14-ounce can chickpeas**
**1 onion**
**2 tablespoons peanut oil**
**1-inch piece fresh gingerroot**
**6 garlic cloves**
**4 tomatoes**
**heaped ½ cup cashews**
**2 teaspoons ground coriander**
**1 teaspoon ground cumin**
**1 teaspoon garam masala**
**½ teaspoon chili powder**
**½ teaspoon turmeric**
**14 ounces new potatoes**
**3 carrots**
**1 small cauliflower**
**7 ounces green beans**
**1 handful of cilantro leaves**
**sea salt**
**COOK THE RICE** in boiling water 10 to 12 minutes, or until soft, or following directions on the package. Drain and rinse the chickpeas in a strainer. In the same strainer, drain the rice then pour the rice and chickpeas back into the pan. Cover the pan with a clean dish towel and then the lid. Let stand so the rice can fluff up.
**MEANWHILE, PEEL AND FINELY CHOP** the onion. Place the oil in a large saucepan over medium heat and add the onion. Cook 4 to 5 minutes, stirring occasionally, until golden.
**PEEL THE GINGER** and garlic, then add both to a blender or food processor with the tomatoes, ⅓ cup of the cashews, the ground coriander, cumin, garam masala, chili powder, turmeric and a good pinch of salt. Blend until smooth. Pour this mixture over the cooked onion, stir well and bring to a boil. Cover, reduce the heat to low and simmer 20 minutes, stirring occasionally.
**QUARTER THE POTATOES** while the sauce cooks. Cook them in boiling water 8 minutes. Peel the carrots, then cut them, with the cauliflower, into small pieces. Cut the beans in half. Add the vegetables to the potatoes. Cook 5 to 6 minutes, or until tender, then drain. Roughly chop the cilantro and set aside. Stir the vegetables into the sauce. Scatter the curry with the cilantro and serve with the remaining cashews.
Beirut Ratatouille SERVES **4** READY IN **45 MINUTES**
**1 red onion**
**4 garlic cloves**
**2 tablespoons olive oil**
**5½ ounces button mushrooms**
**2 red bell peppers**
**1 eggplant**
**1 zucchini**
**14-ounce can chickpeas**
**scant ¼ cup tomato paste**
**14.5-ounce can diced tomatoes**
**3 teaspoons ground cumin**
**2 teaspoons paprika**
**½ teaspoon chili powder**
**½ teaspoon freshly ground black pepper**
**1 large handful of parsley leaves**
**sea salt**
**TO SERVE**
**1 lemon**
**1 bag of mixed salad leaves**
**PEEL AND FINELY CHOP** the onion and garlic. Place the oil in a large saucepan over medium heat, add the onion and garlic and stir well. Roughly slice the mushrooms, then add them to the pan with the onion. Stir everything together and cook 3 to 4 minutes, stirring occasionally, until the mushrooms have cooked down.
**MEANWHILE, SEED THE PEPPERS** , then, chop the peppers, eggplant and zucchini into ¾-inch cubes. Drain and rinse the chickpeas. Transfer the vegetables to the pan with the cooked mushrooms and add the chickpeas, tomato paste, canned tomatoes, cumin, paprika, chili powder, black pepper and a really good pinch of salt.
**POUR IN** 1⅓ cups boiling water and stir well. Increase the heat to high and bring to a boil. Partially cover to allow the excess steam to escape, then reduce the heat to medium and simmer 25 to 30 minutes, stirring occasionally, until the vegetables are cooked through but still have a little bite.
**AS THE RATATOUILLE SIMMERS** , finely chop the parsley and cut the lemon into wedges. Add the salad to a serving bowl. Just before serving, mix the chopped parsley into the ratatouille. Serve with the lemon wedges and the mixed salad.
SOMETHING SPECTACULAR
**There are times when you want to pull out all the stops, get out the fancy tableware, polish the glasses you've been saving for the queen and cook something unbelievable. In this chapter the recipes use fabulous ingredients to create spectacular dinners that can all be made super-quick—and none in more than 45 minutes. My Beautiful Beef Mezze— roasted tenderloin of beef, coated in spices and served with a spinach _raita_ , and a tangy red onion and herb salad—takes only 40 minutes to make. Or my delicious Kashmiri Lamb cutlets, served with a vibrant Pineapple & chili Salad & Mint & Lime raita, are utterly mind-blowing and ready for the table in 30 minutes. My delicate Essaouira Monkfish tagine, flavored with preserved lemon, cumin, paprika and garlic, takes only 30 minutes to make. So, even if you don't have much time you can still impress your guests with something spectacular.**
Chicken with Mexican Chili-Chocolate Mole, Polenta & Fennel Salad SERVES **4** READY IN **45 MINUTES**
**_Mole_ is an exquisite Mexican sauce with a complex flavor. It requires lots of ingredients and time, but I have created an express version that has all the depth of flavor of a traditional _mole_ , without the fuss. Bright yellow polenta is just right to soak up all the intense flavors and is reminiscent of the corn used in Mexican cooking. My fennel salad, with crunchy radishes and a tart dressing, adds vibrancy and balances the flavors of the dish.**
**FOR THE CHILI-CHOCOLATE MOLE**
**6 garlic cloves**
**heaped ⅓ cup peanuts**
**4 cloves**
**2 chipotle chilies**
**1 onion**
**3 tablespoons olive oil**
**14-ounce can diced tomatoes**
**1 teaspoon ground cinnamon**
**1½ teaspoons ground cumin**
**2 teaspoons dried oregano**
**2 teaspoons brown sugar**
**1 ounce semisweet or bittersweet chocolate (70–85% cocoa solids)**
**FOR THE FENNEL SALAD**
**3½ ounces radishes**
**2 fennel bulbs**
**½ lime**
**2 tablespoons olive oil**
**sea salt and freshly ground black pepper**
**FOR THE GRILLED CHICKEN**
**2 tablespoons olive oil**
**4 skinless chicken breasts**
**1 tablespoon sesame seeds**
**FOR THE POLENTA**
**1⅓ cups quick-cook polenta**
**1½ tablespoons butter**
**FIRST, MAKE THE MOLE**. Place a large skillet over medium heat, then peel the garlic and add it to the skillet with the peanuts and cloves. Toast 4 to 5 minutes, shaking the skillet occasionally, until the peanuts have started turning golden. While they toast, put the chilies in a bowl and add 2 tablespoons boiling water to soften them. Peel the onion and cut it into quarters.
**PUT THE TOASTED PEANUTS** , cloves and garlic into a blender or food processor. Add the chilies and their soaking water followed by the onion, oil, tomatoes, cinnamon, cumin, oregano, brown sugar and a really good pinch of salt. Blend 2 minutes until the sauce becomes beautifully smooth. Pour the sauce into a saucepan over medium heat and bring to a boil. Cover, reduce the heat to low and simmer 20 minutes.
**MEANWHILE, MAKE THE SALAD**. Cut the radishes into quarters and put them in a serving bowl. Shave the fennel using a slicer or mandoline and add to the bowl with the radish. Squeeze in the juice of the lime, pour in the oil and season with salt and pepper. Toss everything together really well, then cover loosely with plastic wrap and set aside.
**TO MAKE THE GRILLED CHICKEN** , heat a grill pan until smoking. Meanwhile rub the olive oil all over the chicken breasts. Cook 10 to 12 minutes on each side until cooked through and tender. Remove the pan from the heat and set aside.
**WHEN THE MOLE SAUCE HAS SIMMERED** 20 minutes, break in the chocolate and stir it in well. Cook another 10 minutes, stirring occasionally, to allow the flavors to develop even more.
**MAKE THE POLENTA** while the sauce finishes cooking. Pour the polenta into a saucepan and whisk in 3½ cups boiling water. Cook over low heat 1 to 2 minutes, stirring continuously, until the water is absorbed and the polenta cooked. Stir in the butter and a good pinch of salt and pepper. Serve the polenta with the chicken, with some rich, velvety brown mole sauce poured on top. Scatter each serving with sesame seeds and serve with the salad.
Saffron Chicken Mansaf with Tahini Yogurt & Green Salad SERVES **4** READY IN **40 MINUTES**
**A _mansaf_ is a Jordanian dish traditionally made with lamb and served on a huge platter. The lamb is cooked with a thick yogurt sauce and served on a bed of rice scattered with nuts and herbs. It's a dish meant for sharing, as is this fast interpretation.**
**My version is made with chicken thighs instead of lamb and is seriously spiced up with saffron, cinnamon, cardamom and a heavy grating of nutmeg. Instead of making a traditional yogurt sauce, I have included a speedy variation using yogurt blended with wonderfully rich tahini and a squeeze of fresh lemon juice. Although I have used parsley, pine nuts and almonds to serve with the _mansaf_ , you could add other herbs and nuts instead. Go crazy—for a great _mansaf_ , the more you throw on top the better! The only thing I would insist on is that you share your _mansaf_ with friends and family over a really good bottle of wine.**
**FOR THE SAFFRON CHICKEN MANSAF**
**1¾ cups basmati rice**
**generous 2½ cups chicken stock**
**¼ teaspoon saffron threads**
**2 onions**
**3 tablespoons olive oil**
**6 cardamom pods**
**4 garlic cloves**
**2 teaspoons ground cinnamon**
**3 bay leaves**
**1 pound 2 ounces boneless, skinless chicken thighs**
**heaped ⅓ cup pine nuts**
**1 large handful of parsley leaves**
**½ nutmeg**
**scant ⅔ cup sliced almonds**
**sea salt and freshly ground black pepper**
**FOR THE TAHINI YOGURT**
**scant 1¼ cups yogurt**
**2 tablespoons tahini**
**½ lemon**
**TO SERVE**
**1 bag of green salad**
**PUT THE RICE** in a bowl, cover with cold water and stir. Set aside a few minutes to soak and to release the starch. Add the stock to a saucepan. Bring to a boil over medium heat. Once boiled, add the saffron, stir well and remove from the heat.
**MEANWHILE, PEEL AND SLICE THE ONIONS**. Place the oil in a large, shallow saucepan over medium heat and add the onions. Stir well and cook 4 to 5 minutes, stirring occasionally, until golden.
**CRUSH THE CARDAMOM PODS** by pressing down on them with the flat side of a knife blade. Add them to the cooked onions. Peel and crush in the garlic, then add the cinnamon, bay leaves and a good pinch of salt. Drain the rice and add it to the pan. Stir well to coat the grains in the oil and spices. Pour in the saffron stock and stir gently. Put the chicken thighs on the top of the rice and poke them down with a spoon. Bring to a boil, cover, reduce the heat to low and cook 20 minutes, or until the chicken is cooked through and the rice is tender.
**WHILE THE CHICKEN AND RICE COOK** , put the pine nuts in a small skillet over medium heat and toast 4 to 5 minutes, shaking the pan occasionally, until golden. Remove from the heat and set aside.
**TO MAKE THE TAHINI YOGURT** , pour the yogurt into a serving bowl, add the tahini and a good pinch of salt. Squeeze in the juice of the lemon, stir well and add a grinding of pepper. Set aside.
**FINELY CHOP THE PARSLEY** and set it aside. Add the salad to a serving bowl. Once the saffron mansaf is cooked, grate the nutmeg onto it and add half the pine nuts, sliced almonds and parsley. Season with salt and pepper, and stir everything together well with a fork. Scatter with the remaining nuts and parsley, and serve with the yogurt and green salad on the side.
COOL CHILIES, TEQUILA & TOSTADAS
**The beautiful city of Oaxaca, in southern Mexico, has a really cool arty vibe. Little galleries are scattered throughout the city and the whole place is painted a veritable array of different colors. Art, music, dance and food form the cornerstones of life in Oaxaca, a city that provided a fantastic backdrop for my quest to find the best _tostadas_. _Tostadas_ are the crunchy backbone of Mexican food—a crispy corn tortilla base covered in delicious toppings. It makes the perfect on-the-go street food.**
**I went high end with beautifully grilled octopus _tostadas_ served on a fancy slate board and ate shredded pork _tostadas_ with avocado and chili from a food cart. I also hit on Mercado Benito Juárez, a huge indoor market that was filled with wonderful fresh produce and awesome street food. They had deep-fried grasshoppers covered in salt and chili (the Mexican equivalent of crunchy chili peanuts to have with cheeky _cerveza_ ), spicy broths flavored with cilantro and lime, black beans served with soft tortillas for dunking and absolutely gigantic _tostadas_. The _tostadas_ were actually more like pizzas, having a crispy base slathered in refried beans and topped with the famous Oaxaca _queso_ (cheese).**
**I have combined elements from all my favorite _tostadas_ to create a really fancy street-food-inspired dinner: Duck Tostadas with Black Beans & Salsa. It's a thing of deliciousness and takes only 35 minutes to make. Oh yeah, and add a shot of gold tequila before you eat, and you have a party.**
Duck Tostadas with Black Beans & Salsa SERVES **4** READY IN **35 MINUTES**
**FOR THE ROAST DUCK**
**4 duck breasts**
**(about 5½ ounces each)**
**4 garlic cloves**
**2 teaspoons smoked paprika**
**½ teaspoon chili powder**
**2 tablespoons olive oil**
**FOR THE BLACK BEANS**
**15-ounce can black beans**
**2 tablespoons olive oil**
**1½ teaspoons ground cumin**
**½ lime**
**sea salt and freshly ground black pepper**
**FOR THE SALSA**
**1 red onion**
**heaped ¾ cup drained sun-dried tomatoes in oil**
**1 teaspoon smoked paprika**
**½ lime**
**TO SERVE**
**1 lettuce**
**2 large handfuls of cilantro leaves**
**4 large tortillas**
**PREHEAT THE OVEN** to 400°F. Trim and score the skin of the duck breasts, and put them in a small roasting pan. Peel and crush in the garlic, and add the smoked paprika, chili powder, oil and a good pinch of salt. Stir well to coat the duck completely. Turn the duck skin-side up, then roast 25 to 30 minutes, or until golden on the outside and juicy and pink in the center.
**MEANWHILE, DRAIN AND RINSE** the beans and pour them into a saucepan over medium heat. Mash the beans, using a potato masher, until fairly smooth, then add a scant ¼ cup water, the olive oil and cumin. Squeeze in the juice of the lime, season with salt and pepper, and stir well. Bring to a boil, reduce the heat to low and cook 8 to 10 minutes, stirring occasionally, until warmed through and thick. Remove from the heat, cover and set aside.
**TO MAKE THE SALSA** , peel the onion and cut it into quarters, then add it to a food processor, followed by the sun-dried tomatoes, smoked paprika and a pinch of salt. Squeeze in the juice of the lime, blend until smooth, then pour into a serving bowl.
**FINELY SLICE** the lettuce and cilantro, and put them onto a serving plate. Put the tortillas on four serving plates and cover each one with the beans. Slice up the duck and place it on top of the beans. Serve scattered with the salad and topped with some salsa.
Paprika & Fennel Pork Chops with Lentils & Beet & Goat Cheese Salad SERVES **4** READY IN **30 MINUTES**
**All my favorite flavors are brought together in this meal—pork, paprika, fennel, garlic, chorizo, lentils, beets and goat cheese. Although there's a lot going on, these big flavors go together splendidly and cook super quickly. Fennel seeds and smoked paprika make an aromatic crust for pork chops that are broiled to perfection. Chorizo fried with garlic, plus my favorite sun-dried tomato paste, enrich the lentils. And, finally, a quick salad of arugula, goat cheese and beets adds color, lightness and a little crunch to the meal. All this in 30 minutes—now that really _is_ something spectacular!**
**FOR THE SPICED PORK CHOPS**
**1 tablespoon fennel seeds**
**2 teaspoons smoked paprika**
**4 pork chops (about 7 ounces each)**
**2 tablespoons olive oil**
**FOR THE LENTILS**
**4-ounce piece of chorizo**
**2 garlic cloves**
**1 tablespoon olive oil**
**14-ounce can green lentils**
**2 tablespoons sun-dried tomato paste**
**1 handful of parsley leaves**
**sea salt and freshly ground black pepper**
**FOR THE BEET AND GOAT CHEESE SALAD**
**7 ounces cooked, peeled beets**
**½ orange**
**1 tablespoon olive oil**
**1 handful of arugula leaves**
**2 ounces soft goat cheese**
**¼ red chili**
**PREHEAT THE BROILER** to high. Lightly crush the fennel seeds using a mortar and pestle or a spice grinder. Add them to a mixing bowl followed by the paprika and a good pinch of salt. Put the pork into a separate mixing bowl, pour in the olive oil and stir well to coat.
**TRANSFER THE PORK** to a broiler rack and rub the spice mix over the top of the chops to give them a fantastic spicy crust. Broil the chops 6 to 8 minutes on each side, or until golden and cooked through.
**WHILE THE PORK BROILS** , finely chop the chorizo for the lentils and peel and chop the garlic. Place the oil in a skillet over medium heat and add the chorizo and garlic. Cook 3 to 4 minutes, stirring occasionally, until the chorizo turns golden. Drain and rinse the lentils, then add them to the pan with the cooked chorizo. Add the sun-dried tomato paste and ½ cup boiling water. Season with a pinch of salt and pepper. Stir well, reduce the heat to low and simmer gently, stirring occasionally, while you make the salad.
**ADD THE BEETS** to a mixing bowl and cut into small pieces using a knife and fork (this helps you avoid getting pink hands and a pink cutting board). Squeeze in the juice of the orange, pour in the oil and add a pinch of salt and pepper. Stir well and pour out onto a serving platter. Scatter the arugula over the beets and crumble the goat cheese over the top. Seed and finely chop the chili, then scatter it all over the salad. Cover loosely with plastic wrap and set aside.
**FINELY CHOP THE PARSLEY** for the lentils and add it to the pan with the warmed lentils. Turn the heat up to high, stir well and cook 1 to 2 minutes, stirring continuously, until thick. Serve the pork chops, spice-side up, with the lentils and the salad at the table.
Lao Lap Eggplant & Pork SERVES **4** READY IN **30 MINUTES**
**2 red chilies**
**6 garlic cloves**
**5 tablespoons peanut oil**
**2 eggplants**
**2 tablespoons fish sauce**
**3 tablespoons dark soy sauce**
**1¼ cups jasmine rice**
**2 lemongrass stalks**
**1 handful of dill**
**1 handful of cilantro leaves**
**1 handful of mint leaves**
**1 pound 2 ounces ground pork**
**1 lime**
**1 handful of bean sprouts**
**CUT THE TOP OFF** 1 of the chilies, then slice the chili. Peel the garlic, then slice 3 of the garlic cloves. Place 3 tablespoons of the oil in a large skillet over medium–low heat and add the sliced chili and garlic. Stir well and cook, stirring occasionally, while you prepare the eggplant.
**SLICE THE EGGPLANTS** into ¼-inch disks and layer them in the skillet. Add 1 tablespoon of the fish sauce and 2 tablespoons water. Cover and cook 20 minutes, or until tender, shaking the pan occasionally and turning the eggplant disks halfway through cooking. Remove the lid and add 2 tablespoons of the soy sauce. Turn the heat up to medium and cook 4 to 5 minutes, shaking the pan occasionally, until the eggplant disks have taken on a little color.
**MEANWHILE, COOK THE RICE** in boiling water 10 to 12 minutes, or until soft, or following directions on the package. Drain in a strainer. While the rice cooks, remove the tough outer leaves from the lemongrass and cut off the ends of the stalks. Cut the top off the remaining chili. Put the lemongrass, chili and remaining garlic into a mini food processor. Blend to a rough paste. Finely chop half the herbs and set aside.
**HEAT A WOK** over high heat until smoking. Add the remaining oil and the pork. Stir-fry 2 minutes, then add the spice paste and stir-fry another 2 to 3 minutes, or until the pork is just cooked through. Add the remaining fish sauce and soy sauce. Squeeze in the juice of the lime and stir-fry 1 minute. Turn off the heat, add the chopped herbs, stir well and set aside. Put the cooked eggplant on a large serving plate, spoon the pork on top and scatter with the remaining herbs and the bean sprouts. Serve with the rice.
Kashmiri Lamb Cutlets with Pineapple & Chili Salad & Mint & Lime Raita SERVES **4** READY IN **30 MINUTES**
**These lamb cutlets are flavored with wonderfully mild and beautifully red Kashmiri chilies, with the added warmth of ginger, cloves and garlic. The final grating of creamed coconut onto the lamb adds a hint of richness as it melts through. The flavor of the Kashmiri chilies is unmistakable and makes biting into the charred lamb a joyous experience. With every meal I eat I like to have a balance of flavors and textures, and the lamb cries out for something fresh and juicy. My salad of pineapple, chili, tomatoes, olives, mint and lime freshens things up in a blast of color and flavor, and the whole dish is finished off nicely with a mint and lime _raita_.**
**FOR THE LAMB CUTLETS**
**4 dried Kashmiri chilies**
**8 cloves**
**10 black peppercorns**
**1-inch stick cinnamon**
**1 teaspoon sea salt**
**1 teaspoon sugar**
**1-inch piece fresh gingerroot**
**4 garlic cloves**
**2 tablespoons white wine vinegar**
**2 tablespoons olive oil**
**8 lamb cutlets**
**1 ounce creamed coconut**
**TO SERVE**
**4 flatbreads**
**FOR THE PINEAPPLE AND CHILI SALAD**
**1 red chili**
**½ pineapple**
**1 cup cherry tomatoes**
**1 carrot**
**heaped 1 cup bean sprouts**
**¼ cup pitted black olives**
**1 handful of mint leaves**
**1 lime**
**2 tablespoons olive oil**
**sea salt**
**FOR THE MINT AND LIME RAITA**
**1 cup yogurt**
**½ lime**
**1 handful of mint leaves**
**1 tablespoon olive oil**
**a pinch of chili powder**
**PREHEAT THE BROILER** to high and the oven to 350°F. Put the Kashmiri chilies, cloves, peppercorns, cinnamon, salt and sugar into a spice grinder, and grind to a powder. Peel and add the ginger and garlic with the white wine vinegar and oil, then blend to a smooth paste.
**PUT THE LAMB CUTLETS** in a mixing bowl and add the spice paste. Stir well until the lamb is completely coated in the paste. Place the lamb on a broiler rack and broil 6 to 8 minutes on each side until golden on the outside and pink and juicy in the center.
**WHILE THE LAMB BROILS** , place the flatbreads in the hot oven and turn it off, so that they warm through and don't burn. Next, make the salad. Cut the top off the chili and roll the chili between your hands to remove the seeds, then chop it finely and add it to a large mixing bowl. Cut the top and bottom off the pineapple, then stand it upright on your cutting board. Slice off the skin, cutting downward from top to bottom. Carefully cut out any pieces of skin left on the fruit. Cut the pineapple half in half lengthwise, then slice off the woody core so that you are left with the soft flesh.
**CHOP THE PINEAPPLE FLESH** into small chunks and cut the cherry tomatoes in half. Add them to the bowl with the chili. Peel and then coarsely grate the carrot into the bowl, then add the bean sprouts and olives. Chop the mint leaves, if large, and add them to the bowl with the salad. Squeeze in the juice of the lime, pour in the oil and season with salt. Stir everything together to combine.
**TO MAKE THE RAITA** , pour the yogurt into a serving bowl, squeeze in the juice of the lime and season with a pinch of salt. Finely chop the mint and add it to the bowl. Stir well, drizzle with the oil and top with a pinch of chili powder. Grate the creamed coconut onto the cooked lamb to serve, with the vibrant salad, raita and warmed flatbreads on the side.
Manchurian Lamb with Tamarind Slaw & Grilled Chili Potatoes SERVES **4** READY IN **40 MINUTES**
**FOR THE ROAST LAMB**
**1 teaspoon Szechuan pepper**
**2 tablespoons sesame seeds**
**2 teaspoons cumin seeds**
**1** ¼ **pounds trimmed neck or lamb loin fillet**
**2 tablespoons olive oil**
**sea salt**
**FOR THE GRILLED POTATOES**
**1 pound 2 ounces new potatoes**
**2 tablespoons chili oil**
**FOR THE TAMARIND SLAW**
**2 tablespoons tamarind paste**
**3 teaspoons honey**
**2 teaspoons soy sauce**
**2 teaspoons sesame oil**
**1 white cabbage (about 1 pound in weight)**
**4 scallions**
**½ red chili**
**1 handful of cilantro leaves**
**PREHEAT THE OVEN** to 400°F. Add half the Szechuan pepper, sesame seeds and cumin seeds into a spice grinder and grind until smooth. Pour into a serving bowl and add the remaining spices and a good pinch of salt. Stir together well to combine.
**IF USING LAMB LOIN** , pull off the membrane. Cut the lamb into pieces 3 to 4 inches in size and add to a small roasting pan. Pour the olive oil over the lamb and mix well to coat. Scatter the lamb with two-thirds of the spice mixture and rub it all over meat. Roast 15 to 20 minutes, or until cooked through and really tender.
**MEANWHILE, BOIL THE POTATOES** 12 to 15 minutes, or until tender. While the lamb and potatoes cook, make the slaw. Combine the tamarind paste, honey, soy sauce, sesame oil and 2 tablespoons water in a large mixing bowl. Grate the cabbage using the fine setting of a food processor, then add to the bowl with the dressing. Trim and finely slice the scallions, then finely chop the chili and cilantro. Add them to the bowl with the cabbage and toss together thoroughly. Add to a serving bowl and cover.
**HEAT A GRILL PAN** over high heat. Meanwhile, drain the cooked potatoes and return them to the pan. Pour in the chili oil and add a pinch of the spice mixture and a small pinch of salt. Stir well, and don't be afraid to break up a few of the potatoes. Carefully pour the potatoes onto the hot grill pan and cook 2 minutes on each side, or until they start to crisp up, shaking the pan occasionally. Slice the lamb and sprinkle a little of the spice mixture on top. Serve with the potatoes and slaw, with the remaining spice mixture on the side.
Sticky Malaysian Lamb with Penang Garden Rice SERVES **4** READY IN **40 MINUTES**
**FOR THE STICKY LAMB**
**4 lamb rump steaks (about**
**5½ ounces each)**
**1 teaspoon chinese five-spice powder**
**2 tablespoons rice wine**
**2 tablespoons oyster sauce**
**1 tablespoon light soy sauce**
**1 teaspoon sesame oil**
**1 teaspoon olive oil**
**FOR THE PENANG RICE**
**1¾ cups basmati rice**
**1-inch piece fresh gingerroot**
**1 onion**
**2 lemongrass stalks**
**2 tablespoons peanut oil**
**1 teaspoon fenugreek seeds**
**1-inch stick cinnamon**
**4 cardamom pods**
**3 star anise**
**1¾ cups coconut milk**
**1 small handful of cilantro leaves**
**3 tablespoons fish sauce**
**PREHEAT THE OVEN** to 400°F. Put the lamb in a small roasting pan and add the Chinese five-spice powder, rice wine, oyster sauce, soy sauce, sesame oil and olive oil. Stir well and set aside to marinate.
**PUT THE RICE** in a large saucepan, cover with cold water and stir. Let stand 5 minutes to soak.
**PEEL THE GINGER** and onion, then finely chop both. Bash the fat ends of the lemongrass with a wooden spoon. Place the peanut oil in a shallow saucepan over medium heat and add the fenugreek, cinnamon, cardamom and star anise. Stir-fry 30 seconds until fragrant, then add the onion and ginger. Cook 4 to 5 minutes, stirring occasionally, until the onion has started to turn golden.
**MEANWHILE, PLACE THE LAMB** in the oven 15 to 20 minutes, or until cooked through and tender.
**POUR THE SOAKED RICE** into a strainer, then add it to the pan with the cooked onion and spices. Pour in 1 **¾** cups hot water and the coconut milk. Add the lemon-grass to the pan, then stir and cover. Reduce the heat to low and simmer gently 10 to 15 minutes, or until all the water has been absorbed and the rice is tender. You can always add extra hot water if the rice needs it. Slice the cooked lamb.
**CHOP THE CILANTRO** , then season the cooked rice with the fish sauce. Add to a serving dish. Place the lamb on top of the rice and scatter with cilantro leaves to serve.
Beautiful Beef Mezze SERVES **4** READY IN **40 MINUTES**
**I always enjoy a mezze—a table laden with wonderful homemade food to pass around to great friends and family, while the conversation and wine flow. I couldn't resist including a super-fast version in this book, and this beef mezze, inspired by the Eastern Mediterranean, has it all—spice-encrusted roast beef, a spinach _raita_ , a crunchy salad and warm flatbreads.**
**Before roasting, the beef is smothered in a paste of spices, lemon and garlic, which penetrate the meat while it cooks. My vibrant salad of red onions and tomatoes, with loads of fresh cilantro and parsley, and doused in lime juice and olive oil, acts as a sidekick to the beef. My twist on a traditional _raita_ uses spinach stir-fried with garlic and mixed into the cooling yogurt, topped with toasted pine nuts. It's a heavenly combination. Just make sure you squeeze all the excess moisture out of the cooked spinach first. My favorite way to eat this meal is to stuff a flatbread with beef and salad, drizzle over plenty of _raita_ , roll it all up and go for it!**
**FOR THE ROAST BEEF**
**1** ¼ **-pound piece of beef tenderloin**
**4 garlic cloves**
**2 teaspoons paprika**
**2 teaspoons ground cumin**
**1 teaspoon ground coriander**
**2 tablespoons olive oil**
**1 lemon**
**sea salt and freshly ground black pepper**
**FOR THE SPINACH RAITA**
**2 garlic cloves**
**2 tablespoons olive oil**
**scant ¼ cup pine nuts**
**7 ounces baby spinach scant 1 cup Greek yogurt**
**1 lemon**
**FOR THE ONION, TOMATO AND HERB SALAD**
**2 red onions**
**1½ limes**
**2 large tomatoes**
**2 large handfuls of cilantro leaves**
**2 large handfuls of parsley leaves**
**2 tablespoons olive oil**
**TO SERVE**
**4 flatbreads**
**PREHEAT THE OVEN** to 400°F and take the beef out of the fridge to come to room temperature. Peel the garlic, then add it to a mini food processor, followed by the paprika, cumin and ground coriander. Add the olive oil and a good pinch of salt and pepper. Squeeze in the juice of the lemon and blend until smooth.
**PUT THE BEEF IN A ROASTING PAN** , then add the paste and rub it all over the beef. Roast 30 to 35 minutes, or until charred on the outside and beautifully tender on the inside.
**WHILE THE BEEF COOKS** , peel and slice the garlic for the raita. Heat the oil in a wok over high heat and add the pine nuts. Stir-fry 30 seconds, or until golden, then remove from the pan and set aside. Add the garlic to the pan. Stir-fry for 30 seconds, or until golden, then add the spinach and a pinch of salt. Stir-fry a further 2 to 3 minutes, or until the spinach has completely wilted. Add the spinach to a fine strainer to drain.
**TO MAKE THE SALAD** , peel and finely slice the red onions, then add them to a mixing bowl. Squeeze in the juice of the limes and add a good pinch of salt. Stir to combine and set aside.
**USING THE BACK OF A SPOON** , squeeze any excess moisture out of the spinach. Add to a serving bowl along with the yogurt, then squeeze in the juice of the lemon and season with salt and pepper. Stir well, scatter with the pine nuts, then cover.
**CUT THE TOMATOES** for the salad in half and squeeze out the seeds. Finely chop the flesh and put it into the bowl with the onions. Finely chop the herbs and add them to the bowl. Pour in the oil, add a pinch of pepper and stir well to combine.
**PLACE THE FLATBREADS** in the oven 2 minutes to warm through. When the beef is cooked, remove it from the oven and transfer it to a carving board. Slice the beef and serve it with the warm flatbreads, spinach raita and salad. Oh, and a glass or two of red.
Korean Steaks with Carrot Kimchi & Sanjim SERVES **4** READY IN **40 MINUTES**
**FOR THE CARROT KIMCHI**
**2** ¼ **pounds carrots**
¼ **cup salt**
**1-inch piece fresh gingerroot**
**1 garlic clove**
**1 tablespoon fish sauce**
**2 teaspoons sugar**
**1 teaspoon chili powder**
**3 tablespoons yogurt**
**½ teaspoon honey**
**2 handfuls of chives**
**FOR THE SANJIM**
**1 garlic clove**
**12 scallions**
**½ cup walnuts**
**1 tablespoon light soy sauce**
**2 tablespoons chili sauce**
**2 teaspoons honey**
**2 teaspoons sesame oil**
**FOR THE GRILLED STEAKS**
**2 tablespoons olive oil**
**4 rib-eye steaks (about 9 ounces each)**
**sea salt and freshly ground black pepper**
**TO MAKE THE KIMCHI** , peel the carrots then grate them using a food processor. Add them to a large mixing bowl along with the salt and 3¼ cups boiling water. Stir to combine with a wooden spoon and set aside 20 minutes. Meanwhile, make the dressing for the kimchi. Peel and grate the ginger into a serving bowl, then peel and crush in the garlic. Add the fish sauce, sugar, chili powder, yogurt and honey. Finely chop the chives and add them to the bowl. Stir well, then cover and set aside.
**TO MAKE THE SANJIM** , peel the garlic and trim the scallions, then add them both to a mini food processor, followed by the walnuts. Blend to a coarse mixture. Scoop into a serving bowl and add the soy sauce, chili sauce, honey and sesame oil. Stir well to combine, then cover and set aside.
**TO COOK THE STEAKS** , heat a grill pan over high heat until smoking. Rub the olive oil all over the steaks and season both sides with salt and pepper. Cook the steaks 2 to 3 minutes on each side until beautifully charred on the outside but still perfectly pink in the center. Remove from the heat and set aside to rest the meat.
**DRAIN AND RINSE THE CARROTS** thoroughly under cold water. Repeat several times to remove all the salt. Squeeze out any excess water using your hands and add the carrots to the bowl with the dressing. Stir well and serve with the steaks and sanjim.
Essaouira Monkfish Tagine SERVES **4** READY IN **30 MINUTES**
**1** ¼ **-pound monkfish fillet, membrane removed**
**½ lemon**
**heaped ¾ cup couscous**
**2 carrots**
**4 garlic cloves**
**2 red bell peppers**
**3 tablespoons olive oil**
**2 teaspoons ground cumin**
**1 teaspoon paprika**
**½ teaspoon freshly ground black pepper**
**¼ teaspoon chili powder**
**1 teaspoon sugar**
**14.5-ounce can diced tomatoes**
**1 preserved lemon**
**¼ cup pitted black olives**
**1 large handful of parsley leaves**
**sea salt**
**CUT THE MONKFISH** into 2 pieces and put them in a mixing bowl. Squeeze the juice of the lemon all over the fish, sprinkle with a pinch of salt and set aside. Add the couscous to a large mixing bowl and add ¾ cup warm water. Cover with plastic wrap and leave a minimum of 10 minutes, or until ready to serve.
**PEEL THE CARROTS** and garlic, and seed the peppers, then finely slice them all. Place the oil in a large saucepan over high heat and add the peppers and carrots. Cook 5 to 6 minutes, stirring occasionally, until they start to soften. Reduce the heat to medium and add the garlic, cumin, paprika, black pepper, chili powder, sugar and a pinch of salt, and stir well.
**ADD THE TOMATOES** , pour in a scant 1 cup hot water and stir well to combine. Bring to a boil and add the fish. Partially cover with a lid and cook 5–6 minutes. Turn the fish over, spoon some sauce on top of it, then cover with the lid and cook another 5 to 6 minutes, or until the fish is cooked through and tender.
**WHILE THE FISH COOKS** , remove and discard the flesh from the preserved lemon. Slice the skin into thin strips and set aside. Slice the olives and finely chop the parsley, then set aside. Fluff up the couscous with a fork. Stir the preserved lemon skin, olives and parsley into the pan with the cooked fish, and mix well. To serve, cut the pieces of fish in half and serve with the couscous.
Phuket Snapper with Hoisin Noodles & Herb Salad SERVES **4** READY IN **40 MINUTES**
**This delicious meal was inspired by our family vacation in Phuket a few years ago. I found hanging out and cooking with the superb chef, Jitty, at our villa way more interesting than spending a lazy afternoon by the pool. In her tiny, but immaculate, kitchen she would cook up a storm for every meal. She had trained in Bangkok and knew about the regional cuisines of Thailand. Her repertoire of dishes was incredible, and her use of flavor, color and texture was spot on. I have borrowed a few elements from her glorious kitchen and added my own express twist to them so that you can get a Thai feast on the table in only 40 minutes.**
**The Worcestershire sauce is the secret ingredient in this dish, as used in Thailand. (I would have gone for fish sauce!) Worcestershire sauce adds a wicked flavor that most people won't recognize. It's strange that a British ingredient works so well with Thai flavors, but this is exactly why I love cooking—you can mix and match to create something sublime.**
**FOR THE ROASTED SNAPPER**
**1 tablespoon peanut oil, plus extra for greasing**
**2 red snapper (about 1 pound 2 ounces each), cleaned**
**2 lemongrass stalks**
**1 lime**
**2-inch piece fresh gingerroot**
**1 tablespoon Worcestershire sauce**
**1 teaspoon freshly ground black pepper**
**sea salt**
**FOR THE HERB SALAD**
**2 lemongrass stalks**
**1-inch piece fresh gingerroot**
**½ red chili**
**2 tablespoons fish sauce**
**1½ teaspoons sugar**
**1 red onion**
**1½ limes**
**10½ ounces carrots**
**2 large handfuls of cilantro leaves**
**2 large handfuls of basil leaves**
**1 large handful of mint leaves**
**scant ¼ cup peanuts**
**FOR THE HOISIN NOODLES**
**7 ounces medium egg noodles**
**3 tablespoons hoisin sauce**
**2 tablespoons soy sauce**
**1 tablespoon peanut oil**
**PREHEAT THE OVEN** to 400°F. Oil a piece of foil large enough to wrap the fish in, and put the snapper on top. Finely slice the lemongrass, lime and unpeeled ginger.
**SPOON THE WORCESTERSHIRE SAUCE** into the cavity of the fish and stuff with the sliced lemongrass, lime and ginger, putting a few slices of lime on the top, if you like. Drizzle with the oil and season with black pepper and a good pinch of salt. Wrap the fish tightly in the foil and place in a roasting pan. Roast the fish 25 to 30 minutes, or until cooked through and tender.
**MEANWHILE, MAKE THE SALAD**. Remove the tough outer leaves of the lemongrass and cut off the ends of the stalks. Peel the ginger. Put the lemongrass into a mini food processor with the ginger, chili, fish sauce and sugar, then blend to a smooth paste. Peel, then grate the onion into a large mixing bowl and squeeze the juice of the limes onto the grated onion (this will help take the rawness out of the onions). Stir well to combine. Peel, then grate the carrots on top of the onions.
**FINELY CHOP MOST OF THE HERBS** , reserving a few leaves to garnish, and add to the bowl with the salad. Pour in the spice paste, toss everything together and transfer to a serving bowl. Cover and set aside.
**COOK THE NOODLES** in boiling water 4 to 5 minutes, or until soft, or following directions on the package. Drain the noodles and return them to the pan. Pour in the hoisin sauce, soy sauce and oil. Stir well to combine, then pour the noodles onto a serving dish and set aside. Scatter the salad with the peanuts and reserved herb leaves. Unwrap the cooked fish and set it on a large plate. Serve the fish at the table with the noodles and salad.
Keralan Seafood Curry SERVES **4** READY IN **25 MINUTES**
**1¼ cups basmati rice**
**1-inch piece fresh gingerroot**
**6 garlic cloves**
**1 green chili**
**2 teaspoons ground coriander**
**½ teaspoon turmeric**
**heaped 1¾ cups cherry tomatoes**
**2 tablespoons peanut oil**
**2 teaspoons black mustard seeds**
**2 large pinches dried curry leaves**
**13.5-fluid-ounce can coconut milk**
**½ lime**
**9 ounces boneless tilapia fillets or other white fish fillets**
**¾ pound mixed seafood, such as squid rings, raw shelled jumbo shrimp, shelled mussels**
**1 handful of cilantro leaves**
**sea salt**
**COOK THE RICE** in boiling water 10 to 12 minutes, or until soft, or following directions on the package. Drain in a strainer and return to the pan. Cover the pan with a clean dish towel and then the lid. Set aside to allow the rice to fluff up.
**MEANWHILE, PEEL THE GINGER AND GARLIC** , and cut the top off the chili, then put these ingredients into a mini food processor with the ground coriander, turmeric and a good pinch of salt. Blend to a smooth paste, adding a little water if necessary, and set aside.
**CUT THE CHERRY TOMATOES** in half and reserve. Place the oil in a large saucepan over medium heat and add the mustard seeds and curry leaves. Let them crackle a few seconds, then add the spice paste. Stir-fry 30 seconds, or until fragrant, then pour in the coconut milk. Squeeze in the juice of the lime and add a pinch of salt. Stir everything together well to combine and bring to a boil.
**CHOP THE FISH** into large, bite-size pieces and add to the boiling sauce, then add the seafood and cherry tomatoes and stir gently. Bring back to a boil, cover and reduce the heat to medium-low. Cook 6 to 8 minutes, stirring occasionally, until all the seafood is cooked through and tender. Scatter the cooked curry with the cilantro leaves and serve with the rice.
Iain's Mighty Scallop Ceviche with Buckwheat Noodles & Avocado Salad SERVES **4** READY IN **30 MINUTES**
**This is a super-fast, tangy and spicy dinner inspired by southeastern Asia, with a bit of good old West London in there as well. Iain is one of my best friends, and he cooks a mean scallop. ceviche is simply raw fish, or certain types of shellfish, that has been "cooked" in an acid, such as lime juice or vinegar. Make sure you buy the freshest seafood you can on the day you want to serve the dish. If you want to reduce the chili heat, remove the seeds—and if you like it to be a bit more piquant, throw in an extra chili.**
**FOR THE SCALLOP CEVICHE**
**scant ¼ cup peanuts**
**2 lemongrass stalks**
**3 scallions**
**1 red chili**
**¾ pound scallops**
**2 limes**
**2 tablespoons fish sauce**
**1 teaspoon sugar**
**1 large handful of mint leaves**
**FOR THE BUCKWHEAT NOODLES**
**3 scallions**
**7 ounces buckwheat noodles**
**3 tablespoons soy sauce**
**2 tablespoons olive oil**
**1 teaspoon sesame oil**
**FOR THE AVOCADO SALAD**
**2 tablespoons red wine vinegar**
**2 teaspoons sugar**
**2 tablespoons olive oil**
**1 teaspoon sesame oil**
**1 teaspoon ground coriander**
**2 ripe avocados**
**1 tablespoon pumpkin seeds**
**sea salt**
**ROUGHLY CHOP THE PEANUTS** and put them in a skillet over medium heat. Toast the peanuts 4 to 5 minutes, shaking the pan occasionally, until golden. Remove from the heat and set aside to cool.
**MEANWHILE, REMOVE THE TOUGH** outer leaves from the lemongrass and cut off the ends of the stalks. Trim all the scallions for the ceviche and the noodles. Cut the top off the chili, then finely chop half the chili with 3 scallions and the lemongrass, and put them into a bowl for the ceviche. Finely chop the remaining scallions and chili half, and put them in a separate small bowl to add to the noodles later.
**COOK THE NOODLES** in boiling water 5 to 7 minutes, or until soft, or following directions on the package. While the noodles cook, thinly slice the scallops horizontally and arrange them in an even layer in a shallow serving dish. Squeeze the juice of the limes all over the scallop slices and shake the dish so all the slices are coated. Cover with plastic wrap and set aside 8 to 10 minutes so the scallops can "cook" in the acid and turn slightly opaque in color. Remember to shake the dish from time to time.
**WHEN THE NOODLES HAVE COOKED** , drain them in a strainer, refresh under cold water and drain again. Return them to the pan and dress with the soy sauce, olive oil and sesame oil. Stir well to coat, then add the noodles to a serving bowl. Scatter with the reserved chopped chili and scallions. Cover loosely with plastic wrap and set aside.
**MAKE THE DRESSING** for the salad by whisking the red wine vinegar and sugar together in a mixing bowl until the sugar dissolves. Pour in the olive oil and sesame oil, then add the coriander and a pinch of salt. Whisk everything together well.
**CUT THE AVOCADOS** in half and remove the seeds with a knife. Scoop out small pieces of the flesh using a teaspoon and put them into the bowl with the dressing. Carefully mix everything together so that the avocado does not discolor. Arrange the avocado on a serving plate and scatter with the pumpkin seeds. Cover and set aside.
**ADD THE FISH SAUCE** to the "cooked" scallops, then add the sugar and the reserved chopped chili, scallions and lemongrass, and carefully toss together. Tear up the mint leaves and scatter them, along with the toasted peanuts, onto the scallops. Serve with the noodles and avocado salad.
Panjim Clams with Coconut Okra SERVES **4** READY IN **40 MINUTES**
**FOR THE CLAMS**
**1 onion**
**1 green chili**
**2 tablespoons peanut oil**
**2 teaspoons garam masala**
**1 teaspoon turmeric**
**1¾ cups coconut cream**
**½ lime**
**2¼ pounds picked and cleaned clams**
**1 small handful of cilantro leaves**
**sea salt**
**FOR THE COCONUT OKRA**
**¾ pound okra**
**1 red onion**
**3 garlic cloves**
**1 green chili**
**2 cardamom pods**
**2 tablespoons peanut oil**
**8 black peppercorns**
**¾ cup coconut cream**
**1 large pinch of dried curry leaves**
**3 tablespoons raisins**
**½ lime**
**TO SERVE**
**4 small naan breads**
**PREHEAT THE OVEN** to 350°F. Peel the onion and cut the top off the chili. Finely chop both. Place the oil in a saucepan over medium heat and add both ingredients. Stir-fry 4 to 5 minutes, or until just turning golden.
**ADD THE GARAM MASALA** and turmeric, stir well and pour in the coconut cream. Squeeze in the juice of the lime and add a good pinch of salt. Stir well, reduce the heat to low and simmer gently, stirring occasionally, while you start the okra.
**CUT THE TOPS** off the okra. Peel the red onion and garlic, and cut the top off the chili, then finely chop the onion, garlic and chili. Split the cardamom pods open by pressing down on them with the flat side of a knife blade. Add the oil to a wok over high heat and add the onion, garlic, chili, cardamom and peppercorns. Stir-fry 2 to 3 minutes, or until the garlic is just golden, then add the okra and a good pinch of salt. Stir-fry 2 minutes, then add the coconut cream. Add the curry leaves to the wok by rubbing them between your hands and letting them drop into the wok. Stir well to combine, cover and reduce the heat to low. Let cook 5 minutes.
**MEANWHILE, PLACE THE NAAN** in the oven and switch it off, so that they just warm through. Stir the raisins and the juice of the lime into the half-cooked okra, then cover and cook 5 minutes, or until the okra is tender. While the okra finishes cooking, add the clams to the hot sauce, cover and cook 4 to 5 minutes, shaking the pan occasionally, until the clams have opened. Discard any that remain closed. Chop the cilantro and scatter it onto the clams. Serve with the okra and warmed naan breads.
Rooftop-Roasted Vegetables with Chili Tapenade SERVES **4** READY IN **45 MINUTES**
**FOR THE ROOFTOP-ROASTED VEGETABLES**
**2 red onions**
**2 red bell peppers**
**2 zucchini**
**1 eggplant**
**3 tablespoons olive oil**
**1 tablespoon dried thyme**
**heaped 1¾ cups cherry tomatoes**
**1 loaf of fabulously crusty bread heaped ⅓ cup pine nuts**
**2 large handfuls of mint**
**½ lemon**
**3½ ounces feta cheese**
**sea salt and freshly ground black pepper**
**FOR THE CHILI TAPENADE**
**1 garlic clove**
**⅔ cup pitted black olives**
**4 anchovy fillets**
**1 large handful of parsley leaves**
**¼ teaspoon chili powder**
**1½ teaspoons ground cumin**
**2 tablespoons olive oil**
**½ lemon**
**PREHEAT THE OVEN** to 400°F. Peel the onions and seed the peppers, then cut the onions, peppers, zucchini and eggplant into large bite-size pieces and put them in a roasting pan. Pour the olive oil evenly over the vegetables, then scatter with the thyme and a good pinch of salt and pepper. Stir everything together really well and roast 25 minutes, or until the vegetables are almost cooked through.
**WHILE THE VEGETABLES ARE COOKING** , make the chili tapenade. Peel the garlic and put it into a blender or food processor. Add the olives, anchovies, parsley, chili powder, cumin, oil and a pinch of salt and pepper. Squeeze in the juice of the lemon and blend to a coarse paste. Pour into a serving bowl, cover loosely with plastic wrap and let stand to allow the savory flavors to develop.
**WHEN THE VEGETABLES** have almost cooked, remove from the oven and scatter with the tomatoes. Cook another 8 to 10 minutes, or until all the vegetables are tender and golden and the tomatoes have just started to break down. Put the bread in the oven for the last 5 minutes to warm through.
**PUT THE PINE NUTS** into a small skillet over medium heat and toast 2 to 3 minutes, shaking the pan occasionally, until golden. Remove from the heat and set aside. Strip the mint leaves from the stems. Squeeze the juice of the lemon evenly over the cooked vegetables, then scatter with crumbled feta cheese, the mint leaves and the toasted pine nuts. Serve with the chili tapenade and warm bread.
Sesame Eggplant Curry with Keralan Spinach & Kernel Corn Salad SERVES **4** READY IN **45 MINUTES**
**This vegetarian feast is my take on a classic northern Indian curry. It's served with a fresh spinach and kernel corn dish, hailing from Kerala, which is a cross between a side dish and a salad, and makes the perfect contrast. A lovely touch for maximum flavor when preparing this curry is to cut a slit in the eggplant and then to rub in a little of the spice mix. You can really taste the difference—the eggplant sucks up all the flavor of the spices while it cooks gently in the sauce.**
**For the eggplant**
**1 tablespoon ground coriander**
**1 tablespoon sesame seeds**
**½ teaspoon chili powder**
**½ tablespoon ground cumin**
**1½ teaspoons sea salt**
**¾ pound baby eggplants**
**1 large red onion**
**2 tablespoons peanut oil**
**1-inch piece fresh gingerroot**
**4 garlic cloves**
**3 tomatoes**
**a pinch of sugar**
**1 handful of cilantro leaves**
**½ lemon**
**FOR THE RICE**
**1¼ cups basmati rice**
**FOR THE KERALAN SPINACH AND KERNEL CORN SALAD**
**1 tablespoon peanut oil**
**1 teaspoon cumin seeds**
**heaped ½ cup cashews**
**½ pound spinach**
**1 red onion**
**1 lemon**
**½ red chili**
**heaped ⅔ cup canned whole kernel corn**
**1 ounce creamed coconut**
**sea salt**
**PUT THE GROUND CORIANDER** , sesame seeds, chili powder, ground cumin and salt into a spice grinder, and grind to a fine powder. Remove the stalks from the baby eggplants, if you like, and cut a slit about 1 inch deep into the opposite end. Rub a little of the ground spices into the slits—use about half the spices for this. Peel and finely chop the onion.
**PLACE THE OIL** in a saucepan over medium heat and add the onion. Cook 4 to 5 minutes, stirring occasionally, until golden. While the onion cooks, peel the ginger and garlic, then finely chop the ginger, garlic and tomatoes. Add to the cooked onion and stir well to combine. Add the remaining ground spices, the sugar and the prepared eggplants. Stir everything together really well, then cover and simmer 20 minutes to allow the eggplants to cook through.
**MEANWHILE, COOK THE RICE** in boiling water 10 to 12 minutes, or until soft, or following directions on the package. Drain in a strainer and return to the pan. Cover the pan with a clean dish towel and then the lid. Let stand so the rice can fluff up.
**MAKE THE SALAD** while the rice cooks. Place the oil in a wok over medium heat and add the cumin seeds and cashews. Stir-fry 45 seconds, then add the spinach and a pinch of salt. Continue to stir-fry 2 to 3 minutes, or until the spinach has completely wilted. Remove from the heat and set aside.
**PEEL AND FINELY CHOP THE ONION** , and add it to a mixing bowl. Squeeze the juice of the lemon all over the onion, add a pinch of salt and stir well. Finely chop the chili and add it to the same bowl. Drain the kernel corn and pour it into the bowl, then add the cooked spinach, making sure you scrape all the oil and cumin into the mixing bowl. Stir well to combine, then transfer to a serving bowl. Grate the coconut evenly over the top, then cover loosely with plastic wrap and set aside.
**WHEN THE EGGPLANTS HAVE COOKED** , remove the lid from the pan and cook 5 minutes more, stirring occasionally, to allow the sauce to thicken. Roughly tear up the cilantro. Scatter the cooked curry with the cilantro then squeeze the juice of the lemon evenly over it. Serve with the cooked rice and the colorful salad.
NAUGHTY BUT NICE
**The name says it all really. This chapter is packed with delicious desserts, fabulous drinks and killer cocktails that can all be made so fast you might as well make two at a time! Even the longest recipe only takes 30 minutes from start to finish. My Mint tea & Lemongrass Martini takes less than 10 minutes to make and will get any party started. My Salted Caramel Chocolate Sauce (which is quite simply the greatest sauce there ever was and ever will be) poured generously over vanilla ice cream, takes only 10 minutes to make and will win you a legion of fans with every serving. My beautifully sticky Kika cakes flavored with almonds and vanilla, and served with an Orange & Ginger Glaze, take only 25 minutes to make, proving that there is even time for a bit of gentle baking.**
Vanilla Ice Cream with Salted Caramel Chocolate Sauce SERVES **4** READY IN **10 MINUTES**
**This is probably the best sauce ever! A bold statement, I know, but what could be better than a wickedly sweet salted caramel sauce, loaded up with rich dark chocolate and served warm and oozing over vanilla ice cream? Find an especially good vanilla ice cream to do the sauce justice.**
**FOR THE ICE CREAM**
**17-ounce carton of awesome vanilla ice cream**
**⅓ cup hazelnuts**
**FOR THE SALTED CARAMEL CHOCOLATE SAUCE**
**⅔ cup light brown sugar**
**¼ cup butter**
**scant ¼ cup heavy cream**
**3½ ounces semisweet or bittersweet chocolate (85% cocoa solids)**
**sea salt**
**TAKE THE VANILLA ICE CREAM** out of the freezer to soften slightly. Meanwhile, pour the sugar for the sauce into a saucepan and add 1½ tablespoons water. Bring to a boil over high heat and cook 2 to 3 minutes, shaking the pan occasionally, until all the sugar has dissolved. Roughly chop the nuts while the sugar dissolves.
**REMOVE THE PAN** from the heat and add the butter. Return the pan to low heat and melt the butter, beating continuously. Continue to beat another 1 minute, or until the caramel turns light brown. Add a good pinch of salt and beat well. Pour in the cream and continue to beat until velvety smooth.
**BREAK UP THE CHOCOLATE** into the sauce and beat continuously until it has completely melted and the sauce has thickened a little. Carefully pour the sauce into a heatproof pitcher. Divide the ice cream among four serving dishes, pour some sauce onto each portion of ice cream and scatter with the hazelnuts to serve.
Goan Explosion Truffles SERVES **4** READY IN **30 MINUTES**
**Genuine truffles in 30 minutes—get in! The trick is to get your cake pan really cold and make sure that the truffle mixture goes into it in a thin layer so that it sets really fast. Scoop out the truffle mixture with a teaspoon or a fancy melon baller and drop each ball into the ground pistachios for a speedy coating. Coffee, cardamom and chili funk up these truffles. Use the maddest, greenest pistachios you can find to get the perfect Goan experience.**
**1 handful of ice cubes**
**scant ½ cup heavy cream**
**1 tablespoon butter**
**3½ ounces semisweet or bittersweet chocolate (70% cocoa solids)**
**¼ teaspoon espresso powder**
**¼ teaspoon ground cardamom a pinch of chili powder**
**heaped ⅓ cup shelled green pistachios**
**PUT THE ICE** in a 10-inch cake pan with a fixed base and put it into the freezer. Pour the cream into a small saucepan and add the butter. Heat the cream over medium heat 2 to 3 minutes, stirring occasionally, until the butter melts.
**MEANWHILE, BREAK UP THE CHOCOLATE** into a heatproof bowl. Put it into the microwave and heat a few seconds on high, or until the chocolate just starts to melt. (Alternatively, melt the chocolate in a heatproof bowl over a pan of gently simmering water, making sure the bottom of the bowl doesn't touch the water.) Remove the bowl from the microwave or steamer and add the espresso powder, cardamom and chili powder. Pour over the hot cream and beat together until thick and smooth.
**WORKING AS FAST AS YOU CAN** , take the cake pan out of the freezer, discard the ice and wipe the pan dry with paper towels. Pour the chocolate mixture into the pan. Spread it evenly into a thin layer no deeper than ¼ inch, otherwise it won't set in time. Put the cake pan back into the freezer 20 minutes, or until the mixture has set.
**ADD THE NUTS** to a food processor and blend until just coarse. Pour them into a mixing bowl. Using a teaspoon or melon baller, scoop out the truffle mixture and drop each truffle ball into the bowl of crushed nuts. Give the bowl a shake to make sure all the truffles are coated, then place on a decorative plate to serve.
Pineapple & Lime Pie SERVES **4** READY IN **20 MINUTES**
**I am in love with the USA, and this dessert was inspired by the classic, key lime pie. I have used pineapple, with a hint of chili, instead of the traditional key limes, plus a no-bake crust to make it super-quick.**
**7½ tablespoons butter**
**½ pineapple**
**2¼ tablespoons demerara sugar**
**a pinch of crushed chili flakes**
**5 ounces graham crackers**
**1¾ cups heavy cream**
**2 tablespoons powdered sugar**
**½ lime**
**PUT 5½ TABLESPOONS** of the butter in a small saucepan over medium heat and the remaining 2 tablespoons in a small skillet over medium heat.
**WHILE THE BUTTER MELTS** , cut the top and bottom off the pineapple, then stand it upright on your cutting board. Slice off the skin, cutting downward from top to bottom. Carefully cut out any pieces of skin left on the fruit. Cut the pineapple half in half lengthwise, then slice off the woody core so you are left with the soft fruit. Cut the pineapple flesh into small pieces and add them to the small skillet. Add the demerara sugar and a pinch of chili flakes. Stir well and cook 8 to 10 minutes, shaking the pan occasionally, until the pineapple starts to soften and the sauce has thickened. Remove from the heat and set aside to cool a little.
**PUT THE GRAHAM CRACKERS** into a food processor and blend to coarse crumbs while the pineapple cooks. Add to a mixing bowl, pour in the melted butter from the small saucepan and stir to combine. Line the base and sides of a 7½-inch springform cake pan with parchment paper and press the crust firmly and evenly into the bottom using the back of a spoon. Put the cake pan into the fridge while you beat the cream.
**POUR THE CREAM** into a large mixing bowl and add the powdered sugar. Add the zest of the lime, squeeze in the juice, then beat into firm peaks. Remove the cake pan from the fridge and fill with the cream mixture. Arrange the pineapple pieces on top, drizzle with the sauce from the pineapple, then open the side of the cake pan, remove the paper and serve.
Mango & Vanilla Coconut Pots SERVES **4** READY IN **10 MINUTES**
**Coconut and mango are best friends and appear in various guises in south-eastern Asian desserts. These fresh little pots are inspired by the many varieties I have eaten over the years. I have made my version to be as quick as possible without cutting back on any flavor. The mango is squished together with sugar and orange to soften it and intensify the taste. The sweet fruit is then topped with luscious cream that has been whipped with coconut cream to add that authentic Asian twist.**
**2 ripe mangoes**
**¼ cup powdered sugar**
**½ orange**
**generous 1¼ cups heavy cream**
**generous ¼ cup coconut cream**
**1 teaspoon vanilla extract**
**PEEL THE MANGO** , then slice off the flesh from the sides and around the seed. Chop the flesh into bite-size pieces, then put them into a mixing bowl.
**ADD HALF THE POWDERED SUGAR** and squeeze in the juice of the orange. Mix together using your hands to slightly break up the mango, then set aside.
**POUR THE HEAVY CREAM** into a mixing bowl and beat into firm peaks. Add the coconut cream, remaining powdered sugar and the vanilla extract, and beat together. Divide the mango mixture among four glass serving dishes and add a thick layer of whipped cream to the top of each one to serve.
Pumpkin, Chocolate & Walnut Puddings SERVES **4** READY IN **25 MINUTES**
**This is my version of a classic Turkish dessert of slow-braised pumpkin served with walnuts. My twist is to add chunks of bittersweet chocolate, which melt into the sweet pumpkin, topped with lovely soft whipped cream.**
**1 pumpkin (about 1 pound 10 ounces in weight)**
**½ cup heavy cream**
**1½ tablespoons butter**
**¼ cup demerara sugar**
**6 cloves**
**1 ounce semisweet or bittersweet chocolate (70% cocoa solids)**
**scant ½ cup walnuts**
**PEEL AND SEED THE PUMPKIN** and cut it into 1-inch pieces. Place them in a microwaveproof bowl and add a scant ½ cup water. Cover with plastic wrap and microwave on high 10 minutes, or until the pieces are soft but haven't turned to mush. To check, poke them with a sharp knife—it should slide out very easily.
**BEAT THE CREAM** to soft peaks while the pumpkin cooks, and set aside. Put the butter, sugar and cloves in a skillet and place over low heat. Once the sugar starts to look a bit dry, shake the pan and it will suddenly dissolve into a liquid. Once completely dissolved, remove from the heat—it will look as though it has split from the butter, but don't worry, I promise this is how it's meant to look.
**CUT TWO-THIRDS OF THE CHOCOLATE** into tiny pieces and divide into 4 portions. Break up the walnuts into small pieces over a bowl using your fingers.
**USING A SLOTTED SPOON** , carefully transfer the cooked pumpkin to the skillet with the sugar mixture. Cook over low heat 5 minutes, stirring occasionally.
**ADD ALL BUT 1 TABLESPOON** of the crushed walnuts to the pumpkin and stir to combine. Divide the pumpkin mixture among four heatproof glass dessert dishes, picking out and discarding the cloves. Sprinkle a pile of chocolate all over each one and spoon one-quarter of the cream on top of each. Scatter each portion with the remaining walnuts and grate the last of the chocolate on top. Serve immediately, while the chocolate is oozing through the dessert.
Luang Prabang Coconut Rice Pudding SERVES **4** READY IN **20 MINUTES**
**This is my express version of the classic Lao pudding. Instead of using Lao red rice and steaming it for ages, I use jasmine rice, which I parboil. Then it's finished off in coconut milk, sugar and cardamom. A good grating of nutmeg, plus some sesame seeds, fresh mango and mint leaves provide a contrast of different flavors, colors and textures to the creamy rice.**
**heaped ½ cup jasmine rice**
**scant 1 cup coconut milk**
**3 tablespoons superfine sugar**
**¼ fresh nutmeg**
**3 cardamom pods**
**2 tablespoons sesame seeds**
**1 large mango**
**1 handful of mint leaves**
**COOK THE RICE** in boiling water 8 minutes. Meanwhile, pour the coconut milk into a saucepan. Add the sugar and grate in the nutmeg. Crush the cardamom pods by pressing down on them with the flat side of a knife blade, then add them to the coconut milk. Stir well and bring to a boil over medium heat. Reduce the heat to low and simmer gently while the rice is cooking. Drain the rice in a strainer and set aside.
**MEANWHILE, PUT THE SESAME SEEDS** in a skillet and toast over medium heat, shaking the pan continuously 2 to 3 minutes, or until golden. Remove from the heat and set aside.
**POUR THE COOKED RICE** into the coconut milk and stir well. Cover and cook gently 5 minutes. Remove the lid and cook another minute, stirring continuously, to thicken. The rice should have the consistency of a lovely oozy risotto. Remove the cardamom and discard it if you prefer.
**PEEL THE MANGO** while the rice finishes cooking. Slice the flesh from the sides and around the seed, and chop it into bite-size pieces. Divide the rice among four serving bowls and place a few pieces of mango on top of each serving. Scatter with the sesame seeds and mint leaves to serve.
Kika Cakes with Orange & Ginger Glaze MAKES **10 CUPCAKES** READY IN **25 MINUTES**
**Express cooking can even apply to baking. Vanilla, orange and almonds make the base of my cupcakes, which soak up the yummy marmalade and ginger glaze. I prefer to use a slightly sweet marmalade to make my glaze, so the cakes take on that flavor as well.**
**1 egg**
**heaped ⅔ cup superfine sugar, plus 1 tablespoon for the glaze**
**1 orange**
**2 teaspoons vanilla extract**
**1¼ cups ground almonds**
**1 cup all-purpose flour**
**¾ teaspoon baking powder**
**scant ½ cup marmalade**
**¼ teaspoon ground ginger**
**PREHEAT THE OVEN** to 400°F. Crack the egg into a large mixing bowl and add the heaped ⅔ cup superfine sugar. Beat the egg and sugar together until fluffy and light. Add the zest of the whole orange to the bowl then squeeze in the juice of half the orange. Reserve the other half. Add the vanilla extract and ground almonds, then sift in the flour and baking powder. Gently combine to make a thick batter.
**LINE A MUFFIN PAN** with 10 paper baking cups. Divide the batter evenly among the cups—each cup will hold about 3 tablespoons of batter. Bake 12 to 14 minutes, or until golden on the top and cooked in the center. (They are cooked in the center when a skewer inserted into a cupcake comes out clean.)
**WHILE THE CUPCAKES BAKE** , put the marmalade, ground ginger and the remaining 1 tablespoon sugar into a small nonstick saucepan. Squeeze the juice of the reserved orange half into the pan and bring to a boil over medium-low heat, stirring occasionally, until the glaze ingredients dissolve together.
**REMOVE THE CUPCAKES** from the oven and top each one with the hot glaze. Set aside to cool a couple of minutes, then serve while still warm.
Cinnamon Fig Tarts SERVES **4** READY IN **25 MINUTES**
**Figs are a staple ingredient of desserts across the Middle East, adding color, flavor and texture, and they work beautifully with spices. I have often seen the humble fig transformed into something spectacular in a dish, and it's perfect for a quick dessert. Baking figs intensifies their flavor, so I've arranged them on puff pastry that was sprinkled with demerara sugar, cinnamon and ground ginger. When cooked, they become wrapped in a wonderful, sweet, warm blanket. The clementine and mint cream heightens the flavors and accentuates the warmth of the spices.**
**flour, for dusting**
**5½ ounces puff pastry, defrosted if frozen**
**1 teaspoon demerara sugar**
**½ teaspoon ground cinnamon**
**¼ teaspoon ground ginger**
**6 small or 3 medium figs**
**1 cup heavy cream**
**2 clementines**
**2 tablespoons powdered sugar**
**1 small handful of mint leaves**
**PREHEAT THE OVEN** to 400°F. Line a baking sheet with parchment paper. Crumple it up in your hands and then smooth it out onto the baking sheet again to prevent it from rolling up at the edges.
**DUST THE WORK SURFACE** with flour and roll out the pastry to just under ¼ inch in thickness. Cut the pastry into 4 rectangles, each measuring 4 × 6 inches, and place them on the parchment paper. Prick each pastry a few times with a fork.
**ADD THE DEMERARA SUGAR** , cinnamon and ginger to a bowl, stir to combine, then scatter the mixture evenly over each pastry. Cut the small figs in half, or the medium figs into quarters, and arrange 3 pieces of fig down the center of each rectangle. Bake the tarts 18 to 20 minutes, or until puffed up and golden.
**MEANWHILE, POUR THE CREAM** into a large mixing bowl. Add the zest of one of the clementines and squeeze in the juice of both. Sift in the powdered sugar, then whip the cream until it forms soft peaks. Save a few mint leaves for decoration and finely chop the remainder. Fold the chopped mint leaves into the whipped cream. Serve the hot tarts with a large dollop of the cream and a scattering of mint leaves.
Strawberry Layer Cakes SERVES **4** READY IN **25 MINUTES**
**These awesome crispy, creamy strawberry layer cakes are a nod to my time in Morocco. Cinnamon, orange and vanilla add the exotic flavors and turn this dessert into something out of the ordinary.**
**2⅓ cups strawberries**
**½ teaspoon ground cinnamon, plus a little extra for dusting**
**3 tablespoons powdered sugar**
**½ orange**
**2 large sheets of filo pastry, defrosted if frozen**
**scant 1¼ cups full-fat Greek yogurt**
**1 teaspoon vanilla extract**
**scant ½ cup walnut pieces**
**SLICE AND HULL THE STRAWBERRIES** and put them into a shallow dish. Sprinkle with the cinnamon and 1 tablespoon of the powdered sugar. Squeeze in the juice of the orange and stir gently to combine. Cover with plastic wrap and set aside.
**CUT THE FILO PASTRY** into 12 rectangles, each measuring 3¼ × 4½ inches, then cover the filo with a damp dish towel to stop it from drying out. Heat a large skillet over medium-high heat and pan-fry the filo pastry in batches until golden and crispy. This will take about 1 to 1½ minutes on one side and 30 seconds to 1 minute on the other. Remove from the pan and set carefully aside.
**PUT THE YOGURT** into a mixing bowl while cooking the filo, and add the remaining powdered sugar and the vanilla. Beat together well and set aside.
**WHEN ALL THE FILO IS DONE** you can construct the cakes. Put a piece of cooked filo onto a serving plate and place a spoonful of yogurt on top. Spread it out evenly and cover with a thin layer of strawberries. Place another piece of filo onto the layer of strawberries, and then repeat with more yogurt and a layer of strawberries. Put a third piece of filo onto the strawberries and spread a layer of yogurt evenly on the top. Break up some of the walnuts and scatter them all over the top layer of yogurt, then sprinkle with a pinch of cinnamon. Repeat the process for the other 3 layer cakes. Serve with any remaining strawberries on the side.
TINY TOWNS, CANTO POP & SHENYANG BANANAS
**Shenyang is a town in northeastern China, nestled near the borders of Mongolia and North Korea. It gets very cold, the people are unusually tall and the food is out of this world. By Chinese standards it's considered a small town—by mine it was massive. The "tiny town" of Shenyang consisted of around 8 million people, a plethora of Italian designer stores, underground shopping malls and incredible food everywhere.**
**It wasn't just very cold in Shenyang when I went—it was absolutely freezing! To be exact, 10 degrees below freezing during the daytime, without windchill. Being that cold meant that having a wander was a very hard thing to do. When I did stroll around it was fairly bleak, until I was ushered through what looked like a subway entrance. Bam! There it was—the main street. It was underground, so you could walk around without freezing to death. This was no ordinary shopping street, though. The retailers selling the big brands were at street level, but here underground it was neon lit, pulsating to the sound of canto pop and Chinese techno, and filled with über-cool kids decked out in Hello Kitty and glasses without any lenses.**
**There was street food everywhere—day-glo hot dogs and kebabs, duck heads and tongues, pancakes and rice buns, mashed potatoes and soups, noodles and salads, fruit and amazing battered bananas, which were skewered on a stick and covered in syrup and crunchy sesame seeds. They were delicious and the perfect sugar hit for such cold weather.**
Shenyang Bananas with Honey & Sesame Seeds SERVES **4** READY IN **15 MINUTES**
**I have created a really quick version of the tasty snack from that under-ground shopping street in Shenyang. Sesame seeds and flour form the base of a batter to coat the bananas, and it's flavored with warming ground cloves and chili powder. The flavor of the spices lingers when the bananas are cooked, and it's somehow exaggerated by the honey drizzled over it before serving. This is express cooking at its best.**
**sunflower oil, for shallow-frying**
**1¼ cups all-purpose flour**
**2 tablespoons powdered sugar**
**¾ teaspoon ground cloves**
**¾ teaspoon chili powder**
**heaped ⅓ cup sesame seeds**
**1 egg**
**2 bananas**
**3 tablespoons honey**
**POUR THE OIL** into a saucepan to a depth of ⅝ inch and place over medium-high heat. Meanwhile, sift the flour, powdered sugar, cloves and chili powder into a large mixing bowl, and add 3 tablespoons of the sesame seeds. Crack in the egg, then slowly beat in a scant 1 cup cold water to form a smooth batter.
**PEEL THE BANANAS** and cut them into ½-inch pieces. Put the pieces into the batter and carefully transfer them to the hot oil using a pair of long-handled tongs. Fry the bananas 30 to 45 seconds on each side, or until beautifully golden and crisp.
**REMOVE THE BANANAS** from the pan and put them on a dish lined with paper towels to drain. Transfer the bananas to a serving plate and drizzle with the honey. Scatter with the remaining sesame seeds to serve.
Mint Tea & Lemongrass Martini SERVES **4** READY IN **10 MINUTES**
**Martinis are cool. Fact. We have all seen _Mad Men_! A classic martini still eludes me, though. It's a bit like drinking rocket fuel, so I always go for a flavored one. For my express martini, I take advantage of the clean taste of vodka and add some ingredients with lovely flavors—green tea, lemongrass and mint. Adding honey and lemongrass to the green tea while it brews means that all the flavors infuse in just a couple of minutes. What you get is an instant, flavored sugar syrup—and that means a very quick martini.**
**2 lemongrass stalks**
**1 green tea bag**
**3 tablespoons honey**
**2 handfuls of ice**
**1 handful of mint leaves, plus a few extra leaves to serve**
**scant 1 cup vodka**
**1 lime**
**BASH EACH LEMONGRASS STALK** to break it up, and roughly chop it into 1-inch pieces. Add the lemongrass to a pitcher or cocktail shaker and add the tea bag, honey and scant 1 cup boiling water. Stir well and let infuse 3 minutes.
**MEANWHILE, PUT A FEW ICE CUBES** into four martini glasses and let chill. Remove the tea bag from the syrup and add the mint. Pour in the vodka and squeeze in the juice of the lime. Add a large handful of ice and mix together really well.
**POUR THE ICE OUT** of the martini glasses and discard. Strain the mint tea and lemongrass martini evenly among the four glasses and add a few mint leaves to each glass to serve.
Burnt Lemon & Vanilla Tequila Shots SERVES **4** READY IN **10 MINUTES**
**I love tequila—a real tequila that is golden and made from 100 percent agave. This means the drink is smooth and well rounded, not like horrible paint stripper in a bottle, with a funny Mexican-hat lid and perhaps a rank insect festering at the bottom. When you work with great tequila it's important not to mess around with it too much. The vanilla in my shots accentuates the flavor of the tequila, and the burnt lemon adds to the already smoky taste of the drink. It needs balance and therefore sweetness. In an ideal world, use an agave syrup. But, failing that, a really great honey will work just as well.**
**2 lemons**
**olive oil for brushing**
**scant 1 cup 100% agave light tequila**
**2 tablespoons agave syrup or honey**
**1 teaspoon vanilla extract**
**2 handfuls of ice**
**CUT THE LEMONS** in half and brush the flesh with a little oil. Put the lemons, cut-side down, into a nonstick skillet. Place over medium heat and cook 4 to 4½ minutes, or until the lemons are turning from a golden color to just charred. Remove the pan from the heat and set aside.
**POUR THE TEQUILA** into a small pitcher or cocktail shaker and add the agave syrup and vanilla extract. Carefully squeeze in the juice of the lemons and run a teaspoon around the flesh side to get all the sticky pieces out. Add the ice and mix well. Pour into four tall shot glasses and serve immediately— _Salud_!
Hot & Spicy Bourbon SERVES **4** READY IN **5 MINUTES**
**Bourbon has been my drink of the month for quite some time now. It has a good smoky flavor that comes from the charred oak barrels it is aged in. The hot, sticky Kentucky air speeds up this aging process, so the bourbon ends up being a relatively young drink. This gives it a beautifully smooth and mellow taste. As you can tell, I am seriously into it! In this delicious hot drink the star anise, cinnamon and cloves accentuate the taste of the bourbon, and the orange and honey provide the classic accompanying flavors. This is advanced hot-toddy drinking, people!**
**4 star anise**
**4 cinnamon sticks**
**8 cloves**
**1 orange**
**1 cup bourbon**
**4 tablespoons honey**
**BOIL SOME WATER**. Meanwhile, divide the star anise, cinnamon sticks and cloves among four mugs.
**USING A PEELER** , peel 4 strips of orange zest, give them a twist and add them to the mugs. Cut 4 thin slices from the orange and put one slice in each mug.
**DIVIDE THE BOURBON** and honey between the mugs, then fill each mug to the top with boiling water. Give each mug of hot and spicy bourbon a good stir with its cinnamon stick and serve.
Acknowledgments
**THANK YOU TO:** Annie and Mike; Lizzie and Amish; Little South Island BBQ for the inspiration and good times; Heather at Villa Dinari; my godson Max; Duncan Baird Publishers for doing it again; Rita and family in Goa; Gail in Fez; my brother Tom and his gorgeous wife Rach, for always putting me up.
Picture Credits
**KeY: T** = Top **B** = Bottom **L** = Left **R** = Right
All location photography by John Gregory-Smith except for the following:
**Page 34** holy cow (Kelvintt/Dreamstime.com); **p. 35** cow in road (Paop/Dreamstime.com); **p. 45 L** Grand Bazaar stall (Wojtek Chmielewski/Shutterstock), **BR** man with food cart (Jim Snyders/Alamy); **p. 119 TR** Jamaa el-Fnaa square (Alex Andrei/Shutterstock), **BR** baskets of spices (Heatherfaye/iStockphoto), **L** baskets and mounds of spices (nolimitspictures/iStockphoto); **p. 151 TR** chilies (Stevenallan/iStockphoto), **R** Mexican man (Frans Lemmens/ Corbis), **B** market (Christian Kober/Robert Harding World Imagery/Corbis).
**DEDICATION**
Sal and Al—I love you!
**Mighty Spice express cookbook**
John Gregory-Smith
First published in the UK and USA in 2013 by
Duncan Baird Publishers, an imprint of Watkins
Publishing Limited
Sixth Floor
75 Wells Street
London W1T 3QH
A member of Osprey Group
Copyright © Watkins Publishing Limited 2013
Text and recipes copyright © John Gregory-Smith
2013
Photography copyright © Watkins Publishing
Limited 2013
The right of John Gregory-Smith to be identified as the Author of this text has been asserted in accordance with the Copyright, Designs and Patents Act of 1988.
All rights reserved. No part of this book may be reproduced in any form or by any electronic or mechanical means, including information storage and retrieval systems, without permission in writing from the publisher, except by a reviewer who may quote brief passages in a review.
Managing Editor: Grace Cheetham
Editor: Jan Cutler
Americanizer: Constance Novis
Art Direction and Design: Manisha Patel
Production: Uzma Taj
Commissioned Photography: William Lingwood
Food Stylist: Aya Nishimura
Prop Stylist: Wei Tang
ISBN: 978-1-84899-114-9
10 9 8 7 6 5 4 3 2 1
Typeset in Chaparral Pro and LD Bohemian Filigree
Color reproduction by PDQ, UK
Printed in China
**Publisher's note** While every care has been taken in compiling the recipes for this book, Watkins Publishing Limited, or any other persons who have been involved in working on this publication, cannot accept responsibility for any errors or omissions, inadvertent or not, that may be found in the recipes or text, nor for any problems that may arise as a result of preparing one of these recipes. If you are pregnant or breastfeeding or have any special dietary requirements or medical conditions, it is advisable to consult a medical professional before following any of the recipes contained in this book. Ill or elderly people, babies, young children and women who are pregnant or breastfeeding should avoid recipes containing raw meat or fish or uncooked eggs.
**Notes on the recipes** Unless otherwise stated:
• Use free-range eggs and poultry
• Use large eggs, and medium fruit and vegetables
• Use fresh ingredients, including herbs and chilies
• Wash all meat, fish and poultry, and all unpeeled vegetables and fruits (apart from mushrooms), as well as herbs and salads, and wipe mushrooms before preparation
• 1 tsp. = 5ml 1 tbsp. = 15ml 1 cup = 240ml
| {
"redpajama_set_name": "RedPajamaBook"
} | 8,390 |
Q: Sending notification automatically firebase I have an application that sends data to the firebase realtime database. Now I'm creating a dashboard to manage this data. At the moment I need to receive a notification on the dashboard when the user sends some new data to the firebase. I need to receive a message with the data id he sent and submit a notification similar to a social network.
I'm using FCM, I've already configured and tried to implement the onCreate () function. But when the bank is upgrading, this function is not being performed.
I'm implementing the code in the dashboard
const functions = require("firebase-functions");
const admin = require("firebase-admin");
admin.initializeApp();
exports.makeUppercase = functions.database
.ref("users")
.onCreate((snapshot, context) => {
const original = snapshot.val();
console.log(original);
});
I'm actually lost on how to do this, I read the documentation, but I didn't quite understand the correct steps to follow. Is there anything I should do before that? Or is this method of doing wrong?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,014 |
(function(window)
{
'use strict';
class notifications
{
constructor(cockpit)
{
console.log('System Diagnostics Plugin running');
var self = this;
this.cockpit = cockpit;
this.rov = cockpit.rov;
this.rov.on("plugin.notification.notify", function(notice) {
self.cockpit.emit("plugin.notification.notify", notice);
})
this.rov.withHistory.on('plugin.notification.all-notices', function(notices) {
self.cockpit.emit('plugin.notification.all-notices', notices);
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this.cockpit.on('plugin.notifications.clear', function() {
self.rov.emit('plugin.notifications.clear');
})
}
}
// Add plugin to the window object and add it to the plugins list
var plugins = namespace('plugins');
plugins.notifications = notifications;
window.Cockpit.plugins.push(plugins.notifications);
}(window)); | {
"redpajama_set_name": "RedPajamaGithub"
} | 7,618 |
That's the gambit: make victims of hard-right propaganda believe journalists into seditionist spies when in fact the tag applies qoute aptly to Michael Flynn, Paul Manafort, Carter Page, and Roger Stone.
When the DNC emails came out, these bastards said that the American people deserved to know. If the information was accurate, then what was the problem.
So hoist on your own petard, slimey traitors..
When I see Bannon, I think of Otis, the town drunk of Mayberry. Does he have his own key the let him sneak into a basement room to sober up?
The media is culpable only in how they allowed the propagandists to take a strangle hold on the flow information. They refused to call out foxnews as illegitimate early on, and even welcomed them into press rooms and briefings. They are doing the same now with breitbart and newsmax and infowars. Where will we be when Alec Jones has a front row seat in the whitehouse briefing room?
Once propaganda becomes legitimate, our democracy will not exist.
Why is that homeless guy still in the White House. And why should anyone with a brain give a crap what Steve King (R) has to say about anything? | {
"redpajama_set_name": "RedPajamaC4"
} | 2,288 |
package org.apache.druid.segment.realtime.plumber;
import com.fasterxml.jackson.annotation.JsonSubTypes;
import com.fasterxml.jackson.annotation.JsonTypeInfo;
import org.joda.time.Period;
@JsonTypeInfo(use = JsonTypeInfo.Id.NAME, property = "type")
@JsonSubTypes(value = {
@JsonSubTypes.Type(name = "serverTime", value = ServerTimeRejectionPolicyFactory.class),
@JsonSubTypes.Type(name = "messageTime", value = MessageTimeRejectionPolicyFactory.class),
@JsonSubTypes.Type(name = "none", value = NoopRejectionPolicyFactory.class)
})
public interface RejectionPolicyFactory
{
RejectionPolicy create(Period windowPeriod);
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,407 |
Q: Вопросы по C#.NET Пожалуйста, ответьте на вопросы:
*
*Как можно сделать так, чтобы при нажатии на Button1, запускался, например, проводник и открывал C:\Program Files?
*Как можно сделать так, чтобы картинка (PictureBox1), появлялась в разных местах, и через определенное кол-во времени.
A: Запуск проводника:
...
string PathToMyFolder = "C:\\MyFolder";
Process.Start(PathToMyFolder);
...
на счёт картинки и PictureBox по-подробнее можно?
UPDATE:
private int x;
private int Y;
...
//Переотрисовка формы:
protected override void OnPaint(PaintEventArgs e) {
base.OnPaint(e);
Image santa = Image.FromFile("Santa.jpg");//Ваше изображение
Random rand = new Random();
//по этим координатам зарисуете изображение, чтобы оно исчезло
x = rand.Next(0,Form1.Width);
y = rand.Next(0,Form1.Hight);
Point location = new Point(x, y);//Рандомное место положение изображения
e.Graphics.DrawImage(santa, location);
}
...
//Собственно таймер, System.Windows.Forms.Timer, перетащите на форму, установите myTimer.Interval = 30000, запустите myTimer.Start(), а потом обработайте событие Tick:
private static void TimerEventProcessor(Object myObject,
EventArgs myEventArgs) {
Refresh();//Вызывает OnPaint
}
...
Хотите узнать больше:
*
*Timer
*DrawImage
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,731 |
\section*{Introduction}
In this article we study
the relation between double covers and the origin of double structures. This relation was first studied
in~\cite{Fong}, for hyperelliptic canonical morphisms and the so-called canonical ribbons and in~\cite{GP} for hyperelliptic $K3$ surfaces and $K3$ carpets on rational normal scrolls. Recently, M. Gonz\'alez in~\cite{Gon} and the authors in~\cite{GGP} studied this relation in a much more general setting, namely, finite covers of curves of arbitrary degree on the one hand and one dimensional, locally Cohen-Macaulay multiple structures of arbitrary multiplicity on the other hand.
In the present work we look at the relation between a natural and particularly nice double cover, the \'etale $K3$ double cover of an Enriques surface, and an interesting class of double structures, the {\it $K3$ carpets on Enriques surfaces}
\medskip
Double structures on surfaces have appeared in connection with the study of the zero locus of sections of the Horrocks--Mumford vector bundle (see for example the work of Hulek and Van de Ven in~\cite{HV}). Also, $K3$ carpets on rational normal scrolls have been considered in the study of degenerations of smooth $K3$ surfaces. In this article we study another kind of $K3$ carpets, namely, those supported on Enriques surfaces.
A $K3$ carpet on a smooth Enriques surface $Y$ will be a locally Cohen-Macaulay
double structure on $Y$ with the same invariants as a smooth $K3$ surface (i.e., regular and with trivial canonical sheaf). The surface $Y$ possesses an \'etale $K3$ double cover
$X \overset{\pi} \longrightarrow Y$ associated to the canonical bundle of $Y$, which is $2$-torsion.
We prove that any projective $K3$ carpet on $Y$ arises from a family ${\mathcal{X}} \longrightarrow \mathbf P^N_{T^*}$ of projective embeddings of $K3$ surfaces that degenerates to $\pi$.
As a consequence of this, we show that any projective $K3$ carpet on $Y$ can be {\it smoothed}, i.e., obtained as the flat limit of a family of smooth, irreducible (projective $K3$) surfaces.
\medskip
The reader might probably have noted in the previous paragraph the phrase ``projective $K3$ carpet".
$K3$ carpets on an Enriques surfaces (like indeed double structures on any other surface) need not be projective, unlike ribbons on curves. Thus our first task is to characterize (see Theorem~\ref{nonproj.carpets}) those $K3$ carpets which are projective. This is accomplished in Section~\ref{embedding}. There we also see ``how many" projective $K3$ carpets there are. We do this in two settings. On the one hand, we compare the sizes of the families of
projective $K3$ surfaces on a given (abstract) Enriques surfaces $Y$ and the size of the family of non--projective $K3$ carpets (see Theorem~\ref{nonproj.carpets}). This situation has some strong resemblance to
the case of projective and non--projective smooth $K3$ surfaces, where the former lie on infinite, countably many codimension $1$ families in the moduli space of $K3$ surfaces. On the other hand we also compute the dimension of the space that parametrizes the family of projective $K3$ surfaces supported on a given Enriques surface which is embedded in a projective space (see Theorem~\ref{dim.K3carpet.embedded}).
\medskip
In Section~\ref{smoothing} we prove the results regarding deformation of morphisms and smoothings of carpets. First we show (see Theorem~\ref{coversmoothing}) that the cover $\pi$ can be deformed to a family of embeddings of $K3$ surfaces to projective space. Then, in order to obtain a smoothing of a projective $K3$ carpet $\widetilde{Y}$, one considers a suitable embedding of $\widetilde{Y}$ in projective space, then one chooses the family of embeddings of Theorem~\ref{coversmoothing} suitably, in order to obtain a family of projective schemes consisting of the images of smooth $K3$ surfaces degenerating to $\widetilde{Y}$. From these theorems we obtain a smoothing result for most of the embedded $K3$ carpets (see Theorem~\ref{embsmoothing}) and subsequently we show that any (abstract) projective $K3$ carpet can be smoothed (see Theorem~\ref{absgensmooth}).
\medskip
Finally we devote Section~\ref{hilbert.section} to study the Hilbert points of projective $K3$ carpets. We prove that their Hilbert point are always smooth (see Theorem~\ref{hilbert}), unlike the case of $K3$ carpets on rational normal scrolls (in that case, some Hilbert points are smooth and some are not; see~\cite[Section 4]{GP}).
\medskip
\noindent
{\bf Acknowledgements}: We thank Joseph Lipman for a helpful discussion and for pointing out some references regarding the dualizing sheaf. We also thank N. Mohan Kumar for some useful discussions.
\medskip
\noindent
{\bf Convention.} {\rm We work over $\mathbb{C}$.
Throughout the article, when we talk about a regular or an Enriques surface, we will mean it to be smooth, irreducible and proper over $\mathbb{C}$.}
\section{$K3$ carpets. Characterization}\label{characterization}
Among carpets on an Enriques surface $Y$, we single out a family which deserve special attention as far as they share the invariants of smooth $K3$ surfaces. We call them $K3$ carpets.
In fact, we will give a more general definition: a $K3$ carpet on any regular surface will be a carpet with the same invariants of a smooth $K3$ surface (i.e., trivial dualizing sheaf and irregularity $q=0$; see Definition~\ref{K3carpet} and Proposition~\ref{char2.K3}).
Gallego and Purnaprajna, in~\cite{GP}, studied $K3$ carpets supported on rational normal scrolls.
In this paper we consider carpets on a different type of surfaces possessing a double covering from a smooth $K3$ surface, namely Enriques surfaces.
In this new case, as in~\cite{GP}, the adjective $K3$ is not only justified by the fact that these carpets have the same invariants as smooth $K3$ surfaces, but also from the fact that
projective $K3$ carpets are degenerations of smooth $K3$ surfaces, as we shall prove in this paper.
\medskip
\noindent
We start by recalling the definition of a carpet on a smooth surface.
\noindent
\begin{definition}\label{defrope}
Let $Y$ be a reduced connected scheme and let ${\mathcal{E}}$ be a line bundle on $Y$.
A ribbon on $Y$ with conormal bundle ${\mathcal{E}}$ is a scheme $\widetilde{Y}$ with ${\widetilde{Y}}_{\mathrm{red}}=Y,$ such that
\begin{enumerate}
\item
${\mathcal{I}}_{Y, \widetilde{Y}}^2=0$ and
\item
${\mathcal{I}}_{Y, \widetilde{Y}} \simeq {\mathcal{E}}$ as ${\mathcal{O}}_{Y}$--modules.
\end{enumerate}
When $Y$ is a surface, $\widetilde{Y}$ is called a carpet on $Y$.
\end{definition}
\noindent
We give now the definition of a $K3$ carpet supported on a regular surface. Although our definition does not require the carpet to be a regular scheme, we will see in Proposition~\ref{char2.K3} that a $K3$ carpet defined according to Definition~\ref{K3carpet} is always regular.
\begin{definition}\label{K3carpet}
Let $Y$ be a regular surface. A $K3$ carpet $\widetilde{Y}$ on $Y$ is a carpet on $Y$ such that its dualizing sheaf $\, \omega_{\widetilde{Y}}\simeq {\mathcal{O}}_{\widetilde{Y}}$
\end{definition}
\noindent
The existence of a dualizing sheaf with nice functorial properties on a proper scheme is not obvious.
In Remark~\ref{dualizing} we justify the existence of the dualizing sheaf in Definition~\ref{K3carpet}.
In Lemma~\ref{dualizing.properties} we point out some nice properties of the dualizing sheaf on $\widetilde{Y}$.
The assertions in Remark~\ref{dualizing} and in Lemma~\ref{dualizing.properties} are valid, in general, for ribbons.
\begin{remark}\label{dualizing}
{\rm Let $Y$ be a smooth irreducible proper variety.
\begin{enumerate}
\item Any ribbon $\widetilde{Y}$ on $Y$ is a proper scheme over $\mathbb{C}$.
So, according to, e.g.,~\cite[(7), p. 46]{Kleiman80}, there is a dualizing sheaf $\, \omega_{\widetilde{Y}}$ on $\widetilde{Y}$.
\item Any ribbon $\widetilde{Y}$ on $Y$ is a locally Gorenstein (in fact, locally a complete intersection) scheme. Therefore the dualizing sheaf $\, \omega_{\widetilde{Y}}$ is an invertible sheaf, see \cite[V 9.3, 9.7, VII 3.4]{RD} and \cite[p. 157]{Conrad00}.{\hfill $\square$ \medskip}
\end{enumerate}
}
\end{remark}
\begin{lemma}\label{dualizing.properties}
Let $Y$ be a smooth irreducible proper variety.
Let $\widetilde{Y}$ be a ribbon on $Y$ with conormal bundle ${\mathcal{E}}$ and $\omega_{\widetilde{Y}}$ its dualizing sheaf.
\begin{enumerate}
\item The dualizing sheaf on $Y$ is
\begin{equation*}\label{dualizing1}
{{\mathcal{H}}}om_{\widetilde{Y}}({\mathcal{O}}_Y, \omega_{\widetilde{Y}})= \omega_Y.
\end{equation*}
\item Let ${\mathcal{L}}$ be an invertible sheaf on $Y$.
Then
\begin{equation*}\label{dualizing2}
{{\mathcal{H}}}om_{\widetilde{Y}}({\mathcal{L}}, \omega_{\widetilde{Y}})= {\mathcal{L}}^{-1}\otimes \omega_Y.
\end{equation*}
\item The dualizing sheaf on $\widetilde{Y}$ fits into an extension
\begin{equation}\label{WY-extension.dual.2}
\xymatrix@1@C-5pt{
0 \ar[r] & \omega_{Y} \ar[r] & \omega_{\widetilde{Y}} \ar[r] & {\mathcal{E}}^{-1} \otimes \omega_Y \ar[r] & 0.}
\end{equation}
\end{enumerate}
\end{lemma}
\begin{proof}
(1) From the definition of a dualizing sheaf, see~\cite[p. 241]{RD} or~\cite[(1),(6)]{Kleiman80},
we see that ${{\mathcal{H}}}om_{\widetilde{Y}}({\mathcal{O}}_Y, \omega_{\widetilde{Y}})$ is a dualizing sheaf on $Y$.\\\\
\noindent
(2) Since ${\mathcal{L}}$ is a sheaf on $Y$, notice that ${{\mathcal{H}}}om_{\widetilde{Y}}({\mathcal{L}}, \omega_{\widetilde{Y}})={{\mathcal{H}}}om_{Y}({\mathcal{L}}, {{\mathcal{H}}}om_{\widetilde{Y}}({\mathcal{O}}_{Y}, \omega_{\widetilde{Y}}))$.\\\\
\noindent
(3) From the inclusion ${\mathcal{E}} \hookrightarrow {\mathcal{O}}_{\widetilde{Y}}$, we have a map
$\omega_{\widetilde{Y}} \to {{\mathcal{H}}}om_{\widetilde{Y}}({\mathcal{E}}, \omega_{\widetilde{Y}})$.
We see at once that, since $\omega_{\widetilde{Y}}$ is invertible, this map is surjective.
So applying $\mathcal{H}om_{\widetilde{Y}}(-,\omega_{\widetilde{Y}})$ to
\begin{equation}\label{WY-extension.2}
\xymatrix@1@C-5pt{
0 \ar[r] & {\mathcal{E}} \ar[r] & {\mathcal{O}}_{\widetilde{Y}} \ar[r] & {\mathcal{O}}_{Y} \ar[r] & 0,}
\end{equation}
we obtain~\eqref{WY-extension.dual.2}.
\end{proof}
\medskip
\noindent
Now we characterize $K3$ carpets from its conormal bundle.
\begin{proposition}\label{char.K3}
Let $Y$ be a regular surface and let $\widetilde{Y}$ be a carpet whose reduced part is $Y$.
Let ${\mathcal{E}}$ be the ideal sheaf of $Y$ in $\widetilde{Y}$. Then $\widetilde{Y}$ is a $K3$ carpet iff $\,{\mathcal{E}} \simeq \omega_Y$.
\end{proposition}
\begin{Proof}
Let $\mathcal{E} \simeq \omega_{Y}$.
Look at~\eqref{WY-extension.dual.2}.
Since $H^1(\omega_Y)=0$, the section $1 \in H^0({\mathcal{O}}_Y)$ can be lifted to $H^0(\omega_{\widetilde{Y}})$, and hence, $\omega_{\widetilde{Y}}$ being invertible, we have $\omega_{\widetilde{Y}} \simeq {\mathcal{O}}_{\widetilde{Y}}$.
Now assume $\, \omega_{\widetilde{Y}}\simeq {\mathcal{O}}_{\widetilde{Y}}$.
If we tensor~\eqref{WY-extension.dual.2} with ${\mathcal{O}}_Y$
we get a surjection ${\mathcal{O}}_Y \to {\mathcal{E}}^{-1} \otimes \omega_Y$. Thus ${\mathcal{E}} \simeq \omega_Y$.
\end{Proof}
\noindent
As a consequence of~\ref{char.K3} we see that a $K3$ carpet, as defined in Definition~\ref{K3carpet}, is a regular scheme, as is the case of smooth $K3$ surfaces.
\begin{proposition}\label{char2.K3}
Let $\widetilde{Y}$ be a $K3$ carpet on a regular surface $Y$. Then $H^{1}({\mathcal{O}}_{\widetilde{Y}})=0$.
\end{proposition}
\begin{Proof}
From Proposition~\ref{char.K3}, the conormal bundle ${\mathcal{E}} = \omega_Y$.
Since $Y$ is a regular surface $H^{1}(\omega_{Y})=H^{1}({\mathcal{O}}_{Y})=0$ and hence, from~\eqref{WY-extension.2}, $H^{1}({\mathcal{O}}_{\widetilde{Y}})=0$.
\end{Proof}
\begin{remark}\label{Ext1}
{\rm We have seen that the $K3$ carpets on a given regular surface are the carpets with conormal bundle $\omega_Y$.
Thus (see~\cite[1.4]{BE95}) the space of non--split $K3$ carpets on a given regular surface $Y$ is the projective space of lines in $\mathrm{Ext}_{Y}^1(\Omega_Y, \omega_Y)$.
\noindent
Notice that, when $Y$ is an Enriques surface the dimension of $\mathrm{Ext}_{Y}^1(\Omega_Y, \omega_Y)$ is the Hodge number $h^{1,1}=10$.{\hfill $\square$ \medskip}}
\end{remark}
\section{Projective and non--projective $K3$ carpets}\label{embedding}
\noindent
In contrast to ribbons on curves, not all carpets are
projective, (see ~\cite[III Exercise
5.9]{Hartshorne77}) even if all of them are proper
or if, as is the case with Enriques surfaces, they
are supported on a projective surface.
Thus the very first question about the $K3$ carpets on Enriques
surfaces is whether there exist families of projective $K3$ carpets. This question
has a positive answer as is illustrated in Theorem 2.2 and Theorem 2.3. Next step
is to compute the dimension of the space parametrizing $K3$ carpets on a given Enriques surface.
This is settled in Theorem~\ref{dim.K3carpet.embedded} for the dimension of the family of
embedded (projective) carpets on a given embedded Enriques surface,
and in Theorem ~\ref{nonproj.carpets}, where we compute the size of
the space of projective $K3$ carpets supported on a given (abstract) Enriques
surface $Y$, comparing it also with the space of all $K3$ carpets on $Y$.
As we will see, the situation somehow resembles
that of smooth $K3$ surfaces.
\smallskip
\noindent
To start searching for embedded $K3$ carpets we need to look first for
embeddings of Enriques surfaces in projective space. We recall some
well known facts about this:
\begin{remark}\label{Enriques.embeddings}
{\rm Let $Y$ be an Enriques surface.
\begin{enumerate}
\item
If $Y$ is embedded in $\mathbf P^N$, then $N \geq 5$.
\item
A very ample line bundle on $Y$ has sectional genus $g \geq 6$ and degree $d \geq 10$.
\item
If $N \geq 5$, then the surface $Y$ can be embedded in $\mathbf P^N$.
\end{enumerate}}
\end{remark}
\begin{proof}
By adjunction, there do not exist Enriques
surfaces in $\mathbf P^3$.
On the other hand, applying the formula for the numerical
invariants of a smooth surface $Y$ in $\mathbf P^4$
(see~\cite[A.4.1.3]{Hartshorne77}),
\begin{equation*}
d^{2}-10d-5H K_{Y}-2K_{Y}^2+12+12p_{a}=0,
\end{equation*}
we see at once that there do not exist Enriques surfaces in $\mathbf
P^4$ either. This completes the proof of (1).
Now, a line bundle on $Y$ with sectional genus $g$ has $g$ linearly
independent global section. Then, if the line bundle is very ample,
(1) implies that $g \geq 6$, so its
degree is $2g-2 \geq 10$. This proves (2). Finally,
since $Y$ is projective, $Y$ can be embedded in $\mathbf P^M$,
with $M >> 0$ and we project it isomorphically into $\mathbf P^N$ as far as $N \geq 5$.
\end{proof}
\noindent
Now we want to know how many $K3$ carpets are supported on a given embedded
Enriques surfaces. This will do in Theorem~\ref{dim.K3carpet.embedded}. To do this we will need to know the
dimension of the space of first--order infinitesimal deformations of a morphism from a $K3$ surface to projective space.
Given a morphism $\varphi$ from a variety $X$ to $\mathbb{P}^N$, the normal sheaf ${\mathcal{N}}_{\varphi}$ is defined as the cokernel of the natural map $\mathcal{T}_{X}\longrightarrow \varphi^{\ast} \mathcal{T}_{\mathbb{P}^N}$. Then the first--order infinitesimal deformations of $\varphi$, up to isomorphism, are parametrized by $H^0({\mathcal{N}}_{\varphi})$ (see~\cite[4.2]{Hor}).
In our setting since $X$ is a smooth $K3$ surface, it is a smooth variety. Then, if the image of $\varphi$ has the same dimension as $X$, we have the following exact sequence:
\begin{equation}\label{tan.normal.varphi.1}
0 \longrightarrow \mathcal{T}_{X}\longrightarrow \varphi^{\ast} \mathcal{T}_{\mathbb{P}^N}
\longrightarrow {\mathcal{N}}_{\varphi} \longrightarrow 0.
\end{equation}
\begin{theorem}\label{dim.19}
Let $X$ be a smooth projective $K3$ surface and let $X \xrightarrow{\varphi} \mathbb{P}^N$
be a morphism whose image is a surface.
Let ${\mathcal{N}}_{\varphi}$ be the normal sheaf of $\varphi$. Then,
\begin{enumerate}
\item
the dimension of the image of the connecting map
\begin{equation*}
H^0({\mathcal{N}}_{\varphi}) \to H^1(\mathcal{T}_X)
\end{equation*}
of the long exact sequence of cohomology of~\eqref{tan.normal.varphi.1}
is $19$;
\item
$H^1({\mathcal{N}}_{\varphi})=0$; and
\item $H^2({\mathcal{N}}_{\varphi})=0$.
\end{enumerate}
\end{theorem}
\begin{Proof}
Let us denote $L=\varphi^{\ast}{\mathcal{O}}_{\mathbb{P}^N}(1)$ and let us consider the Atiyah extension of $L$
\begin{equation}\label{Atiyah.L}
0 \longrightarrow {\mathcal{O}}_X \longrightarrow \Sigma_{L} \longrightarrow \mathcal{T}_{X}\longrightarrow 0.
\end{equation}
The space $H^1(\Sigma_L)$ parametrizes first--order infinitesimal deformations of the pair $(X, L)$ up to isomorphism (see \cite[pp. 126--128]{Zar} or \cite[II.2.2]{Sernesi06}) and
the map $H^0({\mathcal{N}}_{\varphi}) \to H^1(\mathcal{T}_X)$ factors through $H^1(\Sigma_L)$.
Taking cohomology on~\eqref{Atiyah.L} yields the exact sequence
\begin{equation*}
H^1(\mathcal O_X) \longrightarrow H^1(\Sigma_L) \longrightarrow H^1(\mathcal{T}_{X}) \longrightarrow H^2(\mathcal O_X).
\end{equation*}
Since $X$ is a $K3$ surface, $h^1(\mathcal O_X)=0$, $h^2(\mathcal O_X)=1$ and
$h^1(\mathcal{T}_{X})$ is the same as the Hodge number
$h^{1,1}$ of $X$, hence
\begin{equation}\label{dim4}
\dim H^{1}(\mathcal{T}_{X})=20.
\end{equation}
On the other hand, $H^{1}(\mathcal{T}_X) \longrightarrow H^2({\mathcal{O}}_X) $ is induced by cup product with the cohomology class $c(L) \in H^1(\Omega_X)$ (see \cite[Proposition II.2.2]{Sernesi06}), so it is surjective, for $L$ is non--trivial (see \cite[p. 57]{Sernesi06}).
Then
\begin{equation}\label{dim.SigmaL}
\dim H^{1}(\Sigma_L) = 19.
\end{equation}
Then, going back to ~\eqref{tan.normal.varphi.1} we have the long exact sequence
\begin{equation*}
H^{0}({\mathcal{N}}_{\varphi}) \xrightarrow{\nu}
H^{1}(\mathcal{T}_X) \longrightarrow
H^{1}(\varphi^{\ast}\mathcal{T}_{\mathbb{P}^{N}}) \longrightarrow H^{1}({\mathcal{N}}_{\varphi}) \longrightarrow 0,
\end{equation*}
where the exactness on the far right comes from $h^2(\mathcal{T}_X)=h^{0,1}=0$.
Then~\eqref{dim.SigmaL} implies that the image of $\nu$ has dimension less than or equal to $19$. On the other hand, taking cohomology on the dual of the Euler sequence restricted to $X$ yields $h^1(\varphi^{\ast}\mathcal{T}_{\mathbb{P}^{N}})=1$, for $H^1(L)=H^2(L)=0$ since $L$ is ample. All this together with~\eqref{dim4} implies that the image of $\nu$ has dimension $19$ and $H^{1}({\mathcal{N}}_{\varphi})=0$.
\noindent
To prove (3) note that taking cohomology on the dual of the Euler sequence restricted to $X$ yields $H^2(\varphi^{\ast}\mathcal{T}_{\mathbb{P}^{N}})=0$, for
$H^2(L)=0$. Then it follows that $H^{2}({\mathcal{N}}_{\varphi})=0$.
\end{Proof}
\noindent
We will use Theorem~\ref{dim.19} in this situation (see e.g. ~\eqref{h1.normal.zero} in the proof of Theorem~\ref{dim.K3carpet.embedded}):
we set $\varphi$ to be the composition of the \'etale $K3$ double cover $X \xrightarrow{\pi} Y$ of an Enriques surface $Y$ followed by an embedding $Y \overset{i}\hookrightarrow \mathbb{P}^N$.
On the other hand, Theorem~\ref{dim.19} can be also used if $\varphi$ is an embedding into projective space, so we recover the following result:
\begin{corollary}\label{smooth.Hilbert}
If $X$ is a smooth projective $K3$ surface embedded in projective space, (not necessarily as a linearly normal variety nor as a non--degenerate variety), then the point of $X$ in the Hilbert scheme is smooth.
\end{corollary}
\noindent
Next theorem gives a quantitative measure on the $K3$ carpets supported on an embedded Enriques surfaces.
Precisely, given an embedded Enriques surface $Y\overset {i}{\hookrightarrow}\mathbf{P}^{N}$ , we find the dimension
of the variety that parametrizes the $K3$ carpets in $\mathbf P^N$, supported on $i(Y)$.
\begin{theorem}\label{dim.K3carpet.embedded}
Let $Y$ be an Enriques surface and let $Y \overset{i}{\hookrightarrow}
\mathbf P^N$ be an embedding of $Y$.
Let $g$ be the sectional genus of $i(Y)$.
The $K3$ carpets embedded in $\mathbf{P}^{N}$ and supported on
$i(Y)$ are parametrized by a non--empty open set in the projective space of lines in
$H^0({\mathcal{N}}_{Y,\mathbb{P}^{N}} \otimes \omega_Y)$, whose dimension is
$g(N+1)+8$.
In particular, if $i$ is induced by the complete linear series of
$\mathcal O_Y(1)$, then the dimension of
this open set is $g^2+8$.
\end{theorem}
\begin{Proof}
Denote $\mathcal I=\mathcal{I}_{i(Y),\mathbb{P}^N}$.
The $K3$ carpets in $\mathbf{P}^{N}$ which are supported on $i(Y)$
are in one--to--one correspondence with the surjective elements in
$\mathrm{Hom} \,(\mathcal{I}/\mathcal{I}^{2},\mathcal{\omega}_{Y})$,
up to nonzero scalar multiple (see ~\cite[Proposition
2.1.(2)]{Gon}; see also ~\cite[Lemma 1.4]{GP} or~\cite{HV}).
\noindent
We start computing the dimension of $\mathrm{Hom}
\,(\mathcal{I}/\mathcal{I}^{2},\mathcal{\omega}_{Y})$.
Recall that $\Omega_Y^{\ast} \otimes \omega_Y \simeq \Omega_Y$. Then,
since $Y$ is regular, and by Serre duality and Hodge Theory,
we have $h^0(\Omega_Y^{\ast} \otimes \omega_Y)= h^2(\Omega_Y^{\ast}
\otimes \omega_Y)=0$. Then, taking cohomology on the conormal sequence
of $i(Y)$, we get
\begin{multline}\label{hom.conormal.seq}
0 \to \mathrm{Hom}\,(\Omega_{\mathbb{P}^N} \otimes {\mathcal{O}}_Y,\omega_Y) \to
\mathrm{Hom}\,(\mathcal{I}/\mathcal{I}^{2},{\omega}_{Y})
\overset{\delta} \longrightarrow
\mathrm{Ext}^{1}(\Omega_{Y},{\omega}_{Y}) \to \\
\to \mathrm{Ext}^{1}(\Omega_{\mathbb{P}^N}\otimes {\mathcal{O}}_Y, \omega_{Y}) \to
\mathrm{Ext}^{1}(\mathcal{I}/\mathcal{I}^{2},{\omega}_{Y}) \to 0.
\end{multline}
To find the dimension of $\mathrm{Hom}
\,(\mathcal{I}/\mathcal{I}^{2},\mathcal{\omega}_{Y})$ we need to
compute the dimensions of the other terms of the sequence~\eqref{hom.conormal.seq}.
Dualizing the restriction to $Y$ of the Euler sequence and tensoring by
$\omega_{Y}$, we have the exact sequence
\begin{equation}\label{euler2}
\xymatrix@1@C-5pt{
0 \ar[r] & \omega_{Y} \ar[r] &
\mathcal{O}_Y^{\oplus
N+1}(1) \otimes \omega_{Y} \ar[r] & \Omega_{\mathbb{P}^N}^{\ast}
\otimes\omega_{Y} \ar[r] & 0.}
\end{equation}
Since
$h^{1}(\mathcal{O}_{Y}(1)\otimes\omega_{Y})=h^{2}(\mathcal{O}_{Y}(1)\otimes\omega_{Y})=0$,
it follows that $h^{1}(\Omega_{\mathbb{P}^N}^{\ast} \otimes
\omega_{Y})=h^{2}(\omega_{Y})=1$.
So
\begin{equation}\label{dim1}
\dim \, \mathrm{Ext}^{1}(\Omega_{\mathbb{P}^{N}} \otimes {\mathcal{O}}_Y, {\omega}_{Y})=
h^{1}(\Omega_{\mathbb{P}^{N}}^{\ast}\otimes {\omega}_{Y})=1.
\end{equation}
\noindent
Also, $h^{0}(\omega_{Y})=h^{1}(\omega_{Y})=0$, so we have
\begin{equation}\label{dim2}
\dim \, \mathrm{Hom}\,(\Omega_{\mathbb{P}^{N}}\otimes {\mathcal{O}}_Y,\omega_{Y})=
(N+1) \cdot h^{0}({\mathcal{O}}_{Y}(1)\otimes\omega_{Y})=g(N+1).
\end{equation}
\noindent
On the other hand (see Remark ~\ref{Ext1})
\begin{equation}\label{dim3}
\dim \, \mathrm{Ext}^{1}(\Omega_{Y},\omega_{Y})=10.
\end{equation}
\noindent
Finally we will see that $\mathrm{Ext}^{1}(\mathcal{I}/\mathcal{I}^{2}, \omega_{Y})=0$.
To do this, let
$X \overset{\pi}\rightarrow Y$ be the \'etale $K3$ double cover of $Y$.
Denote $i \circ \pi=\varphi$.
From Theorem~\ref{dim.19}, (2), for the normal sheaf of $\varphi$ we have
\begin{equation}\label{h1.normal.zero}
H^{1}({\mathcal{N}}_{\varphi})=0.
\end{equation}
\noindent
We will see that $\mathrm{Ext}^{1}(\mathcal{I}/\mathcal{I}^{2}, \omega_{Y})$ is a direct summand of $H^{1}({\mathcal{N}}_{\varphi})$.
\noindent Let ${\mathcal{F}}$ be the kernel of
$\varphi^{\ast}\Omega_{\mathbb{P}^N}\rightarrow\Omega_{X}$.
Since $\pi$ is \'etale, it follows that $\Omega_{X/Y}$ and
$\Omega_{X/\mathbb{P}^N}$ are both $0$,
so we have the following commutative diagram:
\begin{equation*}\label{diagram}
\xymatrix@C-10pt@R-13pt{
& 0 \ar[d] & 0 \ar[d] & & \\
& \pi^{\ast}(\mathcal{I}/\mathcal{I}^2) \ar[d] \ar@{=}[r] &
\pi^{\ast}(\mathcal{I}/\mathcal{I}^2) \ar[d] & & \\
0 \ar[r] & {\mathcal{F}} \ar[d] \ar[r] & \varphi^{\ast}\Omega_{\mathbb{P}^N} \ar[d] \ar[r] & \Omega_X \ar@{=}[d] \ar[r]& 0 \\
& 0 \ar[r] & \pi^{\ast}\Omega_Y \ar[d] \ar[r] & \Omega_X \ar[r]& 0 \\
& & 0.& &}
\end{equation*}
\noindent
Therefore there is an isomorphism
\begin{equation*}
{\mathcal{N}}_{\varphi}\simeq \mathcal{H}om
\,(\pi^{\ast}\mathcal{I}/\mathcal{I}^{2},\mathcal{O}_{X}).
\end{equation*}
Since $\pi_{\ast}\mathcal{O}_{X}=\mathcal{O}_{Y}\oplus \omega_{Y}$,
taking cohomology and using the adjunction isomorphism we get
\begin{multline*}\label{H1normalphi}
H^{1}({\mathcal{N}}_{\varphi})= H^1(\mathcal{H}om \,(\pi^{\ast}\mathcal{I}/\mathcal{I}^{2},\mathcal{O}_{X}))=
\mathrm{Ext}^{1}(\pi^{\ast} \mathcal{I}/\mathcal{I}^{2}, {\mathcal{O}}_{X})= \\
= \mathrm{Ext}^{1}(\mathcal{I}/\mathcal{I}^{2}, {\mathcal{O}}_{Y})
\oplus \mathrm{Ext}^{1}(\mathcal{I}/\mathcal{I}^{2}, \omega_{Y}).
\end{multline*}
Then Theorem~\ref{dim.19}, (2) implies
\begin{equation}\label{dim6}
\mathrm{Ext}^{1}(\mathcal{I}/\mathcal{I}^{2}, \omega_{Y})=0.
\end{equation}
\noindent
Then, from~\eqref{hom.conormal.seq},~\eqref{dim1},~\eqref{dim2},~\eqref{dim3}, and~\eqref{dim6},
we see at once that
\begin{equation*}\label{dimension}
\dim \mathrm{Hom}\,(\mathcal{I}/\mathcal{I}^{2}, \omega_{Y})=g(N+1)+9.
\end{equation*}
\noindent
Recall that the $K3$ carpets on $Y$ embedded in $\mathbf{P}^{N}$ are
in one--to--one correspondence with the surjective homomorphisms in
$\mathrm{Hom}\, (\mathcal{I}/\mathcal{I}^{2},\mathcal{\omega}_{Y})$,
up to nonzero scalar multiple, or equivalently, with the nowhere
vanishing global sections of the $(N-2)$--rank vector bundle ${\mathcal{N}}_{Y,
\mathbb{P}^N} \otimes \omega_Y$, up to nonzero scalar multiple.
Recall also that the elements of $\mathrm{Hom}\,
(\mathcal{I}/\mathcal{I}^{2},\mathcal{\omega}_{Y})$ corresponding to
surjective homomorphisms form an open set (see ~\cite[Lemma4.1]{Gon}).
Therefore, to finish the proof we need to show that there is a nowhere vanishing
section in the space $H^0({\mathcal{N}}_{Y, \mathbb{P}^N} \otimes \omega_Y)$.
Observe first that ${\mathcal{N}}_{Y,\mathbb{P}^{N}}\otimes \omega_{Y}$ is globally generated.
To see this note that we have a surjection
$\Omega_{\mathbb{P}^{N}}^{\ast} \otimes \omega_{Y}
\rightarrow {\mathcal{N}}_{Y,\mathbb{P}^{N}} \otimes \omega_{Y}$
so, from~\eqref{euler2},
we see that ${\mathcal{N}}_{Y,\mathbb{P}^{N}} \otimes \omega_{Y}$ is globally generated
as long as ${\mathcal{O}}_{Y}(1)\otimes\omega_{Y}$ is globally generated.
This follows from Reider's theorem (\cite{Reider}), since
${\mathcal{O}}_{Y}(1)$ is very ample and its degree $d = 2g-2 \geq 10$ (see
Remark ~\ref{Enriques.embeddings}, (2)).
Finally since the rank of ${\mathcal{N}}_{Y,\mathbb{P}^{N}}\otimes
\omega_{Y}$ is $N-2 > \dim \,Y$ (see Remark~\ref{Enriques.embeddings}, (1))
and it is a globally generated vector bundle,
it has a nowhere vanishing section.
Thus the $K3$ carpets inside $\mathbb{P}^{N}$, supported on $i(Y)$ in $\mathbb{P}^{N}$,
are parametrized by a non--empty open set in the projective space of
lines in $H^0({\mathcal{N}}_{Y,\mathbb{P}^{N}} \otimes \omega_Y)$, whose dimension is
$g(N+1)+8$.
\end{Proof}
\smallskip
\noindent
The following theorem is a refinement of ~\cite[III Ex. 5.9]{Hartshorne77}
to characterize non--projective $K3$ carpets.
As result of this theorem, we can say more about the size of the families of
projective $K3$ carpets on a given (abstract) Enriques surface,
compared to the set of non--projective $K3$ carpets.
\begin{theorem}\label{nonproj.carpets}
Let $Y$ be an Enriques surface and let $\widetilde{Y}$ be a
$K3$ carpet on $Y$ corresponding to an element $\tau \in
\mathrm{Ext}^1(\Omega_Y,\omega_Y)$.
\begin{enumerate}
\item The carpet $\widetilde{Y}$ is projective if
and only if there exists an ample divisor $D$ on $Y$ such that $\int_D
\tau =0$, when $\tau$ is thought as an element of $H^{1,1}(Y)=H^2(Y,
\mathbf C)$.
\item
Non--split projective $K3$ carpets on $Y$
are parametrized by a union of (countably infinitely many distinct)
hyperplanes of
the $9$-dimensional projective space of lines in
$\mathrm{Ext}^1(\Omega_Y,\omega_Y)$. These hyperplanes are
in one--to--one correspondence with the set of
classes in NS$(Y)$ of primitive ample divisors on $Y$.
\end{enumerate}
\end{theorem}
\begin{proof}
Recall (see Remark ~\ref{Ext1}) that a $K3$ carpet on $Y$
corresponds to an element
\begin{equation*}
\tau \in \mathrm{Ext}^1(\Omega_Y,\omega_Y) \simeq H^1(\Omega_Y^*
\otimes \omega_Y) \simeq H^1(\Omega_Y)=H^{1,1}(Y)=H^2(Y,
\mathbf C).
\end{equation*}
Since the ideal of $Y$ inside $\widetilde{Y}$ is a square zero ideal,
we have an exact sequence
\begin{equation*}\label{like.exp}
0 \rightarrow \omega_{Y} \rightarrow {\mathcal{O}}_{\widetilde{Y}}^{\ast} \rightarrow
{\mathcal{O}}_{Y}^{\ast} \rightarrow 1.
\end{equation*}
This yields
\begin{equation*}
0 \rightarrow \mathrm{Pic}\, \widetilde{Y} \overset{\gamma}\longrightarrow
\mathrm{Pic}\, Y \overset{\lambda}\longrightarrow
H^{2}(\omega_{Y}) \rightarrow H^{2}({\mathcal{O}}_{\widetilde{Y}}^{\ast}) \rightarrow
H^{2}({\mathcal{O}}_{Y}^{\ast}).
\end{equation*}
The map $\lambda$ works as follows: if $D$ is a divisor on $Y$, then
$\lambda(\mathcal O_Y(D))=\int_D \tau$.
The map
$\gamma$ sends each line bundle on $\widetilde{Y}$ to its restriction to
$Y$. The carpet $\widetilde{Y}$ is projective if and only if it possesses an
ample line bundle.
On the other hand, a line bundle on $\widetilde{Y}$ is ample if and only
if its restriction to $Y$ is ample. Therefore $\widetilde{Y}$ is projective if
and only if there exists an ample line bundle on $Y$ that can be
lifted by $\gamma$ to $\widetilde{Y}$.
This is the same as saying that there
exists an ample line bundle on $Y$ lying in the kernel of $\lambda$.
Thus $\widetilde{Y}$ is projective if and only if there exists an ample divisor $D$
on $Y$ such that $\int_D \tau=0$.
Then, given an ample divisor $D$ on $Y$, the elements $\tau \in
\mathrm{Ext}^1(\Omega_Y,\omega_Y) \simeq H^{1,1}(Y)$ with $\int_D
\tau=0$ form a hyperplane $H_D$ of $\mathrm{Ext}^1(\Omega_Y,\omega_Y)$,
whose elements correspond to projective $K3$ carpets. Then projective
$K3$ carpets are parametrized by the projective lines in
\begin{equation*}
\bigcup_D H_D,
\end{equation*}
where $D$ ranges over the set of primitive ample divisors on $Y$.
\end{proof}
\begin{remark} {\rm Let $Y$ be an Enriques surface.
Theorem~\ref{nonproj.carpets} shows in particular the existence of
non--projective $K3$ carpets on a given Enriques surface $Y$.
Indeed, the non--split non--projective $K3$ carpets on $Y$ are parametrized by the
complement of a union of countably many hyperplanes of the
$9$-dimensional projective space of lines in
$\mathrm{Ext}^1(\Omega_Y,\omega_Y)$.
There are ``more'' non--projective
$K3$ carpets than projective $K3$ carpets.}
\end{remark}
\noindent
The arguments of the proof of Theorem ~\ref{dim.K3carpet.embedded} give
another way of looking at Theorem~\ref{nonproj.carpets}:
\begin{proposition}
Let $Y$ be an Enriques surface. Associated to every
embedding $i$ of $Y$ into some projective space $\mathbf P^N$, there is
a sequence~\eqref{hom.conormal.seq}, arising from the conormal
sequence of $i(Y)$ in $\mathbf P^N$.
For the sequence~\eqref{hom.conormal.seq}
associated to $i$, we will denote by $\delta_i$ the
map $\delta$.
Let $\mathbf{P}(\mathrm{Im}\,\delta_i)$ be the projective space of lines in
$\mathrm{Im}\, \delta_i$.
Then the non--split projective $K3$ carpets on $Y$ are parametrized by
\begin{equation*}
\bigcup_i \mathbf P(\mathrm{Im}\, \delta_i),
\end{equation*}
where $i$ ranges among all the embeddings of $Y$ into some projective space.
For each $i$, $\mathbf P(\mathrm{Im} \, \delta_i)$ is a hyperplane in the
$9$-dimensional projective space of lines in $\mathrm{Ext}^1(\Omega_Y,\omega_Y)$.
\end{proposition}
\begin{proof}
If a $K3$ carpet $\widetilde{Y}$ on $Y$ is projective, it can be embedded in
some projective space $\mathbf P^N$
by the complete linear series of a very ample
line bundle.
This embedding induces
an embedding $i$ of $Y$ as (a degenerate) subvariety of $\mathbf
P^N$. Let $\mathcal I$
be the ideal sheaf of $Y$ in $\mathbf P^N$. Then, the carpet $\widetilde{Y}$
embedded in $\mathbf P^N$ corresponds to an element of
$\mathrm{Hom}(\mathcal I/\mathcal I^2, \omega_Y)$. Thus, the $K3$ carpet
$\widetilde{Y}$, considered as an abstract scheme, corresponds to a point
lying in the image of the map $\delta_i$. From ~\eqref{dim1} and
~\eqref{dim6} we gather
that the cokernel
of $\delta_i$ has dimension $1$, hence the image of $\delta_i$ in
$\mathrm{Ext}^1(\Omega_Y,\omega_Y)$ is a hyperplane. Thus the class
in $\mathrm{Ext}^1(\Omega_Y,\omega_Y)$
of every
projective $K3$ carpet lies in the image of the map $\delta_i$
associated to some embedding $i$ of $Y$ into some projective space. Since
obviously the classes lying in the image of any of the maps $\delta_i$
correspond to projective $K3$ carpets, we see that non--split projective $K3$
are parametrized by
\begin{equation*}
\bigcup_i \mathbf{P}(\mathrm{Im}\, \delta_i)
\end{equation*}
where $i$ ranges among all the embeddings of $Y$ into some projective space.
\end{proof}
\medskip
\noindent
In Theorem ~\ref{dim.K3carpet.embedded} and Theorem~\ref{nonproj.carpets}
we saw how many projective
$K3$ carpets there are supported on an Enriques surface.
In the next observation, we describe how embeddings by a complete linear
series of a $K3$ carpet look like.
\begin{remark}\label{K3carpet.embeddings}
{\rm Let $Y$ be an Enriques surface and let $\widetilde{Y}$ be a
projective $K3$ carpet on $Y$.
Assume that $\widetilde{Y}$ is embedded, as a non--degenerate subscheme into some
projective space, by the complete linear series of a very ample line
bundle.
Let $g$ be the sectional genus of ${\mathcal{O}}_Y(1)={\mathcal{O}}_{\widetilde{Y}}(1) \otimes
{\mathcal{O}}_Y$.
Then, from $H^1( {\mathcal{O}}_Y(1)\otimes\omega_Y )=0$ and the exact sequence
\begin{equation*}
\xymatrix@1{
0 \ar[r] & \omega_Y(1) \ar[r] & {\mathcal{O}}_{\widetilde{Y}}(1) \ar[r] & {\mathcal{O}}_Y(1) \ar[r] & 0,}
\end{equation*}
we have
\begin{equation*}
H^0({\mathcal{O}}_{\widetilde{Y}}(1))=H^0({\mathcal{O}}_Y(1))\oplus H^0( \omega_Y(1) ).
\end{equation*}
Therefore the embedding induced on $Y$ is also given by the complete
linear series of ${\mathcal{O}}_Y(1)$ and there is a diagram
\begin{equation*}\label{complete.embedding}
\xymatrix@C+5pt{
{\widetilde{Y} \;} \ar@{^{(}->}[r] & {\;\mathbb{P}^{2g-1}=\mathbb{P}(H^0({\mathcal{O}}_Y(1))\oplus
H^0(\omega_Y(1)))}\\
{Y \;} \ar@{^{(}->}[u] \ar@{^{(}->}[r] & {\;\mathbb{P}^{g-1}=\mathbb{P}(H^0({\mathcal{O}}_Y(1))).} \ar@{^{(}->}[u]}
\end{equation*}
}
\end{remark}
\section{Deformation of morphisms and smoothing of projective
$K3$ carpets}\label{smoothing}
\noindent In this section we prove two results.
First we show in Theorem ~\ref{coversmoothing} that the \'etale
$K3$ double cover $\pi$ of an Enriques
surface can be deformed, in many different ways, to a family of
projective embeddings. Second, as a consequence of Theorem
~\ref{coversmoothing} we show (see Theorem ~\ref{embsmoothing} and
Corollary ~\ref{absgensmooth}) that
every projective
$K3$ carpet $\widetilde{Y}$ on an
Enriques surface can be smoothed.
By this we mean that we can find a flat, proper, integral family ${\mathcal{Y}}$
over a smooth affine curve $T$, such that over for $0 \in T$,
${\mathcal{Y}}_0=\widetilde{Y}$ and for $t \in T, t \neq 0$, ${\mathcal{Y}}_t$ is a
smooth, irreducible, and, in our case, projective $K3$ surface.
\medskip
\noindent
The key point that connects Theorems~\ref{coversmoothing}
and~\ref{embsmoothing} is the fact that $\widetilde{Y}$,
after being embedded in
some projective space $\mathbb{P}^N$, arises as the central fiber
of the image of a first--order infinitesimal deformation
of the composition of $\pi$ with the inclusion of $Y$ in $\mathbb{P}^N$:
\begin{theorem}\label{infsmoothing}
Let $\, \widetilde{Y} \subset \mathbb{P}^N$ be a projective $K3$ carpet on a smooth
Enriques surface $Y$. Let $X \overset{\pi}\to Y$ be the \'etale $K3$ double cover of $Y$
and let $X\overset{\varphi}\to \mathbb{P}^N$ be the morphism obtained by composing
$\pi$ with the inclusion of $\,Y$ in $\mathbb{P}^N$.
Then $\widetilde{Y}$ is the central fiber of the image of some first--order
infinitesimal deformation of $\,\varphi$.
\end{theorem}
\begin{Proof}
Since $\pi$ is \'etale, we have ${\mathcal{N}}_{\pi}=0$. Then the result follows
from~\cite[Theorem 3.9]{Gon}.
\end{Proof}
\noindent
Next we show that $\varphi$ can be deformed to a
family of embeddings to $\mathbf P^N$. We do so by proving something
stronger, namely, that any infinitesimal
deformation of ${\varphi}$ can be extended to a family of embeddings
of smooth $K3$ surfaces in $\mathbb{P}^N$. Theorem~\ref{coversmoothing} is,
in the present setting, the counterpart of ~\cite[Theorem 2.1]{GGP},
where the authors showed that
a finite cover of a curve can be deformed to a family of embeddings.
\begin{theorem}\label{coversmoothing}
Let $X \overset{\pi} \longrightarrow Y$ be the \'etale $K3$ double
cover of an Enriques surface $Y$, embedded in $\mathbf P^N$ with
sectional genus $g$ and satisfying $N \leq 2g-1$. Let
$\varphi$ denote the composition of $\pi$ with the inclusion of $Y$ in
$\mathbf P^N$.
Let $\Delta=\text{Spec}\ {\mathbf k[\epsilon]}/{\epsilon^2}$. Then for
every first--order infinitesimal deformation
\begin{equation*}
\widetilde{X} \overset{\widetilde{\varphi}}\longrightarrow \mathbb{P}_{\Delta}^N
\end{equation*}
of $X \overset{\varphi}\longrightarrow \mathbb{P}^N$, there exists
a smooth irreducible family ${\mathcal{X}}$, proper and flat over a smooth
pointed affine curve $(T, 0)$, and a $T$--morphism ${\mathcal{X}}
\overset{\Phi}\longrightarrow \mathbb{P}_T^{N}$ with the following features:
\begin{enumerate}
\item the general fiber ${\mathcal{X}}_t \overset{\Phi_t}\longrightarrow \mathbb{P}^N$,
$\, t \in T-0,$ is a closed immersion of a smooth $K3$ surface; and
\item the fiber of ${\mathcal{X}} \overset{\Phi}\longrightarrow \mathbb{P}_T^{N}$ over
the tangent vector at $0 \in T$ is $\widetilde{X}
\overset{\widetilde{\varphi}}\longrightarrow \mathbb{P}_{\Delta}^{N}$; in particular, the
central fiber ${\mathcal{X}}_0 \overset{\Phi_0}\longrightarrow \mathbb{P}^{N}$ is $X
\overset{\varphi}\longrightarrow \mathbb{P}^{N}$
\end{enumerate}
\end{theorem}
\begin{remark}
{\rm We require $N \leq 2g-1$ in the statement of
Theorem~\ref{coversmoothing}. This hypothesis is, in fact, quite natural.
Indeed, if $\, \widetilde{Y} \subset \mathbb{P}^N$ is non--degenerate (i.e., not contained in a hyperplane),
then $N \leq 2g-1$ (see Remark~\ref{K3carpet.embeddings}).
The hypothesis is used in Step 2 of the proof
of Theorem~\ref{coversmoothing} (see~\eqref{bound}).}
\end{remark}
\noindent
Before proving Theorem~\ref{coversmoothing} we need the following
lemma:
\begin{lemma}\label{veryample}\noindent
Let $Y$ be an Enriques surface, embedded in projective space
with sectional genus $g$,
and let $X \overset{\pi}
\longrightarrow Y$ be its \'etale $K3$ double cover.
Then, if $L=\pi^{\ast}{\mathcal{O}}_Y(1)$, $L$ is very ample.
\end{lemma}
\begin{Proof}
From Remark ~\ref{Enriques.embeddings} it follows that $L^2=4g-4 \geq 20$.
Then, to prove that $L$ is very ample, it suffices to check the
following (see \cite[4.2, 5.2, 6.1]{SaintDonat74}):
\begin{enumerate}
\item there is no irreducible curve $E$ such that $p_a(E)=1$ and $L
\cdot E=2$, and
\item there is no smooth rational curve $E$ such that $L \cdot E=0$.
\end{enumerate}
The first condition holds because $L$ is base-point-free and the
second condition holds because $L$ is ample.
\end{Proof}
\begin{Proofof}\emph{Theorem ~\ref{coversmoothing}.}
{Step 1.} To obtain $\Phi$ we first construct, in a suitable way, a
pair
$({\mathcal{X}},{\mathcal{L}})$, where ${\mathcal{X}}$ is a family of smooth $K3$ surfaces and ${\mathcal{L}}$
is a family of very ample line bundles.\\
Let us denote
$\widetilde{L}=\widetilde{\varphi}^{\ast}{\mathcal{O}}_{\mathbb{P}_{\Delta}^{N}}(1)$.
Then $\widetilde{L}$ restricts to $L$ on $X$ and
the $\Delta$--module $\Gamma(\widetilde{L})$ is free of rank $h^0(L)$ and
$\Gamma(\widetilde{L})\otimes k[\epsilon]/\epsilon k[\epsilon]= H^0(L)$. \\
Now we want to obtain a family $({\mathcal{X}},{\mathcal{L}})$, proper and flat over a
smooth pointed affine curve $(T, 0)$, whose central fiber is $(X,L)$,
whose restriction to the tangent vector to $T$ at $0$ is $(\widetilde{X},\widetilde{L})$
and whose general member $({\mathcal{X}}_t,{\mathcal{L}}_t)$ consists of a smooth
irreducible $K3$ surface and a very ample line bundle ${\mathcal{L}}_t$.\\
Note that $L$ has degree $4g-4$ and $h^0(L)=2g$.
Then, from Lemma~\ref{veryample} we know that $L$ is very ample and,
by Corollary~\ref{smooth.Hilbert}, its
complete linear series $|L|$ defines an embedding
which determines a smooth point $[X]$ in a single
component of the Hilbert scheme of surfaces of degree $4g-4$ in $\mathbf
P^{2g-1}$.
The general point $[X']$ in this component represents a smooth
irreducible $K3$ surface.
Then we may consider an open neighborhood $H$ of $[X]$ in its Hilbert
component, with $H$ parametrizing only smooth $K3$ surfaces.
Moreover, since $L$ is very ample and $H^1(L)=0$,
also $\widetilde{L}$ is very ample relative to $\Delta$ and the embedding $X
\overset{|L|}\hookrightarrow \mathbb{P}^{2g-1}$ extends to an embedding $\widetilde{X}
\hookrightarrow \mathbb{P}_{\Delta}^{2g-1}$.
So the image of $\widetilde{X} \hookrightarrow \mathbb{P}_{\Delta}^{2g-1}$ is a flat
family over $\Delta$ which corresponds to a tangent vector to $H$ at
$[X]$.
We can take the embedding $\widetilde{X} \hookrightarrow \mathbb{P}_{\Delta}^{2g-1}$ so
that this tangent vector is nonzero.
Now, since $[X]$ is a smooth point in $H$, we can take a smooth
irreducible affine curve $T$ in $H$ passing through $[X]$ with tangent
direction the given tangent vector.\\
Let $0 \in T$ denote the point corresponding to $[X]$.
Then the pullback to $T$ of the universal family provides a family
$({\mathcal{X}},{\mathcal{L}})$, proper and flat over $T$, whose central fiber is $(X,
L)$, whose restriction to the tangent vector to $T$ at $0$ is
$(\widetilde{X},\widetilde{L})$ and whose general member $({\mathcal{X}}_t, {\mathcal{L}}_t)$ consists of a
smooth irreducible $K3$ surface and a very ample line
bundle ${\mathcal{L}}_t$,
with $H^1({\mathcal{L}}_t)=H^2({\mathcal{L}}_t)=0$,
and hence, with $h^0({\mathcal{L}}_t)=h^0(L)=2g$.
\medskip
\noindent{Step 2.} Once we have the pair $({\mathcal{X}},{\mathcal{L}})$, we are going to use it to construct a relative morphism
\begin{equation*}
{\mathcal{X}}
\overset{\Phi}\longrightarrow \mathbb{P}_T^{N}
\end{equation*}
with the properties described in the statement.
\medskip
\noindent Recall that ${\mathcal{L}}$ is very ample relative to $T$ and that $h^0({\mathcal{L}}_t)=h^0(L)=2g$ and $h^1({\mathcal{L}}_t)=0$ for all $t \in T$.
Then formation of $p_*$ commutes with base extension and, after shrinking $T$, we may assume that $\Gamma({\mathcal{L}})$ is a free ${\mathcal{O}}_T$--module.
Then ${\mathcal{L}}$ induces a morphism
\begin{equation*}
{\mathcal{X}}
\overset{\Psi}\longrightarrow \mathbb{P}_T^{2g-1}
\end{equation*}
which is a closed immersion at each fiber.
The morphism $\widetilde{\varphi}$ is the composition $\widetilde{\rho} \circ \Psi_\Delta$, for some linear projection
$\mathbb{P}_{\Delta}^{2g-1} \overset{\widetilde{\rho}}\dashrightarrow \mathbb{P}_{\Delta}^N$.
Now we look at some $t$ near (but different from) $0$. Since
\begin{equation}\label{bound}
N \leq 2g-1 =\dim \, |{\mathcal{L}}_t|,
\end{equation}
we can find a linear projection $\rho_t$ mapping $\Psi_t({\mathcal{X}}_t)$ to $\mathbf P^N$.
On the other hand, Remark ~\ref{Enriques.embeddings} implies $N \geq
5$. Then choosing $\rho_t$ sufficiently general, we may assume the composition $\rho_t \circ \Psi_t$ to be a closed immersion.
We lift $\widetilde{\rho}$ and $\rho_t$ to a linear projection $\rho$ to $\mathbb{P}^N_T$.
Finally we define $\Phi$ as the composition $\rho \circ \Psi$. Since the restriction $\Phi_t$ is a closed immersion, by~\cite[4.6.7]{EGA3-1} so are the restrictions of $\Phi$ to the nearby fibers. Then, maybe shrinking $T$ we can conclude that the restriction of $\Phi$ to $\Delta$ is $\widetilde{\varphi}$ and that the restrictions $\Phi_t$ are closed immersions for all $t \in T$, $t \neq 0$. \end{Proofof}
\medskip
\noindent
Now we use Theorems~\ref{infsmoothing} and~\ref{coversmoothing} to
show that $\widetilde{Y}$ is the limit of the images of a family of embeddings
$\Phi_t$ of smooth $K3$ surfaces, degenerating to
$\varphi$. Precisely, we want to extend the infinitesimal deformation
of $\varphi$ in such a way that, if we call the image of the family of
morphisms ${\mathcal{Y}} \subset \mathbb{P}^N \times T$, then ${\mathcal{Y}}_0=\widetilde{Y}$. All this is
done in the next theorem:
\begin{theorem}\label{embsmoothing}
Let $\widetilde{Y}$ be a projective $K3$ carpet embedded in $\mathbb{P}^N$, and
supported on an Enriques surface $Y$ embedded in $\mathbf P^N$
with sectional genus $g$ and $N \leq 2g-1$.
Then there exists a family of morphisms $\Phi$ over an affine curve
$T$ as described in Theorem~\ref{coversmoothing} such that the image
${\mathcal{Y}}$ of $\Phi$ is a closed integral subscheme ${\mathcal{Y}} \subset \mathbb{P}_T^N$,
flat over $T$, with the following features:
\begin{enumerate}
\item the general fiber $\,{\mathcal{Y}}_t, \, t \in T-0,$ is a smooth
irreducible projective non--degenerate $K3$ surface in $\mathbb{P}^N$,
\item the central fiber $\,{\mathcal{Y}}_0 \subset \mathbb{P}^N$ is $\,\widetilde{Y} \subset \mathbb{P}^N$.
\end{enumerate}
\end{theorem}
\begin{Proof}
We use the notations of the proof of the Theorem~\ref{coversmoothing}.\\
From Theorem~\ref{infsmoothing} we know that there exists a first
order infinitesimal deformation
\begin{equation*}
\widetilde{X} \overset{\widetilde{\varphi}}\to \mathbb{P}_{\Delta}^{N}
\end{equation*}
of $\varphi$ such that the central fiber of the image of $\widetilde{\varphi}$ is
equal to $\widetilde{Y}$.\\
Therefore there is a family ${\mathcal{X}} \to T$ and a $T$--morphism ${\mathcal{X}} \overset{\Phi}\to \mathbb{P}_T^{N}$ as in Theorem~\ref{coversmoothing}.\\
Let ${\mathcal{Y}}$ be the image of the $T$--morphism ${\mathcal{X}} \overset{\Phi}\to \mathbb{P}_T^{N}$.
The total family ${\mathcal{X}}$ is smooth and irreducible so ${\mathcal{Y}}$ is integral.
Furthermore, $\Phi$ is a closed immersion over $T-0$ since,
by~Theorem~\ref{coversmoothing}, $\Phi_t$ is a closed immersion for
every $t \in T-0$ (see e.g. \cite[4.6.7]{EGA3-1}).
Therefore for $t \in T-0$ we have the equality ${\mathcal{Y}}_t =
\,\mathrm{im}\,(\Phi_t)$. Since ${\mathcal{X}}_t$ is smooth, this proves (1).
Finally, the fact that $T$ is an integral smooth curve and ${\mathcal{Y}}$ is
integral and dominates $T$ implies that ${\mathcal{Y}}$ is flat over $T$.
So the fiber ${\mathcal{Y}}_0$ of ${\mathcal{Y}}$ at $0 \in T$ is the flat limit of the
images of ${\mathcal{X}}_t \overset{\Phi_t} \to \mathbb{P}^{N}$ for $t \neq 0$.
Moreover, this fiber ${\mathcal{Y}}_0$ contains the central fiber
$\,(\mathrm{im}\,\widetilde{\varphi})_0$ of the image of $\widetilde{\varphi}$.
Since $\widetilde{Y}$ has conormal bundle ${\mathcal{E}}$ and $\pi$ has trace zero module
${\mathcal{E}}$, both ${\mathcal{Y}}_0$ and $(\mathrm{im}\,\widetilde{\varphi})_0$ have
the same Hilbert polynomial, so they are equal.
\end{Proof}
\medskip
We highlight this consequence of Theorem~\ref{embsmoothing}:
\begin{theorem}\label{absgensmooth}
Any projective $K3$ carpet $\, \widetilde{Y}$ on a Enriques surface $Y$
is smoothable.
\end{theorem}
\begin{proof}
Let us embed $\widetilde{Y}$ in projective space by the complete linear series
of a very ample line bundle.
Then Remark~\ref{K3carpet.embeddings} implies
that the condition $N \leq 2g-1$ is satisfied, so
the result follows from
Theorem~\ref{embsmoothing}.
\end{proof}
\section{The Hilbert point of a projective $K3$ carpet}\label{hilbert.section}
In this section we prove, in Theorem~\ref{hilbert}, that the Hilbert point of a projective $K3$ carpet on an Enriques surface is smooth. This is in sharp contrast with the result on Hilbert points corresponding to
$K3$ carpets on a rational normal scroll, as shown in [GP97].
First we state some preliminary results valid in general for ribbons.
\begin{lemma}\label{dualizante-WY}
Let $\widetilde{Y}$ be a ribbon on a smooth irreducible proper variety $Y$ with conormal bundle ${\mathcal{E}}$.
There is an isomorphism
\begin{equation}\label{omega.WY.restricted}
{\omega_{\widetilde{Y}} |}_{Y}={\mathcal{E}}^{-1} \otimes \omega_{Y}.
\end{equation}
\end{lemma}
\begin{Proof}
Restricting the sequence~\eqref{WY-extension.dual.2}
to $Y$ gives the isomorphism.
\end{Proof}
\begin{lemma}\label{Hilbert}
Let $\, Y \subset \widetilde{Y} \subset \mathbb{P}^N$ be an embedded ribbon, with conormal bundle ${\mathcal{E}}$, on a smooth irreducible projective variety $Y$.
Then there are exact sequences
\begin{equation}\label{first-sequence-bis-twisted}
\xymatrix@1{
0 \ar[r] & {{\mathcal{N}}_{\widetilde{Y},\mathbb{P}^N} |}_{Y}\otimes {\mathcal{E}} \ar[r] & {\mathcal{N}}_{\widetilde{Y},\mathbb{P}^N} \ar[r] & {{\mathcal{N}}_{\widetilde{Y},\mathbb{P}^N} |}_{Y} \ar[r] & 0,}
\end{equation}
\begin{equation*}\label{seq4.}
\xymatrix@1{
0 \ar[r] & {\mathcal{E}}^{-1} \ar[r] & {\mathcal{N}}_{Y, \mathbb{P}^N} \ar[r]& \mathcal{H}om_{Y}({\mathcal{I}}_{\widetilde{Y},\mathbb{P}^N}/{\mathcal{I}}_{Y,\mathbb{P}^N}^2, {\mathcal{O}}_Y) \ar[r] & 0,}
\end{equation*}
and
\begin{equation*}\label{seq1.}
\xymatrix@1{
0 \ar[r] & \mathcal{H}om_{Y}({\mathcal{I}}_{\widetilde{Y},\mathbb{P}^N}/{\mathcal{I}}_{Y,\mathbb{P}^N}^2, {\mathcal{O}}_Y) \ar[r] & {{\mathcal{N}}_{\widetilde{Y}, \mathbb{P}^N} |}_{Y} \ar[r]& {\mathcal{E}}^{-2} \ar[r] & 0.}
\end{equation*}
\end{lemma}
\begin{Proof}
We know that $\widetilde{Y}$ is a local complete intersection so ${\mathcal{N}}_{\widetilde{Y},\mathbb{P}^N}$ is locally free. Therefore from
\begin{equation*}\label{first-sequence-bis}
\xymatrix@1{
0 \ar[r] & {\mathcal{E}} \ar[r] & {\mathcal{O}}_{\widetilde{Y}} \ar[r] & {\mathcal{O}}_Y \ar[r] & 0,}
\end{equation*}
we obtain the sequence~\eqref{first-sequence-bis-twisted}.
Also ${\mathcal{I}}_{\widetilde{Y}, \mathbb{P}^N}/{\mathcal{I}}_{\widetilde{Y},\mathbb{P}^N}^2$ is locally free so we have
\begin{equation*}
{\mathcal{H}om_{\widetilde{Y}}({\mathcal{I}}_{\widetilde{Y}, \mathbb{P}^N}/{\mathcal{I}}_{\widetilde{Y},\mathbb{P}^N}^2,{\mathcal{O}}_{\widetilde{Y}}) |}_{Y}= \mathcal{H}om_{Y}({{\mathcal{I}}_{\widetilde{Y}, \mathbb{P}^N}/{\mathcal{I}}_{\widetilde{Y},\mathbb{P}^N}^2 |}_{Y}, {\mathcal{O}}_Y).
\end{equation*}
Furthermore ${{\mathcal{I}}_{\widetilde{Y}, \mathbb{P}^N}/{\mathcal{I}}_{\widetilde{Y},\mathbb{P}^N}^2 |}_{Y}= {\mathcal{I}}_{\widetilde{Y},\mathbb{P}^N}/{\mathcal{I}}_{Y,\mathbb{P}^N}{\mathcal{I}}_{\widetilde{Y},\mathbb{P}^N}$ so we have an exact sequence
\begin{equation*}
\xymatrix@1{
0 \ar[r] & ({\mathcal{E}}')^{-1} \ar[r] & {{\mathcal{I}}_{\widetilde{Y}, \mathbb{P}^N}/{\mathcal{I}}_{\widetilde{Y},\mathbb{P}^N}^2 |}_{Y} \ar[r]& {\mathcal{I}}_{\widetilde{Y},\mathbb{P}^N}/{\mathcal{I}}_{Y,\mathbb{P}^N}^2 \ar[r] & 0,}
\end{equation*}
where ${\mathcal{E}}'$ is an invertible sheaf on $Y$.
So there is an exact sequence
\begin{equation}\label{seq1}
\xymatrix@1{
0 \ar[r] & \mathcal{H}om_{Y}({\mathcal{I}}_{\widetilde{Y},\mathbb{P}^N}/{\mathcal{I}}_{Y,\mathbb{P}^N}^2, {\mathcal{O}}_Y) \ar[r] & {{\mathcal{N}}_{\widetilde{Y}, \mathbb{P}^N} |}_{Y} \ar[r]& {\mathcal{E}}' \ar[r] & 0,}
\end{equation}
Furthermore from
\begin{equation*}\label{seq3}
\xymatrix@1{
0 \ar[r] & {\mathcal{I}}_{\widetilde{Y},\mathbb{P}^N}/{\mathcal{I}}_{Y,\mathbb{P}^N}^2 \ar[r] & {\mathcal{I}}_{Y,\mathbb{P}^N}/{\mathcal{I}}_{Y,\mathbb{P}^N}^2 \ar[r]& {\mathcal{E}} \ar[r] & 0,}
\end{equation*}
we obtain the exact sequence
\begin{equation}\label{seq4}
\xymatrix@1{
0 \ar[r] & {\mathcal{E}}^{-1} \ar[r] & {\mathcal{N}}_{Y, \mathbb{P}^N} \ar[r]& \mathcal{H}om_{Y}({\mathcal{I}}_{\widetilde{Y},\mathbb{P}^N}/{\mathcal{I}}_{Y,\mathbb{P}^N}^2, {\mathcal{O}}_Y) \ar[r] & 0,}
\end{equation}
Moreover, since $\widetilde{Y}$ is a local complete intersection, we have
\begin{equation*}\label{seq6}
\bigwedge^{c}{\mathcal{N}}_{\widetilde{Y}, \mathbb{P}^N} =\omega_{\widetilde{Y}}\otimes \omega_{\mathbb{P}^N}^{-1}= \omega_{\widetilde{Y}}\otimes {\mathcal{O}}_{\widetilde{Y}}(N+1),
\end{equation*}
where $c$ is the codimension of $Y$.\\
So
\begin{equation*}\label{seq7}
{\bigwedge^{c}{\mathcal{N}}_{\widetilde{Y}, \mathbb{P}^N} |}_Y ={ \omega_{\widetilde{Y}} |}_Y \otimes {\mathcal{O}}_Y(N+1),
\end{equation*}
and from the isomorphism~\eqref{omega.WY.restricted}
\begin{equation*}\label{seq8}
{\bigwedge^{c}{\mathcal{N}}_{\widetilde{Y}, \mathbb{P}^N} |}_Y =\omega_Y \otimes {\mathcal{E}}^{-1} \otimes {\mathcal{O}}_Y(N+1).
\end{equation*}
Moreover
\begin{equation*}\label{seq9}
\bigwedge^{c}{\mathcal{N}}_{Y, \mathbb{P}^N} =\omega_{Y}\otimes {\mathcal{O}}_{Y}(N+1),
\end{equation*}
so
\begin{equation}\label{seq10}
{\bigwedge^{c}{\mathcal{N}}_{\widetilde{Y}, \mathbb{P}^N} |}_Y =\bigwedge^{c}{\mathcal{N}}_{Y, \mathbb{P}^N} \otimes {\mathcal{E}}^{-1}.
\end{equation}
I claim that
\begin{equation}\label{SE'=SE-2}
{\mathcal{E}}'={\mathcal{E}}^{-2}.
\end{equation}
Indeed, from~\eqref{seq1} we obtain
\begin{equation*}\label{seq11}
{\bigwedge^{c}{\mathcal{N}}_{\widetilde{Y}, \mathbb{P}^N} |}_Y =\bigwedge^{c-1} \mathcal{H}om_{Y}({\mathcal{I}}_{\widetilde{Y},\mathbb{P}^N}/{\mathcal{I}}_{Y,\mathbb{P}^N}^2, {\mathcal{O}}_Y)\otimes {\mathcal{E}}',
\end{equation*}
and from~\eqref{seq4}
\begin{equation*}\label{seq12}
\bigwedge^{c}{\mathcal{N}}_{Y, \mathbb{P}^N} =\bigwedge^{c-1} \mathcal{H}om_{Y}({\mathcal{I}}_{\widetilde{Y},\mathbb{P}^N}/{\mathcal{I}}_{Y,\mathbb{P}^N}^2, {\mathcal{O}}_Y)\otimes {\mathcal{E}}^{-1}.
\end{equation*}
So from~\eqref{seq10} we obtain~\eqref{SE'=SE-2}.
\end{Proof}
\begin{theorem}\label{hilbert}
Let $\widetilde{Y}$ be a projective $K3$ carpet on an Enriques surface $Y$ embedded in $\mathbb{P}^{N}$ as in Theorem~\ref{embsmoothing}.
Then the Hilbert point of $\,\widetilde{Y}$ is nonsingular.
\end{theorem}
\begin{Proof}
We have proved in Theorem~\ref{embsmoothing} that $\widetilde{Y}$ admits an embedded smoothing.
Moreover, from Theorem~\ref{dim.19}, we know that for any $K3$ surface $X \subset \mathbb{P}^N$ we have $H^1 ({\mathcal{N}}_{X,\mathbb{P}^N})= H^2 ({\mathcal{N}}_{X,\mathbb{P}^N})=0$.
So, from an straightforward computation, we see that the dimension of a component parametrizing $K3$ surfaces in $\mathbb{P}^{N}$ is $18+2g(N+1)$. Therefore the $K3$ carpet $\widetilde{Y}$ represents a smooth point in the Hilbert scheme iff $h^0({\mathcal{N}}_{\widetilde{Y},\mathbb{P}^{N}})=18+2g(N+1)$.\\
As a consequence of Theorem~\ref{embsmoothing} or by direct computation using
the sequences in Lemma~\ref{Hilbert}, we see that the Euler characteristic is $\chi({\mathcal{N}}_{\widetilde{Y},\mathbb{P}^{N}})=18+2g(N+1)$.
Therefore we have to show that
\begin{equation*}
h^1({\mathcal{N}}_{\widetilde{Y},\mathbb{P}^{N}})-h^2({\mathcal{N}}_{\widetilde{Y},\mathbb{P}^{N}})=0.
\end{equation*}
Indeed, first we see at once that
\begin{equation*}\label{h-Y=0}
H^1({\mathcal{N}}_{Y,\mathbb{P}^{N}})=H^2({\mathcal{N}}_{Y,\mathbb{P}^{N}})=H^2({\mathcal{N}}_{Y,\mathbb{P}^{N}}\otimes \omega_Y)=0.
\end{equation*}
In addition,~\eqref{dim6} says that
\begin{equation*}\label{h-Y=0.2}
H^1({\mathcal{N}}_{Y,\mathbb{P}^{N}}\otimes \omega_Y)=0.
\end{equation*}
Therefore, from the sequences in Lemma~\ref{Hilbert}, we obtain
\begin{equation*}\label{for1}
H^2(\mathcal{H}om_{Y}({\mathcal{I}}_{\widetilde{Y},\mathbb{P}^{N}}/{\mathcal{I}}_{Y,\mathbb{P}^{N}}^2, {\mathcal{O}}_Y))=0,
\end{equation*}
\begin{equation*}\label{for2}
H^2(\mathcal{H}om_{Y}({\mathcal{I}}_{\widetilde{Y},\mathbb{P}^{N}}/{\mathcal{I}}_{Y,\mathbb{P}^{N}}^2, {\mathcal{O}}_Y)\otimes \omega_Y)=0,
\end{equation*}
\begin{equation*}\label{for3}
H^1(\mathcal{H}om_{Y}({\mathcal{I}}_{\widetilde{Y},\mathbb{P}^{N}}/{\mathcal{I}}_{Y,\mathbb{P}^{N}}^2, {\mathcal{O}}_Y))=H^2(\omega_Y^{-1})=\mathbb{C},
\end{equation*}
\begin{equation*}\label{for4}
H^1(\mathcal{H}om_{Y}({\mathcal{I}}_{\widetilde{Y},\mathbb{P}^{N}}/{\mathcal{I}}_{Y,\mathbb{P}^{N}}^2, {\mathcal{O}}_Y)\otimes \omega_Y)=H^2({\mathcal{O}}_Y)=0.
\end{equation*}
Then we obtain
\begin{equation*}\label{for8}
H^1({{\mathcal{N}}_{\widetilde{Y},\mathbb{P}^{N}}|}_Y \otimes \omega_Y)=0,
\end{equation*}
\begin{equation*}\label{for5}
H^2({{\mathcal{N}}_{\widetilde{Y},\mathbb{P}^{N}}|}_Y \otimes \omega_Y)=H^2(\omega_Y^{-1})=\mathbb{C},
\end{equation*}
\begin{equation*}\label{for6}
H^2({{\mathcal{N}}_{\widetilde{Y},\mathbb{P}^{N}}|}_Y)=0,
\end{equation*}
and
\begin{equation*}\label{for7}
H^1({{\mathcal{N}}_{\widetilde{Y},\mathbb{P}^{N}}|}_Y)=0 \;\, \mathrm{or} \;\, \mathbb{C}.
\end{equation*}
Finally, from sequence~\eqref{first-sequence-bis-twisted}, we see that $h^1({\mathcal{N}}_{\widetilde{Y},\mathbb{P}^{N}})-h^2({\mathcal{N}}_{\widetilde{Y},\mathbb{P}^{N}})=0 \;\,\mathrm{or}\;\, -1$, but now observe that, since our component has dimension $18+2g(N+1)$, we know that $h^0({\mathcal{N}}_{\widetilde{Y},\mathbb{P}^{N}})\geq \chi({\mathcal{N}}_{\widetilde{Y},\mathbb{P}^{N}})$, so $h^1({\mathcal{N}}_{\widetilde{Y},\mathbb{P}^{N}})-h^2({\mathcal{N}}_{\widetilde{Y},\mathbb{P}^{N}}) \geq 0$.
\end{Proof}
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Managing Your Property Obligations BCL67
by BCLbusinessTV Team | Jan 13, 2015 | BCL Watch Again, Legal | 0 comments
Managing Your Property Obligations
https://www.businessconnectionslive.com/ Managing Your Property Obligations
On tonight's edition of Business Connections Live, we talk to Peter Levaggi, Partner at Charles Russell Speechlys. Peter is a Solicitor Advocate with Higher Rights of Audience. He has a thriving commercial property litigation practice dealing with every aspect of contentious landlord and tenant work.
Many SMEs (and larger companies) have been affected by the use of interest rate hedging products by banks as part of their lending apparatus over the last five years. Commercial occupiers (retailers, professional businesses, and businesses leasing premises of all kinds) have all been affected and faced very difficult times with their banks during this period.
The financial downturn created an unprecedented rise in the number of receiver appointed by banks over mortgaged commercial property. Sometimes these receiverships are referred to as LPA Receivers (as they are nominally regulated under the Law of Property Act 1925 – although most standard charge documents vary and/or exclude the provisions of the Act, giving the bank and their receivers extremely wider powers).
Meanwhile a substantial number of the same commercial occupiers (alleged to be in default with their banks) have been determined to be victims of a serious bank mis-selling scandal. The majority of small and medium size companies were sold interest rate hedging products (IRHPs) by their banks.
The misselling of these IRHPs was subject to the Financial Conduct Authority ("FCA") (the Financial Services Authority ("FSA") as it then was) review. The FSA found serious failings in the sale of many products to small businesses.
IRHPs are products that were sold to protect against interest rate movements. A variety of products were sold to purportedly protect customers including caps to limit interest rate rises, swaps to enable a customer to fix their interest rate, collars to place a cap on interest rate rises to within a range (i.e. a ceiling and a floor) and the complicated structured collars. These overly complex arrangements often caused businesses serious losses. Where an IRHP was mis-sold, the banks are having to compensate these businesses to a cost of billions.
How best to deal with Bank finance in relation to property
The necessity of taking proper advice in relation to alleged bank default
Managing liabilities when vacating a commercial premises
Seeking and obtaining redress in the case of these mis sold hedge products
6 key benefits
When negotiating an exit from a commercial premises, a business can save substantial amounts of money if proper legal advice is taken. Liabilities owed to banks and landlords depend greatly on the terms of the subject mortgage or lease.
Landlords are bringing an increasing number of dilapidations claims at the end of the lease. However such claims should be resisted particularly when it is apparent that the landlord intends to redevelop the property.
Lease liabilities are often a question of detail — in relation to the terms and conditions of the lease. Landlord sometimes purport to be able to recover costs and expenses in circumstances where the lease does not allow.
Negotiating comprehensively before the lease is executed is essential to avoid misunderstandings and unreasonable liabilities arising.
Peter has a strong reputation in the property litigation field and has a substantial national client base. He also specialises in insolvency issues arising in the context of property. He is the Head of the Property Insolvency Group and the Property Litigation Group. He is named as leader in his field in Legal 500 and Chambers who say he "heads up the practice and is extremely well reputed for his crisp delivery and deep knowledge." Peter regularly writes articles and books on property and insolvency issues (he was the author of the Law Society's Guide to Enforcement Law published in 2008 – second edition published in December 2014 and Jordon's Property Insolvency published in 2009 – second edition published to be published February 2015). He chairs the Lexis Commercial property series of webinars, and is a regular speaker for the Property bar Association, the Law Society and RICS.
http://www.charlesrussellspeechlys.com/
Business Connections Live Programme 67
This is the Business Connections Live Business Channel on YouTube Business Connections Live Programme 67. Broadcast 14th January 2015 | {
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} | 2,673 |
Jean l'Aumônier, d'Alexandrie ou Jean de Chypre, appelé aussi Jean le Miséricordieux, né dans la seconde moitié du et mort entre 616 et 621 sur l'île de Chypre, est patriarche d'Alexandrie de 610 à sa mort.
Saint patron de la ville de Casarano, il est fêté le par l'Église catholique et le lendemain par l'Église orthodoxe.
Biographie
Entre 550 et 556, Jean naquit à Chypre près de Limassol où son père Épiphane était préfet. Il se maria, et devint lui-même père de famille de deux enfants, et fonctionnaire impérial. Se retrouvant assez vite privé des siens, veuf et seul, il commença une vie de solitaire se montrant sensible envers les nécessiteux. Il se fit de plus en plus connaître pour ses actes de charité et ses qualités spirituels lui valurent l'honneur des hommes.
D'autre part, il était un proche de l'empereur Héraclius, et uni avec le cousin de ce dernier, le patrice Nicétas, par un lien de parenté ou de fraternité spirituelle. Lorsque le trône patriarcal d'Alexandrie devint vacant, Héraclius lui demanda d'aller occuper la charge.
Il assuma dignement son service épiscopal, se préoccupant du bien-être moral et dogmatique de son troupeau. En tant que patriarche, il dénonça toutes les hérésies qui lui semblaient détruire l'âme, et lutta contre le monophysisme en chassant d'Alexandrie l'un de ses représentants Phyllonos d'Antioche.
Son autre action importante concerna les pauvres de son diocèse. Son hagiographe Léontios raconte que dès le début de son patriarcat, Jean ordonna aux économes et au chef de la police de dresser une liste des pauvres qui avaient besoin d'une aide quotidienne, notamment pour signaler à l'opinion publique le fait que l'activité caritative serait l'une de ses priorités. Il en fut compté sept mille cinq cents. Jean les logea tous dans son palais patriarcal et la nourriture ne manqua jamais grâce aux prières et miracles de celui-ci.
Lors de l'invasion de la Palestine par les Perses, de nombreux réfugiés vinrent se cacher à Alexandrie qui était alors la deuxième cité de l'Empire romain. Jean les accueillit chez lui avec une grande générosité. De même, il visita les hospices, soigna lui-même des blessés, créa plusieurs hôpitaux et fonda la première maternité pour que les femmes accouchent dignement.
D'après la Légende dorée, il donna tout ce qu'il possédait aux pauvres, qu'il appelait ses « seigneurs ». Un riche, qui vit que Jean n'avait sur son lit plus que des guenilles, lui offrit une couverture très précieuse. Mais durant la nuit qui suivit, Jean ne put dormir en songeant à tous ses « seigneurs » qui auraient pu être couverts grâce à sa valeur, aussi le lendemain la vendit-il et distribua l'argent aux pauvres. Le riche le découvrit, et lui racheta une couverture, que Jean revendit aussitôt. Le riche racheta encore une couverture, en disant à Jean : « Nous verrons qui se lassera, toi de vendre, ou moi de racheter ».
Quand arrivèrent à Alexandrie des populations qui avaient fui la Syrie occupée par les Perses, les blessés et malades furent accueillis, les autres réfugiés bénéficiant de distributions en faveur des pauvres.
Jean aurait envoyé chez les Perses des hommes chargés de récupérer les prisonniers en échange d'argent. Il envoya également des moyens (or, blé, huile, vin, vêtements) en Palestine occupée par les Perses pour aider les chrétiens et les nonnes. Il apporta son soutien aux moines basiliens de Saint Lazare au Moyen-Orient. Il a également été le premier mécène de l'hôpital fondé par les marchands amalfitains à Jérusalem.
Lorsque les Perses envahirent à son tour l'Égypte et menacèrent Alexandrie, voyant ses habitants commencer à fuir, Jean et Nicétas partir pour Constantinople afin de solliciter un envoi immédiat de troupes pour défendre la ville. Mais faisant une halte sur son île de naissance, il mourut soudainement dans sa ville d'Amathonte. La date estimée est 619 (entre 616 et 621).
Postérité
Après sa mort, il fut appelé Jean le Miséricordieux, et proclamé saint par les Églises catholique et orthodoxe. Ses reliques furent transportées d'Alexandrie à Venise en 1249, où son corps intact et quelques vêtements sont encore vénérés dans une chapelle à droite du chœur de l'église San Giovanni in Bragora.
La vie de Jean l'Aumônier a été écrite dans deux hagiographies, celle de Jean Moschus et de Sophrone de Jérusalem qui ont fait un bref résumé de sa vie, perdu, et celle de l'évêque Léontios de Néapolis qui en a fait un récit plus important en 640. Léontios n'a pas connu personnellement Jean l'Aumônier, et les passages où il peut raconter l'avoir connu sont en fait des artifices littéraires, courants à l'époque.
Notes et références
Annexes
Bibliographie
Léontios de Néapolis, Vie de Syméon le Fou et Vie de Jean de Chypre, Éd. A.J. Festugière, L. Ryden, Paris, Librairie orientaliste Paul Geuthner, 1974.
E. Dawes (dir.), Three Byzantine Saints: Contemporary Biographies of St. Daniel the Stylite, St. Theodore of Sykeon and St. John the Almsgiver, Londres, 1948.
Leonzio di Napoli, Vita di S. Giovanni Elemosiniere, patriarca di Alessandria, Monza, 1866.
Jacques de Voragine, La Légende dorée, Bibliothèque de la Pléiade, Gallimard, 2004, publication sous la direction d'Alain Boureau.
sous la direction de Jean-Yves Empereur, Alexandrie médiévale 2, Institut français d'archéologie orientale , le Caire , 2002.
Ewa Wipszycka, « L'économie du patriarcat alexandrin à travers les vies de saint Jean l'Aumônier », dans Alexandrie médiévale 2, C. Décobert (Éd.), Le Caire, 2002, .
Claudia Rapp, « All in the Family: John the Almsgiver, Nicetas and Heraclius », dans Néa Romè 1, Rome, 2004, .
Liens externes
Liste des évêques et patriarches d'Alexandrie, G-Catholic.org
Vie de saint Jean l'Aumônier dans la Légende dorée
La chapelle Saint Jean l'Aumônier de l'église San Giovanni in Bragora
Jean Aumonier
Jean Aumonier
Jean Aumonier
Naissance à Chypre
Date de naissance non renseignée (VIe siècle)
Date de décès non renseignée (VIIe siècle)
Patriarche du VIIe siècle
Personnalité du haut Moyen Âge par nom
Héraclius | {
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} | 1,112 |
{"url":"https:\/\/mattermodeling.stackexchange.com\/questions\/859\/autocorrelation-function-problem-in-monte-carlo-simulation-of-2d-ising-model","text":"# Autocorrelation function problem in Monte Carlo simulation of 2D Ising model\n\nCurrently, I did a Monte Carlo simulation with the local update and Wolff cluster updated in 2D classical Ising model. I use the autocorrelation function to compare 2 different algorithm in critical temperature (T ~ 2.269). That's what I got. Is it correct? The local updated algorithm didn't show the exponential decay in the beginning. And it will become negative as it pass through 0. What I expect is that it has an exponential decay in the beginning and fluctuate around 0 once the sample become decorrelated. The equation I used to evaluate the autocorrelation function is $$A(\\tau)=\\frac{\\langle Q_kQ_{k+\\tau}\\rangle-\\langle Q_k\\rangle^2}{\\langle Q_k^2\\rangle-\\langle Q_k\\rangle^2}.$$\n\nFirst, some general remarks:\n\n\u2022 The measurements should be made after the system has equilibrated, i.e., a large number of the first iterations should be discarded before the analysis.\n\n\u2022 They should also be averaged over a number of runs, in order to reduce noise.\n\n\u2022 This plot is better appreciated with a log scale in the vertical axis.\n\n\u2022 Later on, it's important to consider different system sizes. See finite-size analysis.\n\n\u2022 Local updates perform very poorly (see taciteloquence's answer) at the critical temperature - so the general relative behavior of both curves seems fine enough.\n\nWith respect to\n\nit will become negative as it pass through 0\n\nif it's a robust trend, there seems to be something wrong - you can check a good source such as Janke's book (especially Chap. 3 [pdf]), Sandvik notes, or this question in Physics SE.\n\n@stafusa's answer is great, but there is a specific phenomenon you are encountering here called critical slowing down, which is especially bad for the single-spin-flip Metropolis Algorithm.\n\nNear the critical point, the typical cluster size diverges. For the single-spin-flip algorithm, it's really hard to flip these huge clusters, so the autocorrelation time can increase dramatically. Cluster algorithms sidestep this issue by flipping big groups of spins at once.\n\nWhat you are seeing for the local updates is an exponential decay with a really long time constant, which causes it to look linear. To see an exponential decay in the autocorrelations for the local updates, try moving away from $$T_c$$.\n\nTo learn more you can take a look at \"Overcoming critical slowing down\", Gould and Tobochnik, Computers in Physics 3, 82 (1989). Or you can look at p. 79 of \"Monte Carlo Methods in Statistical Physics\" by Newman and Barkema.\n\n\u2022 +1 That's a much more complete description than \"Local updates perform very poorly at the critical temperature\". :) \u2013\u00a0stafusa May 27 at 8:58","date":"2020-09-26 09:33:55","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 2, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6365242004394531, \"perplexity\": 611.8038493245458}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-40\/segments\/1600400238038.76\/warc\/CC-MAIN-20200926071311-20200926101311-00280.warc.gz\"}"} | null | null |
\section{Introduction}
Modern resistive random access memory (RRAM) devices are about 100-300 nm thick including two metal electrodes and the the insulator layer of about 10-70nm thickness. For the the insulator thickness of $\sim 10$ nm and and bias voltage of $\sim 1$ V, the electric field strength in the insulator $E \sim 10^8$ V/m. In response to that field, a conductive path through the insulator can be created in the form of a conductive filament. The regime of continuous conductive filament corresponds to the device ON state created at the SET transition and discontinued at the RESET transition. When the current flows through the filament, a significant Joule heat is liberated creating a temperature distribution that affects the device operations. Here, we present an analysis of that temperature distribution with the emphasis on its underlying physics facilitating the device understanding and design. This is achieved by (1) numerically generating the temperature distribution by means of COMSOL multiphysics package and (2) comparing the latter with two analytically solved limiting cases: (a) heat transport to the electrodes dominated by the metal filament without lateral spreading , vs. (b) that dominated by the lateral spreading of thermal energy preceding its dissipation at the electrodes. Based on our conclusions, we present a related expression for the filamentary RRAM SET voltage that possesses a high degree of universality.
\begin{figure}[t]
\centering
\includegraphics[width=0.45\textwidth]{heat1.png}
\caption{Parameters describing the geometry of a simple cylindrical RRAM device which consist of two metal electrodes, insulator layer, and a metallic filament. The device is thermally insulated except for the top and bottom boundary of the metal layer which is fixed at an ambient temperature $T_0$ and is subjected to an external bias of $V$ volts. We fix the origin of our cylindrical co-ordinate system at the center of the filament. Additional material parameters not shown in the figure are the thermal and electrical conductivities of the metal, filament, and insulator layer which are respectively ($\kappa_m$, $\sigma_m$), ($\kappa_f$, $\sigma_f$), and ($\kappa_i$, $\sigma_i$) required to solve the heat transfer problem. Note: Figure not drawn to scale($H>h$)}\label{Fig:MIM}
\end{figure}
\section{Numerical Modeling}\label{sec:num}
We use an axillary symmetric model of a RRAM device, the cross-section of which is shown in Fig.\ref{Fig:MIM}; a description of its COMSOL modeling routine is presented in Appendix \ref{appendix0}. The dielectric layer corresponds to the metal oxide HfO$_2$. (As widely accepted, the oxygen sweeps creating oxygen vacancies that form a conductive filament of a non-stoichiometric composition HfO$_{2-x}$.) Following a number of implementations \cite{Govoreanu 2013,Fantini 2012}, we choose TiN for the metal electrode materials. The material properties are listed in Table \ref{tab:param}.
\begin{table}[t]\footnotesize
\centering
\caption{Material parameters used in numerical modeling\cite{Panzer 2009,Hildebrandt 2011,Govoreanu 2013,Samani 2013,Yaw 2015,Lide 2008}}\label{tab:param}
\begin{threeparttable}
\begin{tabular}{ |c | c | c | c | c |}
\hline
Material & TiN & HfO$_2$ & HfO$_{2-x}$ & Hf \\ \hline
Thermal Conductivity[W/K.m] & 11.9 & 0.5 & 20\tnote{a} & 23 \\
Electrical Conductivity[S/m] & 10$^6$ & 10$^{-2}$ & 10$^5$ & 3$\cdot10^6$ \\
Specific Heat\tnote{c} [J/kg.K] & 545.33 & 120 & 130\tnote{a} & 144 \\
Relative Permittivity &-$\infty$\tnote{b} & 25 &-$\infty$\tnote{a}\tnote{ ,b} &-$\infty$\tnote{b} \\
Density[kg/m$^3$] & 5220 & 9680 & 12000\tnote{a} & 13310 \\
\hline
\end{tabular}
\begin{tablenotes}
\item[a]Assumed value such that it lies in between Hf and HfO$_2$
\item[b]-10$^6$ was used instead of -$\infty$ for practical purpose
\item[c]Specific heat capacity at constant pressure
\end{tablenotes}
\end{threeparttable}
\end{table}
\begin{table}[t]\footnotesize
\centering
\caption{Device dimensions used in numerical modeling}\label{tab:dimen}
\begin{threeparttable}
\begin{tabular}{ |c | c | c | c | c |}
\hline
Device/Dimension (nm) & $H$ & $h$ & $l$ & $d$ \\ \hline
Device I & 30 & 10 & 100 & 6 \\
Device II & 100 & 50 & 100 & 20 \\
\hline
\end{tabular}
\end{threeparttable}
\end{table}
Two device dimensions chosen for modeling are described in Table \ref{tab:dimen}. The top electrode is connected to a source voltage of 0.5 V while the bottom one is grounded. An ambient temperature of 300K is maintained at the top and bottom. The side walls of the device are taken to be electrically and thermally insulated, which reflects an array geometry with zero inter-device currents. With those boundary conditions, COMSOL solves the coupled heat and electrostatic equations producing the temperature distributions presented in Fig. \ref{Fig:COMSOLtempdist}.
As shown in Figs. \ref{Fig:COMSOLtempdistA10nm}, \ref{Fig:COMSOLtempdistA50nm}, \ref{Fig:COMSOLtempdistB10nm}, and \ref{Fig:COMSOLtempdistB50nm}, the temperature distributions are a maximum of about 610 K and 576 K at the center of the filament for the Devices I and II respectively. The temperature decay scales in the axial and lateral directions are comparable, although the functional forms are different. The similarity of the two decay scales is due to the mutually balancing competing factors: a better thermal conductivity in a metal vs. the greater area facing the dielectric. In conceivable cases of different material parameters or geometrical dimensions, one of those factors can dominate.
\begin{figure}
\centering
\subfigure[Longitudinal temperature distribution for device I .]
{\includegraphics[width=0.22\textwidth]{Long10nm.PNG}\label{Fig:COMSOLtempdistA10nm}}
\hspace{0.001\textwidth}
\subfigure[Longitudinal temperature distribution for device II]
{\includegraphics[width=0.22\textwidth]{Long50nm.PNG}\label{Fig:COMSOLtempdistA50nm}}
\subfigure[Radial temperature distribution for device I.]
{\includegraphics[width=0.22\textwidth]{Trans10nm.PNG}\label{Fig:COMSOLtempdistB10nm}}
\hspace{0.001\textwidth}
\subfigure[Radial temperature distribution for device II.]
{\includegraphics[width=0.22\textwidth]{Trans50nm.PNG}\label{Fig:COMSOLtempdistB50nm}}
\caption{Temperature distribution along the Longitudinal and Transverse direction in the mid-layer of the metal-insulator-metal structured RRAM device. In the longitudinal temperature distribution plots, Figs. \ref{Fig:COMSOLtempdistA10nm} and \ref{Fig:COMSOLtempdistA50nm}, Analytical I curve corresponds to Eq.(\ref{eq:Parabolic}) and Analytical II curve corresponds to Eq.(\ref{eq:TempDist1}) while in the radial temperature distribution plots, Figs. \ref{Fig:COMSOLtempdistB10nm} and \ref{Fig:COMSOLtempdistB50nm}, Analytical curve corresponds to Eq.(\ref{eq:tempdist})}.
\label{Fig:COMSOLtempdist}
\end{figure}
\section{Limiting cases}\label{sec:lim}
For comparison, we present below the two limiting cases corresponding to (a) the 1D heat transfer along the filament and (b) the dominating radial transport of heat from the filament to the insulator. At the end, we combine the two limiting cases as the thermal resistance in parallel to obtain a single heat transport model.
\subsection{1D Thermal Transport}\label{sec:1D}
Assuming the thermal conductivity of the insulating layer much less than that of the filament material, the heat will flow only through the filament corresponding to a 1D problem. Consider a filament of length $h$ embedded in an insulator sandwiched between two metal electrodes and subjected to an external voltage V as shown in Fig. (\ref{Fig:MIM}). The ends of the filament are at the filament-junction temperature $T_j$ which depends on the ambient temperature $T_0$ maintained at the surface of the metal electrodes.
Consider a steady state heat equation with Joule heat as a source term,
\begin{equation}\label{eq:heateq1}
-\nabla(\kappa(T)\nabla T)= \bf{J}\cdot\bf{E}.
\end{equation}
where, $\bf{J}$ is the current density and $\bf{E}$ is the electric field in the filament. Since $\delta\kappa/\kappa \ll \delta T/T$, we treat thermal conductivity to be a constant; a broader analysis is presented in \cite{John1985}. Using the Ohms law, $\bf{J}= \sigma\bf{E}$, the above equation takes the form,
\begin{equation}\label{eq:heateq2}
\nabla^{2}T = -\frac{\sigma}{\kappa}E^{2}\equiv -\frac{E^{2}}{L}\frac{1}{T}.
\end{equation}
Here we have accounted for the Wiedemann-Franz-Lorenz Law\cite{W-F 1853} ,\cite{Lorenz 1872}, stating that $\sigma/ \kappa=1/LT$ where $L$ is the Lorenz number. Sommerfeld\cite{sommerfeld 1927}, showed that for `good' metals, $L = (\pi k_B)^2/3e^2 = 2.44 \cdot 10^{-8}$ W$\Omega$K$^{-2}$ where, $k_B$ is the Boltzmann's constant and $e$ is the electron charge.
In reality, the measured $L$ varies between different metals metals and can be temperature dependent, off from the Sommerfeld's value within an order of magnitude. \cite{kumar 1993} In particular, for the case under consideration, the values from Table \ref{tab:param} lead to $L\approx 6.67\cdot 10^{-7}$ W$\Omega$K$^{-2}$, significantly different from the Sommerfeld's prediction. That may indicate that the filament material is not a homogeneous metal representing perhaps a mixture of metallic and insulating phases \cite{kruchihin2015}. Earlier, the Wiedemann-Franz-Lorenz relation was used in modeling of phase change memory devices \cite{kencke2007}.
Eq. (\ref{eq:heateq2}) has a simple solution for the regime of low heat, $\delta T\ll T$, predicting the parabolic temperature distribution,
\begin{equation}\label{eq:Parabolic}
T(z) = T_j + \frac{E^2h^2}{8LT_j}\left[1-\left(\frac{2z}{h}\right)^2\right]
\end{equation}
with the maximum (center) temperature by,
\begin{equation}\label{eq:weaklim}
\delta T=\frac{E^2h^2}{8LT_j}
\end{equation}
above the junction (at $z=\pm h/2$) temperature $T_j$.
\begin{figure}[t]
\centering
\includegraphics[width=0.45\textwidth]{Temp2.PNG}
\caption{The COMSOL calculated temperature distributions in Device I along the z-axis. Curve 1 represents the distribution when the room temperature (300K) is assumed at the electrode-dielectric interface; curve 2 corresponds to the case when the free surface of the electrode is at room temperature, while the electrode-dielectric interface temperature is derived as explained in the text.}\label{Fig:junctiontemp}
\end{figure}
The latter solution was earlier presented in \cite{John1985} and \cite{ielimini2011}. It was assumed \cite{ielimini2011}, that the junction filament temperature is the same as the ambient temperature, $T_j = T_0$, which may seem intuitively justified because of the high thermal conductivity of the metal electrode . An important correction here is that $T_j$ can be significantly higher than $T_0$ because the thermal transport in the electrode is dominated by the geometrically small region adjacent to the filament tip that plays the role of the point heat source at the electrode interface. Indeed, the thermal resistance of the series of elemental co-centric semi-spherical layers centered at the tip, is determined by the small distance contributions, $r\sim d$. The significant difference between $T_j$ and $T_0$ is illustrated in Fig. \ref{Fig:junctiontemp}.
Analytically, the temperature distribution at distance $r$ in the electrode from the above point source satisfying the condition that $T(r)=T_0$ at $r\rightarrow \infty$, takes the form,
\begin{equation}\label{eq:Tr}
T_r =(T_j - T_0)\frac{d}{2r} +T_0
\end{equation}
The corresponding heat flow through a hemispherical surface of radius $d/2$ in the electrode, $2\pi (d/2)^2 \kappa_m \nabla T$ with $T$ from Eq. (\ref{eq:Tr}) must be equal to that supplied by the filament, $(2\delta T/h)(\pi d/2^2)$ as follows from Eq. (\ref{eq:Parabolic}). That equality yields,
\begin{equation}\label{eq:tempjunction}
T_j = T_0 + \frac{1}{2}\sqrt{T_0 ^2 + \frac{\kappa_f}{\kappa_m} \frac{E^2 h d}{4L}}
\end{equation}
The maximum temperature is now given by,
\begin{equation}\label{eq:Tmax}T_{\max}=T_j+\delta T\end{equation}
with $T_j$ from Eq. (\ref{eq:tempjunction}) and $\delta T$ from Eq. (\ref{eq:weaklim}).
For numerical estimate, we use $L\approx 6.67\cdot 10^{-7}$ W$\Omega$K$^{-2}$, $T_0=300$ K, and $V=0.5$V, yielding $\delta T\equiv T_\textrm{max}-T_j\approx 91$ K and $94$ K respectively for Device I and Device II, while the junction temperatures are $T_j \approx 514$ K and $495$ K respectively, which is close to the numerical solution presented in Figs. \ref{Fig:COMSOLtempdistA10nm} and \ref{Fig:COMSOLtempdistA50nm}.
As shown in Appendix \ref{appendix1} and the earlier general treatment \cite{John1985}, Eq. (\ref{eq:heateq2}) can be integrated more accurately to result in
\begin{equation}\label{eq:TempDist1}
T(z)=T_\mathrm{max}\exp\left[-\left(\mathrm{erf}^{-1}\left(\frac{\mp z}{T_\mathrm{max}}\sqrt{\frac{2E^{2}}{\pi L}}\right)\right)^2\right]
\end{equation}
where erf$^{-1}$ is the inverse error function, and the maximum temperature is defined by the transcendental equation
\begin{equation}\label{eq:T_max}
\frac{T_\mathrm{max}}{T_j}\mathrm{erf}\left(\sqrt{\ln\left(\frac{T_\mathrm{max}}{T_j}\right)}\right) = \mp\frac{h}{2 T_j}\sqrt{\frac{2E^{2}}{\pi L}}.
\end{equation}
These results are plotted in Figs. \ref{Fig:COMSOLtempdistA10nm} and \ref{Fig:COMSOLtempdistA50nm} predicting $\delta T\equiv T_\textrm{max}-T_j\approx 85$ K and 80 K, for Device I and Device II respectively, rather close to the above COMSOL result.
\subsection{Radial temperature distribution}\label{sec:rad}
In spite of the relatively small thermal conductivity of an insulator, the heat flowing from the filament to the metal electrodes through the insulator can be significant because of the large areas of the filament/dielectric and dielectric/electrode interfaces. To understand the corresponding radial distribution of temperature, we adopt a simplified model of a very thin insulating layer where the transversal temperature variation can be neglected, thus approximating $T$ with its average value $\overline{T}(\rho)$.
Equating the radial component of the divergence of heat flow $\kappa _ih\rho ^{-1}(\partial /\partial \rho)\rho (\partial /\partial \rho)\overline{T}$ to the heat $\kappa _m(\overline{T}-T_0)/H$ absorbed by the electrodes leads to the equation,
\begin{equation}\label{eq:divT}
\frac{1}{\rho}\frac{d}{d \rho}\rho\frac{d \overline{T}}{d \rho} + \beta ^2 (T_0 -\overline{T})=0\ {\rm with}\ \beta =\sqrt{2\frac{\kappa_m}{\kappa_iHh}}
\end{equation}
where $\beta$ plays the role of the temperature reciprocal decay length.
The solution to Eq. (\ref{eq:divT}) is expressed through the Bessel function with the coefficient determined by the condition that the heat flux $\pi hd(d\overline{T}/d\rho )$ at $\rho =d/2$ equals the filament generated Joule heat. As shown in Appendix (\ref{appendix2}), this results in
\begin{equation}\label{eq:tempdist}
\overline{T}(\rho) = \frac{V^2d}{4 h \kappa_i \beta(h/\sigma_f+2H/\sigma_m)K_1(\beta d/2)} K_0(\beta\rho) + T_0
\end{equation}
where $K_0$ and $K_1$ are the modified Bessel functions of order 1 and 0.
For numerical estimate, we use the above presented device parameters, which yields the temperature decay length $1/\beta = 2.51$ nm and 10.24 nm for Device I and Device II respectively.
The resulted temperature distribution inside the insulator is plotted in Fig. \ref{Fig:COMSOLtempdistB10nm} along with the numerically solved (COMSOL) temperature distribution. A somewhat overestimated temperature of the filament is due to the approximation neglecting thermal exchange through the filament bases.
\subsection{Parallel Transport}
A more accurate temperature estimate can be obtained by considering the parallel connection of the thermal resistance from 1D heat transport $R_{th1D}$, and that of radial heat transfer, $R_{thrad}$, which are derived from respectively Eq.(\ref{eq:weaklim}) and Eq.(\ref{eq:tempdist}),
\begin{eqnarray}\label{eq:thermalRes}
R_\mathrm{th1D}&=&\frac{R}{8LT_j}\quad \mathrm{and}\\
R_\mathrm{thrad} &=&\frac{R d K_0(\beta d/2)}{4 h \kappa_i \beta(h/\sigma_f+2H/\sigma_m)K_1(\beta d/2)}
\end{eqnarray}
where $R$ is the electrical resistance. The parallel connection results in a smaller total thermal resistance, $ 1/R_\textrm{th} = 1/ R_\textrm{th1D} + 1/ R_\textrm{thrad}$.
The maximum temperature can be calculated using $\delta T = R_\textrm{th} \cdot V^2/R$. For numerical estimate of Device I and Device II, we use the above presented parameters, which yields $\delta T \equiv T_\textrm{max}-T_j\approx 82$ K and 79 K, respectively. In Sec. \ref{sec:lim}, we obtained $T_j$ to be 514 K and 495 K for Device I and II respectively, using which the maximum temperature, $T_\textrm{max}$, of the filament is found to be 596 K and 574 K which is yet closer to the COMSOL numerical solution.
\section{SET Voltage}
Our thermodynamic analysis of resistive switching relates $V_{\textrm{SET}}$ as in [\cite{Karpov2016}, eq.(8)],
\begin{equation}\label{eq:VSET}
V_\mathrm{SET} = h\sqrt{\frac{\delta \mu}{\sigma _f\tau_T}}.
\end{equation}
where $\delta \mu$ is the difference in chemical potentials (per volume) between the insulating phase and the conducting phase of the filament, and $\tau_T$ is the thermalization time. In the approximation of 1D heat transfer, one gets $\tau_T = h^2/\chi$. The thermal diffusivity, $\chi = \kappa/ C$ where $C$ is the volumetric heat capacity. Hence $V_{\textrm{SET}}$ can be written as,
\begin{equation}\label{eq:VSET2}
V_\mathrm{SET} \approx \sqrt{\frac{\kappa \delta \mu}{\sigma C}}.
\end{equation}
Using the Einstein model, $C = 3nk_B$ where $n$ is the number density ($N$/$Vol$) of atoms. The chemical potential can be expressed in terms of chemical potential per atom ($\delta \mu_{a}$) as $\delta \mu = n\delta \mu_{a} $. Estimating $\delta\mu _a\approx k_BT$ where $T$ is the temperature at which the filament phase is formed, and adopting the notations of
Widemann-Franz-Lorenz law the SET voltage is then expressed as,
\begin{equation}\label{eq:VSETfin}
V_\mathrm{SET} \approx \sqrt{\frac{L}{3}}T.
\end{equation}
For numerical estimate, we take the above discussed $T = 600$K and $L = 6.67 \cdot 10^{-7}$ W$\Omega$K$^{-2}$ which yields $V_{\textrm{SET}} \sim 0.3$ V which is in the ballpark of measured SET voltages \cite{Fantini 2012, wouters2012}. Perhaps more importantly, Eq. (\ref{eq:VSETfin}) predicts that RRAM devices in which the filament materials have low Lorenz numbers can operate at the correspondingly lower SET voltages.
\section{Conclusion}
We have presented the accurate COMSOL modeling of thermal transport in filamentary devices in comparison with simplified analytical models, one neglecting the radial heat propagation, while the other approximating the temperature distribution as uniform in transversal direction. Our results show that for the typical device parameters, both approximations somewhat overestimate the filament temperature, although the errors ($\lesssim$ 10\%) are not very significant. In particular, we have shown that the model of 1D (along the filament) thermal transport is surprisingly accurate when amplified with a realistic heat transport through the electrode suggested here. These simplified models can serve as a convenient express analysis tool. Our predicted values of filament temperature fall in the ballpark of the earlier measured and modeled values \cite{kim2013,yalon2014,yalon2015}; some differences can be attributed to the particular structural and material parameter choices, and the effects of interfacial resistances \cite{kencke2007} neglected here.
Also, we have demonstrated that the Wiedemann-Franz-Lorenz law can be used in device analysis when the value of Lorenz parameter is taken to correspond the experimental data on electric and thermal conductivity, which can result in significant deviations from its Sommerfeld's value.
Finally, we have presented an approximate expression for the SET voltage in filamentary RRAM structures, possessing high degree of universality and correctly predicting the measured values. That expression points at the filament materials wilt low Lorenz numbers as candidates for the future low switching voltage devices.
\section{Acknowledgement}
We are grateful to I. V. Karpov, R. Kotlyar, and V. I. Kozub for useful discussions.
\appendices
\section{COMSOL Model}\label{appendix0}
Our COMSOL algorithm is as follows.\\
1) Open the \textbf{Model Wizard}.\\
2) Choose \textbf{2D Axisymmetric} as \textbf{Space Dimension}\\
3) Choose 2D \textbf{AC/DC} module and add \textbf{Electric Currents} sub module in \textbf{Physics}.\\
4) Choose \textbf{Heat Transfer Module} and add \textbf{Heat Transfer in Solids} submodule in \textbf{Physics}.\\
5) Create the \textbf{Geometry} of the MIM structure as in Fig(\ref{Fig:MIM}).\\
6) Create \textbf{Blank Materials} in the \textbf{Materials} node and add material parameters given in Table I to create the required materials.\\
7) Assign the materials to the corresponding domains.\\
8) The \textbf{Heat Transfer in Solids} submodule will have four different necessary default subnodes - add \textbf{Temperature} boundary condition and select the top boundary of the top electrode and bottom boundary of the bottom electrode and choose 300K in the user defined temperature section.\\
9) The \textbf{Electric Currents} submodule also has four different necessary default subnodes - add \textbf{Electric Potential} boundary condition, select the top boundary of the top electrode and set 0.5 V in the \textbf{Electric Potential box}, add \textbf{Ground} boundary condition, select the bottom boundary of the bottom electrode.\\
10) In \textbf{Multiphysics} node select all the domain in \textbf{Electromagnetic Heat Source} sub-node to couple the \textbf{Electric Currents} submodule and \textbf{Heat Transfer in Solids} submodule,\\
11) Create \textbf{Mesh}.\\
12) Select \textbf{Study}.\\
13) Obtain results in desired form from the \textbf{Results} node.
\section{1D Heat Transfer}\label{appendix1}
In this appendix, we present the solution to the 1D heat transfer problem discussed in Section \ref{sec:1D}.
Multiplying Eq.(\ref{eq:heateq2}) with $dT/dz$ and integrating yields,
\begin{equation}\label{appen:Integrate1}
\int_{0}^{(T'(z))^{2}}d\left(\frac{dT}{dz}\right)^{2}=-\frac{2E^2}{L}\int_{T_\mathrm{max}}^{T}\frac{dT}{T}.
\end{equation}
or,
\begin{equation}\label{appen:Integrate2}
\frac{dT}{dz} = \pm\sqrt{\frac{2E^{2}}{L}}\sqrt{\ln\left(\frac{T_\mathrm{max}}{T}\right)}
\end{equation}
where the origin is at the center of filament.
Define $t\equiv T/ T_\textrm{max}$. Integrating Eq. \ref{appen:Integrate2} from $t(0)= 1$ to $t(z) = T/T_\textrm{max}$ gives the temperature distribution in the filament.
\begin{equation}\label{appen:Integrate4}
\int_{1}^{T/T_\mathrm{max}}\frac{dt}{\sqrt{\ln(1/t)}}=\pm\frac{1}{T_\mathrm{max}}.\sqrt{\frac{2E^{2}}{L}}\int_{0}^{z}dz.
\end{equation}
With a substitution of $y^2 = \ln(1/t)$, the integration changes to,
\begin{equation}\label{appen:Integrate5}
-2\int_{0}^{\sqrt{\ln(T_\mathrm{max}/T)}}\exp(-y^2)dy = \pm \frac{1}{T_\mathrm{max}}.\sqrt{\frac{2E^{2}}{L}} z.
\end{equation}
The LHS of the Eq. (\ref{appen:Integrate5}) is an error function. Hence we get the following temperature distribution after the integration.
\begin{equation}\label{appen:TempDist1}
T(z)=\frac{T_\mathrm{max}}{\exp\left(\left(\mathrm{erf}^{-1}\left(\frac{\mp z}{T_\mathrm{max}}\sqrt{\frac{2E^{2}}{\pi L}}\right)\right)^2\right)}.
\end{equation}
The maximum temperature can be calculated by integrating Eq. (\ref{appen:Integrate2}) from $t(0)=1$ to $t(h/2) =T_j/T_\textrm{max}$. The integration results in a transcendental equation of the form,
\begin{equation}\label{appen:T_max}
\frac{T_\mathrm{max}}{T_j}\mathrm{erf}\left(\sqrt{\ln\left(\frac{T_\mathrm{max}}{T_j}\right)}\right) = \mp\frac{h}{2 T_j}\sqrt{\frac{2E^{2}}{\pi L}}.
\end{equation}
which can be solved numerically.
\section{Radial Heat Transfer}\label{appendix2}
In this appendix, we present more in detail derivation of Eq. (\ref{eq:divT}) for the radial heat transfer and its solution in Section \ref{sec:rad}.
Writing the heat equation in cylindrical coordinate,
\begin{equation}\label{appen:heat2}
-\kappa_i\left[\frac{1}{\rho}\frac{\partial}{\partial \rho}\rho\frac{\partial}{\partial \rho}T(\rho,z) +\frac{\partial^2}{\partial z^2}T(\rho ,z)\right] = 0.
\end{equation}
Since, $h/H \ll 1$ the ratio $\delta T /T \ll 1$ along $z$-direction, hence replacing $T(\rho,z)$ by average temperature $\overline{T(\rho)}$ and integrating along z-axis from $z=-h/2$ to $z=h/2$, Eq.(\ref{appen:heat2})
\begin{equation}\label{appen:heat4}
\frac{h}{\rho}\frac{d}{d \rho}\rho\frac{d \overline{T(\rho)}}{d \rho} + \left[\frac{\partial T(\rho,z)}{\partial z}|_{z=h/2} - \frac{\partial T(\rho,z)}{\partial z}|_{z=-h/2}\right]=0.
\end{equation}
The second term of the LHS of the Eq.(\ref{appen:heat4}) can be reduced to averages after applying the Neumann boundary condition at the metal-insulator interface. The condition states that,
\begin{equation}\label{appen:BC1}
-\kappa_i\frac{\partial T(\rho,z)}{\partial z}=-\kappa_m\frac{\partial T(\rho,z)}{\partial z}.
\end{equation}
The temperature gradient in the electrode is replaced by the slope $\Delta T /\Delta z$ and also by using the average temperature $\overline{T}(\rho)$ as the boundary temperature of the metal-insulator junction, Eq.(\ref{appen:heat4}) becomes,
\begin{equation}\label{appen:heat5}
\frac{h}{\rho}\frac{d}{d \rho}\rho\frac{d \overline{T}(\rho)}{d \rho} + 2\frac{\kappa_m}{\kappa_i}\left(\frac{T_0 -\overline{T}(\rho)}{H}\right)=0.
\end{equation}
Eq.(\ref{appen:heat5}) can be rewritten as,
\begin{equation}\label{appen:bessel}
\rho^2\frac{d^2\overline{T(\rho)}}{d\rho^2}+\rho\frac{d\overline{T}(\rho)}{d\rho}-\beta^2 \rho^2( \overline{T}(\rho)-T_0) = 0 .
\end{equation}
The solution to Eq. (\ref{appen:bessel}) is the linear combination of zeroth order modified bessel functions $I_0$ and $K_0$,
\begin{equation}\label{appen:tempdist}
\overline{T}(\rho)=C_1 I_0(\beta\rho)+C_2 K_0[\beta\rho]+ T_0.
\end{equation}
where, the constants $C_1$ and $C_2$ is determined by the Neumann boundary condition. We omit $I_0$($C_1 = 0$) from the solution as it increases with $\rho$. Hence the radial temperature distribution is given by,
\begin{equation}\label{appen:tempdist1}
\overline{T(\rho)}=C_2 K_0(\beta\rho)+ T_0.
\end{equation}
The Neumann boundary condition becomes,
\begin{equation}\label{appen:BC1}
-\kappa_f\frac{\partial T(\rho,z)}{\partial z}=-\kappa_i\frac{\partial T(\rho,z)}{\partial z}.
\end{equation}
The filament receives power $P=V^2/R$ from the external bias source, where the electrical resistance $R$ is given by sum of electrodes and filament resistances $R=h/\sigma_f \pi r_f^2+2H/\sigma_m \pi r_f^2$, assuming the current takes the shortest path through electrode to filament having the same cross section area as the filament. The power generated by the filament is given by the product of heat flux ($-\kappa_f dT/d\rho$) and the surface area of the cylinder at $r=d/2$. Using the boundary condition and equating the power received and generated we obtain,
\begin{eqnarray}\label{appen:BC2}
&&C_2=\frac{-1}{\beta K_1(\beta\rho)}\frac{d\overline{T}(\rho)}{d\rho} \qquad\mathrm{and,}\\
&&\frac{d \overline{T}(\rho)}{d\rho}|_{\rho=d/2}=\frac{-V^2 d}{4h\kappa_i(h/\sigma_f+2H/\sigma_m)}.
\end{eqnarray}
Substituting the latter equations, the radial temperature distribution in the insulator becomes,
\begin{equation}\label{appen:tempdist}
\overline{T}(\rho) = \frac{V^2 d}{4 h \kappa_i \beta (h/\sigma_f+2H/\sigma_m)K_1(\beta d/2)} K_0(\beta\rho) + T_0.
\end{equation}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,913 |
namespace Microsoft.Zelig.Runtime
{
using System;
using System.Runtime.CompilerServices;
using TS = Microsoft.Zelig.Runtime.TypeSystem;
public abstract class MarkAndSweepCollector : GarbageCollectionManager
{
protected interface MarkAndSweepStackWalker
{
void Process( Processor.Context ctx );
}
//--//
struct MarkStackForArrays
{
//
// State
//
private UIntPtr m_address;
private uint m_elementSize;
private int m_numOfElements;
private TS.VTable m_vTableElement;
//
// Helper Methods
//
#if !GC_PRECISE_PROFILING
[Inline]
#endif
internal unsafe void Push( ArrayImpl array ,
uint elementSize ,
int numOfElements ,
TS.VTable vTableElement )
{
m_address = new UIntPtr( array.GetDataPointer() );
m_elementSize = elementSize;
m_numOfElements = numOfElements;
m_vTableElement = vTableElement;
}
#if !GC_PRECISE_PROFILING
[Inline]
#endif
internal unsafe void Visit( MarkAndSweepCollector owner )
{
UIntPtr address = m_address;
TS.VTable vTable = m_vTableElement;
if(--m_numOfElements == 0)
{
//
// Pop entry.
//
m_address = new UIntPtr();
m_vTableElement = null;
owner.m_markStackForArrays_Pos--;
}
else
{
//
// Move to next element.
//
m_address = AddressMath.Increment( m_address, m_elementSize );
}
if(vTable != null)
{
owner.VisitHeapObjectFields( address, vTable );
}
else
{
UIntPtr* ptr = (UIntPtr*)address.ToPointer();
UIntPtr obj = ptr[0];
if(obj != UIntPtr.Zero)
{
owner.VisitHeapObject( obj );
}
}
}
}
//
// State
//
private OutOfMemoryException m_outOfMemoryException;
private MarkAndSweepStackWalker m_stackWalker;
private bool m_fFirstLevel;
private UIntPtr[] m_maskStackForObjects;
private int m_maskStackForObjects_Pos;
private MarkStackForArrays[] m_markStackForArrays;
private int m_markStackForArrays_Pos;
private ObjectHeader.GarbageCollectorFlags m_markForNonHeap;
private uint[] m_trackFreeBlocks;
private int m_perf_gapCount;
private int m_perf_freeCount;
private int m_perf_deadCount;
private int m_perf_objectCount;
private int m_perf_stat_calls;
private uint m_perf_stat_freeMem;
private long m_perf_time_baseline;
private long m_perf_time_start;
private long m_perf_time_walk;
private long m_perf_time_global;
private long m_perf_time_sweep;
private long m_perf_time_ret;
//
// Helper Methods
//
protected virtual int MarkStackForObjectsSize
{
get { return 1024; }
}
protected virtual int MarkStackForArraysSize
{
get { return 128; }
}
//--//
protected abstract MarkAndSweepStackWalker CreateStackWalker( );
public unsafe override void InitializeGarbageCollectionManager()
{
m_outOfMemoryException = new OutOfMemoryException();
m_stackWalker = CreateStackWalker();
m_maskStackForObjects = new UIntPtr [ MarkStackForObjectsSize ];
m_markStackForArrays = new MarkStackForArrays[ MarkStackForArraysSize ];
if(Configuration.TraceFreeBlocks)
{
m_trackFreeBlocks = new uint[32];
}
//--//
foreach(var handler in this.ExtensionHandlers)
{
handler.Initialize();
}
//--//
MemorySegment* heapLow = null;
MemorySegment* heapHigh = null;
for(MemorySegment* heap = MemoryManager.Instance.StartOfHeap; heap != null; heap = heap->Next)
{
if(heapLow == null || AddressMath.IsGreaterThan( heapLow->Beginning, heap->Beginning ))
{
heapLow = heap;
}
if(heapHigh == null || AddressMath.IsLessThan( heapHigh->End, heap->End ))
{
heapHigh = heap;
}
}
BugCheck.Assert( heapLow != null && heapHigh != null, BugCheck.StopCode.NoMemory );
BrickTable.Instance.Initialize( heapLow->Beginning.ToUInt32(), heapHigh->End.ToUInt32() );
RebuildBrickTable();
if(Configuration.ValidateHeap)
{
VerifyBrickTable();
}
}
[Inline]
public override void NotifyNewObject( UIntPtr ptr ,
uint size )
{
BrickTable.Instance.MarkObject( ptr, size );
}
public override UIntPtr FindObject( UIntPtr interiorPtr )
{
UIntPtr address = BrickTable.Instance.FindLowerBoundForObjectPointer( interiorPtr );
if(address != UIntPtr.Zero)
{
while(true)
{
ObjectHeader oh = ObjectHeader.CastAsObjectHeader( address );
ObjectHeader.GarbageCollectorFlags flags = oh.GarbageCollectorState;
switch(flags)
{
case ObjectHeader.GarbageCollectorFlags.FreeBlock | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.FreeBlock | ObjectHeader.GarbageCollectorFlags.Marked :
{
UIntPtr nextAddress = oh.GetNextObjectPointer();
if(AddressMath.IsLessThan( interiorPtr, nextAddress ))
{
//
// Don't return the address of a heap free block.
//
return UIntPtr.Zero;
}
address = nextAddress;
}
break;
case ObjectHeader.GarbageCollectorFlags.GapPlug | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.GapPlug | ObjectHeader.GarbageCollectorFlags.Marked :
address = AddressMath.Increment( address, sizeof(uint) );
break;
case ObjectHeader.GarbageCollectorFlags.ReadOnlyObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.ReadOnlyObject | ObjectHeader.GarbageCollectorFlags.Marked :
BugCheck.Raise( BugCheck.StopCode.HeapCorruptionDetected );
return UIntPtr.Zero;
case ObjectHeader.GarbageCollectorFlags.UnreclaimableObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.UnreclaimableObject | ObjectHeader.GarbageCollectorFlags.Marked :
BugCheck.Raise( BugCheck.StopCode.HeapCorruptionDetected );
return UIntPtr.Zero;
case ObjectHeader.GarbageCollectorFlags.NormalObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.NormalObject | ObjectHeader.GarbageCollectorFlags.Marked :
case ObjectHeader.GarbageCollectorFlags.SpecialHandlerObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.SpecialHandlerObject | ObjectHeader.GarbageCollectorFlags.Marked:
case ObjectHeader.GarbageCollectorFlags.AllocatedRawBytes | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.AllocatedRawBytes | ObjectHeader.GarbageCollectorFlags.Marked:
{
UIntPtr nextAddress = oh.GetNextObjectPointer();
if(AddressMath.IsLessThan( interiorPtr, nextAddress ))
{
return oh.Pack( ).ToPointer( );
}
address = nextAddress;
}
break;
default:
BugCheck.Raise( BugCheck.StopCode.HeapCorruptionDetected );
return UIntPtr.Zero;
}
}
}
return UIntPtr.Zero;
}
public override uint Collect()
{
#if DEBUG_MARK_SWEEP
BugCheck.Log( "Collecting on Thread 0x%x", (int)ObjectHeader.Unpack( ThreadManager.Instance.CurrentThread ).ToPointer( ) );
#endif
if(Configuration.CollectPerformanceStatistics)
{
m_perf_stat_calls++;
m_perf_time_baseline = System.Diagnostics.Stopwatch.GetTimestamp();
}
uint mem;
long gcTime;
// Take the memory manager lock so we make sure there's no in-process memory allocation as we
// mark and sweep the memory.
using(SmartHandles.YieldLockHolder hnd = new SmartHandles.YieldLockHolder( MemoryManager.Lock ))
{
while(true)
{
using(SmartHandles.InterruptState hnd2 = SmartHandles.InterruptState.Disable())
{
if(IsThisAGoodPlaceToStopTheWorld())
{
if(Configuration.CollectPerformanceStatistics)
{
m_perf_time_start = System.Diagnostics.Stopwatch.GetTimestamp() - m_perf_time_baseline;
}
long gc_start = 0;
long gc_stop = 0;
if(Configuration.CollectMinimalPerformanceStatistics)
{
gc_start = System.Diagnostics.Stopwatch.GetTimestamp();
}
StartCollection();
if(Configuration.CollectMinimalPerformanceStatistics)
{
gc_stop = System.Diagnostics.Stopwatch.GetTimestamp();
}
gcTime = gc_stop - gc_start;
mem = MemoryManager.Instance.AvailableMemory;
if(Configuration.CollectPerformanceStatistics)
{
m_perf_time_ret = System.Diagnostics.Stopwatch.GetTimestamp() - m_perf_time_baseline;
m_perf_stat_freeMem = mem;
}
break;
}
}
ThreadImpl.CurrentThread.Yield();
}
}
foreach(var handler in this.ExtensionHandlers)
{
handler.RestartExecution();
}
DumpFreeBlockTracking();
if(Configuration.CollectMinimalPerformanceStatistics)
{
BugCheck.WriteLineFormat( "GC: Free mem: {0} Time: {1}msec", mem, ToMilliseconds( gcTime ) );
}
if(Configuration.CollectPerformanceStatistics)
{
BugCheck.WriteLineFormat( "m_perf_gapCount : {0,9}", m_perf_gapCount );
BugCheck.WriteLineFormat( "m_perf_freeCount : {0,9}", m_perf_freeCount );
BugCheck.WriteLineFormat( "m_perf_deadCount : {0,9}", m_perf_deadCount );
BugCheck.WriteLineFormat( "m_perf_objectCount: {0,9}", m_perf_objectCount );
BugCheck.WriteLineFormat( "m_perf_time_start : {0}msec", ToMilliseconds( m_perf_time_start ) );
BugCheck.WriteLineFormat( "m_perf_time_walk : {0}msec", ToMilliseconds( m_perf_time_walk ) );
BugCheck.WriteLineFormat( "m_perf_time_global: {0}msec", ToMilliseconds( m_perf_time_global ) );
BugCheck.WriteLineFormat( "m_perf_time_sweep : {0}msec", ToMilliseconds( m_perf_time_sweep ) );
BugCheck.WriteLineFormat( "m_perf_time_ret : {0}msec", ToMilliseconds( m_perf_time_ret ) );
}
return mem;
}
private static int ToMilliseconds( long ticks )
{
return (int)(1000.0 * ticks / System.Diagnostics.Stopwatch.Frequency);
}
public override long GetTotalMemory()
{
return MemoryManager.Instance.AllocatedMemory;
}
public override void ThrowOutOfMemory( TS.VTable vTable )
{
throw m_outOfMemoryException;
}
public override bool IsMarked( object obj )
{
if(obj == null)
{
return true;
}
ObjectHeader oh = ObjectHeader.Unpack( obj );
ObjectHeader.GarbageCollectorFlags flags = oh.GarbageCollectorState;
switch(flags)
{
case ObjectHeader.GarbageCollectorFlags.ReadOnlyObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.ReadOnlyObject | ObjectHeader.GarbageCollectorFlags.Marked :
case ObjectHeader.GarbageCollectorFlags.UnreclaimableObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.UnreclaimableObject | ObjectHeader.GarbageCollectorFlags.Marked :
return true;
case ObjectHeader.GarbageCollectorFlags.NormalObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.SpecialHandlerObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
return false;
case ObjectHeader.GarbageCollectorFlags.NormalObject | ObjectHeader.GarbageCollectorFlags.Marked :
case ObjectHeader.GarbageCollectorFlags.SpecialHandlerObject | ObjectHeader.GarbageCollectorFlags.Marked :
return true;
default:
BugCheck.Raise( BugCheck.StopCode.HeapCorruptionDetected );
return false;
}
}
public override void ExtendMarking( object obj )
{
var objImpl = (ObjectImpl)obj;
if(objImpl != null)
{
VisitHeapObject( objImpl.ToPointer() );
}
}
//--//
protected virtual bool IsThisAGoodPlaceToStopTheWorld()
{
ThreadImpl thisThread = ThreadImpl.CurrentThread;
Processor.Context ctx = thisThread.ThrowContext; // Reuse the throw context for the current thread to unwind the stack.
//
// TODO: LT72: Only the RT.Threadmanager can implement this method correctly at this time
//
ThreadManager tm = ThreadManager.Instance;
for(KernelNode< ThreadImpl > node = tm.StartOfForwardWalkThroughAllThreads; node.IsValidForForwardMove; node = node.Next)
{
ThreadImpl thread = node.Target;
if(thread == thisThread)
{
continue;
}
if(thread.IsAtSafePoint( ctx ) == false)
{
return false;
}
}
return true;
}
private void StartCollection()
{
m_fFirstLevel = true;
m_maskStackForObjects_Pos = -1;
m_markStackForArrays_Pos = -1;
m_markForNonHeap ^= ObjectHeader.GarbageCollectorFlags.Marked;
foreach(var handler in this.ExtensionHandlers)
{
handler.StartOfMarkPhase( this );
}
WalkStackFrames();
if(Configuration.CollectPerformanceStatistics)
{
m_perf_time_walk = System.Diagnostics.Stopwatch.GetTimestamp() - m_perf_time_baseline;
}
MarkGlobalRoot();
ProcessMarkStack();
foreach(var handler in this.ExtensionHandlers)
{
handler.EndOfMarkPhase( this );
}
if(Configuration.CollectPerformanceStatistics)
{
m_perf_time_global = System.Diagnostics.Stopwatch.GetTimestamp() - m_perf_time_baseline;
}
foreach(var handler in this.ExtensionHandlers)
{
handler.StartOfSweepPhase( this );
}
Sweep();
foreach(var handler in this.ExtensionHandlers)
{
handler.EndOfSweepPhase( this );
}
if(Configuration.CollectPerformanceStatistics)
{
m_perf_time_sweep = System.Diagnostics.Stopwatch.GetTimestamp() - m_perf_time_baseline;
}
if(Configuration.ValidateHeap)
{
VerifyBrickTable();
}
}
protected virtual void WalkStackFrames()
{
ThreadImpl thisThread = ThreadImpl.CurrentThread;
Processor.Context ctx = thisThread.ThrowContext; // Reuse the throw context for the current thread to unwind the stack.
//
// TODO: LT72: Only the RT.Threadmanager can implement this method correctly at this time
//
ThreadManager tm = ThreadManager.Instance;
for(KernelNode< ThreadImpl > node = tm.StartOfForwardWalkThroughAllThreads; node.IsValidForForwardMove; node = node.Next)
{
ThreadImpl thread = node.Target;
if(thread == thisThread)
{
ctx.Populate();
}
else
{
ctx.Populate( thread.SwappedOutContext );
}
#if DEBUG_MARK_SWEEP
BugCheck.Log(
"Walking thread stack 0x%x, 0x%x -> 0x%x",
(int)ObjectHeader.Unpack( thread ).ToPointer( ),
(int)ctx.StackPointer,
(int)ctx.BaseStackPointer );
#endif
m_stackWalker.Process( ctx );
}
}
private void MarkGlobalRoot()
{
object root = TS.GlobalRoot.Instance;
UIntPtr address = ((ObjectImpl)root).ToPointer();
VisitHeapObject( address );
}
private unsafe void Sweep()
{
ResetFreeBlockTracking();
var brickTable = BrickTable.Instance;
brickTable.Reset();
if(Configuration.CollectPerformanceStatistics)
{
m_perf_gapCount = 0;
m_perf_freeCount = 0;
m_perf_deadCount = 0;
m_perf_objectCount = 0;
}
for(MemorySegment* heap = MemoryManager.Instance.StartOfHeap; heap != null; heap = heap->Next)
{
UIntPtr address = heap->FirstBlock;
UIntPtr end = heap->End;
bool fLastWasFree = false;
UIntPtr freeStart = UIntPtr.Zero;
heap->FirstFreeBlock = null;
heap->LastFreeBlock = null;
while(AddressMath.IsLessThan( address, end ))
{
ObjectHeader oh = ObjectHeader.CastAsObjectHeader( address );
ObjectHeader.GarbageCollectorFlags flags = oh.GarbageCollectorState;
bool fFree = true;
UIntPtr addressNext;
switch(flags)
{
case ObjectHeader.GarbageCollectorFlags.FreeBlock | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.FreeBlock | ObjectHeader.GarbageCollectorFlags.Marked :
if(Configuration.CollectPerformanceStatistics)
{
m_perf_freeCount++;
}
addressNext = oh.GetNextObjectPointer();
break;
case ObjectHeader.GarbageCollectorFlags.GapPlug | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.GapPlug | ObjectHeader.GarbageCollectorFlags.Marked :
if(Configuration.CollectPerformanceStatistics)
{
m_perf_gapCount++;
}
addressNext = AddressMath.Increment( address, sizeof(uint) );
break;
case ObjectHeader.GarbageCollectorFlags.ReadOnlyObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.ReadOnlyObject | ObjectHeader.GarbageCollectorFlags.Marked :
BugCheck.Raise( BugCheck.StopCode.HeapCorruptionDetected );
return;
case ObjectHeader.GarbageCollectorFlags.UnreclaimableObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.UnreclaimableObject | ObjectHeader.GarbageCollectorFlags.Marked :
BugCheck.Raise( BugCheck.StopCode.HeapCorruptionDetected );
return;
case ObjectHeader.GarbageCollectorFlags.NormalObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.AllocatedRawBytes | ObjectHeader.GarbageCollectorFlags.Unmarked:
if(Configuration.CollectPerformanceStatistics)
{
m_perf_deadCount++;
}
#if DEBUG_MARK_SWEEP
BugCheck.Log( "Object swept up: 0x%08x, size: %d", (int)oh.ToPointer( ), (int)oh.TotalSize );
String name;
if(flags == ObjectHeader.GarbageCollectorFlags.AllocatedRawBytes)
{
name = "<raw bytes>";
}
else
{
var type = oh.VirtualTable.TypeInfo;
if(type is TS.SzArrayReferenceTypeRepresentation)
{
var arrayType = (TS.SzArrayReferenceTypeRepresentation)type;
BugCheck.Log( "Array of:" );
name = arrayType.UnderlyingType.Name ?? "<unknown>";
}
else
{
name = type?.Name ?? "<unknown>";
}
}
BugCheck.Log( name );
#endif
addressNext = oh.GetNextObjectPointer();
break;
case ObjectHeader.GarbageCollectorFlags.NormalObject | ObjectHeader.GarbageCollectorFlags.Marked :
case ObjectHeader.GarbageCollectorFlags.AllocatedRawBytes | ObjectHeader.GarbageCollectorFlags.Marked :
if(Configuration.CollectPerformanceStatistics)
{
m_perf_objectCount++;
}
addressNext = oh.GetNextObjectPointer();
oh.GarbageCollectorState = (flags & ~ObjectHeader.GarbageCollectorFlags.Marked);
brickTable.MarkObject( address, AddressMath.RangeSize( address, addressNext ) );
fFree = false;
break;
case ObjectHeader.GarbageCollectorFlags.SpecialHandlerObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
if(Configuration.CollectPerformanceStatistics)
{
m_perf_deadCount++;
}
addressNext = oh.GetNextObjectPointer();
break;
case ObjectHeader.GarbageCollectorFlags.SpecialHandlerObject | ObjectHeader.GarbageCollectorFlags.Marked :
{
if(Configuration.CollectPerformanceStatistics)
{
m_perf_objectCount++;
}
addressNext = oh.GetNextObjectPointer();
var ext = FindExtensionHandler( oh.VirtualTable );
if(ext == null)
{
BugCheck.Raise( BugCheck.StopCode.HeapCorruptionDetected );
}
else
{
ext.Sweep( this, oh.Pack() );
}
oh.GarbageCollectorState = (flags & ~ObjectHeader.GarbageCollectorFlags.Marked);
brickTable.MarkObject( address, AddressMath.RangeSize( address, addressNext ) );
fFree = false;
break;
}
default:
BugCheck.Raise( BugCheck.StopCode.HeapCorruptionDetected );
return;
}
if(fLastWasFree != fFree)
{
if(fFree)
{
freeStart = address;
}
else
{
TrackFreeBlock( freeStart, address );
heap->LinkNewFreeBlock( freeStart, address );
}
fLastWasFree = fFree;
}
address = addressNext;
}
if(fLastWasFree)
{
TrackFreeBlock( freeStart, end );
heap->LinkNewFreeBlock( freeStart, end );
}
}
}
//--//
private void ResetFreeBlockTracking()
{
if(Configuration.TraceFreeBlocks)
{
Array.Clear( m_trackFreeBlocks, 0, m_trackFreeBlocks.Length );
}
}
private void TrackFreeBlock( UIntPtr start ,
UIntPtr end )
{
if(Configuration.TraceFreeBlocks)
{
uint size = AddressMath.RangeSize( start, end );
for(int i = 0; i < 32; i++)
{
if(size < (1u << i))
{
m_trackFreeBlocks[i]++;
break;
}
}
}
}
private void DumpFreeBlockTracking()
{
if(Configuration.TraceFreeBlocks)
{
for(int i = 0; i < 32; i++)
{
if(m_trackFreeBlocks[i] != 0)
{
BugCheck.WriteLineFormat( "Size: {0,9} = {1}", 1u << i, m_trackFreeBlocks[i] );
}
}
}
}
//--//
[NoInline]
protected void VisitInternalPointer( UIntPtr address )
{
VisitInternalPointerInline( address );
}
[NoInline]
protected void VisitHeapObject( UIntPtr address )
{
VisitHeapObjectInline( address );
}
#if !GC_PRECISE_PROFILING
[Inline]
#endif
private void VisitInternalPointerInline( UIntPtr address )
{
UIntPtr objAddress = FindObject( address );
if(objAddress != UIntPtr.Zero)
{
VisitHeapObject( objAddress );
}
}
#if !GC_PRECISE_PROFILING
[Inline]
#endif
private void VisitHeapObjectInline( UIntPtr address )
{
if(Configuration.ValidateHeap)
{
BugCheck.Assert( MemoryManager.Instance.RefersToMemory( address ), BugCheck.StopCode.NotAMemoryReference );
}
ObjectHeader oh = ObjectHeader.Unpack( ObjectImpl.FromPointer( address ) );
ObjectHeader.GarbageCollectorFlags flags = oh.GarbageCollectorState;
switch(flags)
{
case ObjectHeader.GarbageCollectorFlags.FreeBlock | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.FreeBlock | ObjectHeader.GarbageCollectorFlags.Marked :
return;
case ObjectHeader.GarbageCollectorFlags.GapPlug | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.GapPlug | ObjectHeader.GarbageCollectorFlags.Marked :
return;
case ObjectHeader.GarbageCollectorFlags.ReadOnlyObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.ReadOnlyObject | ObjectHeader.GarbageCollectorFlags.Marked :
return;
case ObjectHeader.GarbageCollectorFlags.AllocatedRawBytes | ObjectHeader.GarbageCollectorFlags.Unmarked:
oh.GarbageCollectorState = flags | ObjectHeader.GarbageCollectorFlags.Marked;
return;
case ObjectHeader.GarbageCollectorFlags.AllocatedRawBytes | ObjectHeader.GarbageCollectorFlags.Marked:
return;
case ObjectHeader.GarbageCollectorFlags.UnreclaimableObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
if(m_markForNonHeap == ObjectHeader.GarbageCollectorFlags.Unmarked)
{
return;
}
flags ^= ObjectHeader.GarbageCollectorFlags.Marked;
break;
case ObjectHeader.GarbageCollectorFlags.UnreclaimableObject | ObjectHeader.GarbageCollectorFlags.Marked :
if(m_markForNonHeap == ObjectHeader.GarbageCollectorFlags.Marked)
{
return;
}
flags ^= ObjectHeader.GarbageCollectorFlags.Marked;
break;
case ObjectHeader.GarbageCollectorFlags.NormalObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
flags |= ObjectHeader.GarbageCollectorFlags.Marked;
break;
case ObjectHeader.GarbageCollectorFlags.NormalObject | ObjectHeader.GarbageCollectorFlags.Marked :
return;
case ObjectHeader.GarbageCollectorFlags.SpecialHandlerObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
{
var ext = FindExtensionHandler( oh.VirtualTable );
if(ext == null)
{
BugCheck.Raise( BugCheck.StopCode.HeapCorruptionDetected );
}
else
{
ext.Mark( this, oh.Pack() );
}
flags |= ObjectHeader.GarbageCollectorFlags.Marked;
break;
}
case ObjectHeader.GarbageCollectorFlags.SpecialHandlerObject | ObjectHeader.GarbageCollectorFlags.Marked :
return;
default:
{
BugCheck.Log ( "Corruption! address=0x%08x, flags=0x%08x", (int)address.ToUInt32( ), (int)flags );
BugCheck.Raise( BugCheck.StopCode.HeapCorruptionDetected );
}
return;
}
oh.GarbageCollectorState = flags;
TS.VTable vTable = oh.VirtualTable;
if(vTable.IsArray)
{
PushArrayReference( address, vTable );
}
else
{
PushObjectReference( address, vTable );
}
}
[NoInline]
private void VisitHeapObjectFields( UIntPtr fieldAddress ,
TS.VTable vTable )
{
VisitHeapObjectFieldsInline( fieldAddress, vTable );
}
#if !GC_PRECISE_PROFILING
[Inline]
#endif
private void VisitHeapObjectFieldsInline( UIntPtr fieldAddress ,
TS.VTable vTable )
{
TS.GCInfo.Pointer[] pointers = vTable.GCInfo.Pointers;
int numOfPointers = pointers.Length;
for(int i = 0; i < numOfPointers; i++)
{
VisitHeapObjectField( fieldAddress, ref pointers[i] );
}
}
#if !GC_PRECISE_PROFILING
[Inline]
#endif
private unsafe void VisitHeapObjectField( UIntPtr fieldAddress ,
ref TS.GCInfo.Pointer pointer )
{
UIntPtr* field = (UIntPtr*)fieldAddress.ToPointer( );
UIntPtr referenceAddress = field[pointer.OffsetInWords];
if(referenceAddress != UIntPtr.Zero)
{
switch(pointer.Kind)
{
case TS.GCInfo.Kind.Heap:
VisitHeapObjectInline( referenceAddress );
break;
case TS.GCInfo.Kind.Internal:
case TS.GCInfo.Kind.Potential:
VisitInternalPointerInline( referenceAddress );
break;
}
}
}
#if !GC_PRECISE_PROFILING
[Inline]
#endif
private void PushObjectReference( UIntPtr address ,
TS.VTable vTable )
{
TS.GCInfo.Pointer[] pointers = vTable.GCInfo.Pointers;
if(pointers == null)
{
//
// No pointers, nothing to do.
//
return;
}
if(m_fFirstLevel)
{
m_fFirstLevel = false;
int numOfPointers = pointers.Length;
UIntPtr fieldAddress = ObjectImpl.FromPointer( address ).GetFieldPointer( );
for(int i = 0; i < numOfPointers; i++)
{
VisitHeapObjectField( fieldAddress, ref pointers[i] );
}
ProcessMarkStack();
m_fFirstLevel = true;
}
else
{
BugCheck.Assert( m_maskStackForObjects_Pos < MarkStackForObjectsSize - 1, BugCheck.StopCode.NoMarkStack );
m_maskStackForObjects[++m_maskStackForObjects_Pos] = address;
}
}
#if !GC_PRECISE_PROFILING
[Inline]
#endif
private void PushArrayReference( UIntPtr address ,
TS.VTable vTable )
{
ArrayImpl array = ArrayImpl.CastAsArray( ObjectImpl.FromPointer( address ) );
int numOfElements = array.Length;
if(numOfElements == 0)
{
//
// Empty array, nothing to do.
//
return;
}
TS.VTable vTableElement = vTable.TypeInfo.ContainedType.VirtualTable;
if(vTableElement.IsValueType)
{
if(vTableElement.GCInfo.Pointers == null)
{
//
// It's an array of value types with no pointers, no need to push it.
//
return;
}
//
// The address is for an array with embedded structures.
//
}
else
{
//
// The address is for an object reference.
//
vTableElement = null;
}
BugCheck.Assert( m_markStackForArrays_Pos < MarkStackForArraysSize - 1, BugCheck.StopCode.NoMarkStack );
m_markStackForArrays[++m_markStackForArrays_Pos].Push( array, vTable.ElementSize, numOfElements, vTableElement );
if(m_fFirstLevel)
{
m_fFirstLevel = false;
ProcessMarkStack();
m_fFirstLevel = true;
}
}
private void ProcessMarkStack()
{
while(true)
{
int pos;
pos = m_maskStackForObjects_Pos;
if(pos >= 0)
{
UIntPtr address = m_maskStackForObjects[pos];
m_maskStackForObjects_Pos = pos - 1;
ObjectImpl obj = ObjectImpl.FromPointer( address );
TS.VTable vTable = TS.VTable.Get( obj );
VisitHeapObjectFieldsInline( obj.GetFieldPointer(), vTable );
continue;
}
pos = m_markStackForArrays_Pos;
if(pos >= 0)
{
m_markStackForArrays[pos].Visit( this );
continue;
}
break;
}
}
//--//
private unsafe void RebuildBrickTable()
{
var brickTable = BrickTable.Instance;
brickTable.Reset();
for(MemorySegment* heap = MemoryManager.Instance.StartOfHeap; heap != null; heap = heap->Next)
{
UIntPtr address = heap->FirstBlock;
UIntPtr end = heap->End;
while(AddressMath.IsLessThan( address, end ))
{
ObjectHeader oh = ObjectHeader.CastAsObjectHeader( address );
ObjectHeader.GarbageCollectorFlags flags = oh.GarbageCollectorState;
switch(flags)
{
case ObjectHeader.GarbageCollectorFlags.FreeBlock | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.FreeBlock | ObjectHeader.GarbageCollectorFlags.Marked :
{
UIntPtr addressNext = oh.GetNextObjectPointer();
//
// The arrays used to wrap the free blocks are marked as outside the heap.
// We should not add them to the brick table, because otherwise the whole brick table will look allocated
// and we don't care for pointers into the free list.
//
address = addressNext;
}
break;
case ObjectHeader.GarbageCollectorFlags.GapPlug | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.GapPlug | ObjectHeader.GarbageCollectorFlags.Marked :
address = AddressMath.Increment( address, sizeof(uint) );
break;
case ObjectHeader.GarbageCollectorFlags.ReadOnlyObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.ReadOnlyObject | ObjectHeader.GarbageCollectorFlags.Marked :
BugCheck.Raise( BugCheck.StopCode.HeapCorruptionDetected );
return;
case ObjectHeader.GarbageCollectorFlags.UnreclaimableObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.UnreclaimableObject | ObjectHeader.GarbageCollectorFlags.Marked :
BugCheck.Raise( BugCheck.StopCode.HeapCorruptionDetected );
return;
case ObjectHeader.GarbageCollectorFlags.NormalObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.NormalObject | ObjectHeader.GarbageCollectorFlags.Marked :
case ObjectHeader.GarbageCollectorFlags.SpecialHandlerObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.SpecialHandlerObject | ObjectHeader.GarbageCollectorFlags.Marked :
case ObjectHeader.GarbageCollectorFlags.AllocatedRawBytes | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.AllocatedRawBytes | ObjectHeader.GarbageCollectorFlags.Marked :
{
UIntPtr addressNext = oh.GetNextObjectPointer();
brickTable.MarkObject( address, AddressMath.RangeSize( address, addressNext ) );
address = addressNext;
}
break;
default:
BugCheck.Raise( BugCheck.StopCode.HeapCorruptionDetected );
return;
}
}
}
}
//--//
[TS.WellKnownMethod( "DebugBrickTable_VerifyBrickTable" )]
private unsafe void VerifyBrickTable()
{
for(MemorySegment* heap = MemoryManager.Instance.StartOfHeap; heap != null; heap = heap->Next)
{
UIntPtr address = heap->FirstBlock;
UIntPtr end = heap->End;
while(AddressMath.IsLessThan( address, end ))
{
FindObject( AddressMath.Increment( address, sizeof(uint) ) );
ObjectHeader oh = ObjectHeader.CastAsObjectHeader( address );
ObjectHeader.GarbageCollectorFlags flags = oh.GarbageCollectorState;
switch(flags)
{
case ObjectHeader.GarbageCollectorFlags.FreeBlock | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.FreeBlock | ObjectHeader.GarbageCollectorFlags.Marked :
{
UIntPtr addressNext = oh.GetNextObjectPointer();
address = addressNext;
}
break;
case ObjectHeader.GarbageCollectorFlags.GapPlug | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.GapPlug | ObjectHeader.GarbageCollectorFlags.Marked :
address = AddressMath.Increment( address, sizeof(uint) );
break;
case ObjectHeader.GarbageCollectorFlags.ReadOnlyObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.ReadOnlyObject | ObjectHeader.GarbageCollectorFlags.Marked :
BugCheck.Raise( BugCheck.StopCode.HeapCorruptionDetected );
return;
case ObjectHeader.GarbageCollectorFlags.UnreclaimableObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.UnreclaimableObject | ObjectHeader.GarbageCollectorFlags.Marked :
BugCheck.Raise( BugCheck.StopCode.HeapCorruptionDetected );
return;
case ObjectHeader.GarbageCollectorFlags.NormalObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.NormalObject | ObjectHeader.GarbageCollectorFlags.Marked :
case ObjectHeader.GarbageCollectorFlags.SpecialHandlerObject | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.SpecialHandlerObject | ObjectHeader.GarbageCollectorFlags.Marked :
case ObjectHeader.GarbageCollectorFlags.AllocatedRawBytes | ObjectHeader.GarbageCollectorFlags.Unmarked:
case ObjectHeader.GarbageCollectorFlags.AllocatedRawBytes | ObjectHeader.GarbageCollectorFlags.Marked :
{
UIntPtr addressNext = oh.GetNextObjectPointer();
address = addressNext;
}
break;
default:
BugCheck.Raise( BugCheck.StopCode.HeapCorruptionDetected );
return;
}
}
}
}
//
// Access Methods
//
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,045 |
export * from "./state";
export * from "./reducers";
export * from "./actions";
export * from "./sagas"; | {
"redpajama_set_name": "RedPajamaGithub"
} | 2,392 |
We offer weekly classes for adults pre bookable in six weekly half term blocks. Maximum six students per class.
Develop your confidence and skills in a supportive and friendly environment. The classes can be used to work on individual projects, taking into account the space available and your sewing level. We offer advice and guidance to help you to choose suitable projects and materials. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,078 |
Chile's Galileo Information Centre launches a series of webinars to introduce Galileo and Galileo Services in Latin America
The Galileo Information Centres (GIC), an initiative of the European Commission and DG-DEFIS, are facilitating the introduction of EGNSS in Latin America. The recently-established Centre in Chile - providing services to the Galileo user community in Argentina, Bolivia, Chile, Colombia and Ecuador - is organising a series of webinars to introduce Galileo to the Latin America user community, and showcase the benefits that the European GNSS can bring to the regional markets and stakeholders.
The webinar series is starting on 3 September (source: Vanessa Ramos – ©KIM Global)
The Galileo Information Centres, funded by the European Commission (EC) and the DG Defence Industry and Space (DG-DEFIS), are promoting the introduction of the European GNSS (EGNSS) programmes, Galileo and EGNOS, in Latin America. The Centres monitor local and regional satellite navigation initiatives, identifying potential markets and stakeholders, and providing support to users in developing new applications through cooperation between Latin American and European industry. Additionally, the Centres are responsible for disseminating information in different languages about EGNSS and supporting the user community to enhance local awareness and understanding of the European GNSS services. Galileo Information Centres in Chile (serving Argentina, Bolivia, Ecuador and Colombia) and Brazil (serving the Portuguese-speaking community), have started providing services in summer 2020, while the Centre in Mexico (covering Mexico, Central America and the Caribbean) is expected to open in the coming months.
Webinars series
Recently inaugurated, the GIC in Chile has already started its activities training the user community about Galileo Systems and Services and the opportunities the EGNSS can bring to Latin America. This week, the centre is launching the webinar series to introduce in detail the GIC and the services it provides regionally. The webinars will also introduce the mission, services and activities currently performed by the European GNSS Service Centre (GSC) at a global level.
To register to each webinar:
"Galileo Information Centre: Strengthening the Galileo user community in Latin America", 3rd September
"Galileo: The system, features and services", 30th September
"Galileo markets and applications", 15th October
The webinars will be in Spanish.
GSC and GICs: a close coordination.
The Galileo Service Center (GSC), as the single global interface between the Galileo User Community and the Galileo Service Provider, is committed to strengthen the coordination with the different Galileo Information Centres and support them in the delivery of their mission enhancing the impact of the European satellite navigation activities in Latin America.
Media note: This feature can be republished without charge provided the European GNSS Agency (GSA) is acknowledged as the source at the top or the bottom of the story. You must request permission before you use any of the photographs on the site. If you republish, we would be grateful if you could link back to the GSA website (http://www.gsa.europa.eu). | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,398 |
Engagement and Challenges in Advocacy: Experiences from the Western United States
Lori M. Martin, Past President, Western Division of the American Fisheries Society; Colorado Parks and Wildlife, 711 Independent Avenue, Grand Junction, CO 81505. E-mail: [email protected]
Leanne H. Roulson, Chair, American Fisheries Society, Resource Policy Committee; HydroSolutions Inc., Bozeman, MT
Hilda Sexauer, Past President, Western Division of the American Fisheries Society; Wyoming Game and Fish Department, Pinedale, WY
Water bodies are used globally for multiple purposes, including water supplies, energy development, transportation, and recreation. Regulatory systems exist to evaluate those uses and their potential or resulting environmental impacts, including alteration of aquatic ecosystems. Often, these evaluations involve American Fisheries Society (AFS) members, who are vexed when the resulting regulatory or policy decisions ignore the best scientific information provided and instead rely on political influences. There are also instances where fisheries experts may feel compelled to make decisions that ignore the best scientific information out of fear of retribution within their workplace or from other political entities when assessing proposed actions that may alter aquatic ecosystems. Determining when and how to contest a decision counter to the best available science can be difficult. The AFS and its Units can assist their members by providing effective procedures (e.g., resolutions, comment letters) that address those environmental concerns, thereby both protecting individuals and providing the best and most scientifically accurate information for decision makers.
Fisheries management inherently includes making decisions regarding how fisheries and aquatic habitats will be sustained and protected. The wealth of experience and knowledge within AFS can be a resource for seasoned and new professionals when contentious environmental issues arise. As AFS members, we are justly concerned with our reputation as objective scientists, in particular when a decision regarding a project ignores or is contrary to substantial evidence, current scientific information, analysis, and/or conclusions. Our responsibility as aquatic scientists is to identify and communicate such discrepancies, and to document and emphasize critical data when making fishery management decisions.
Advocating for fisheries and aquatic systems by addressing environmental issues and policies is no easy task, and often presents multiple challenges and difficulties. Complications involve staying apprised and informed of current environmental concerns, and possessing readily available resources to develop a timely and effective response. American Fisheries Society members must also determine how to actively participate without incurring unpleasant repercussions from their employers or communities. Fortunately, various AFS Units, including AFS Chapters and Divisions, have Environmental Concerns and/or Resource Policy committees to assist in overcoming these challenges. For example, the Resource Policy and Environmental Concerns Committee (RPECC) of the Western Division of the American Fisheries Society (WDAFS) was recently revived and restructured to include at least one member from each Chapter, preferably those concurrently serving as chair of the Chapter's comparable RPECC. The restructuring of the RPECC will ensure: (1) identification of potential and time-sensitive environmental concerns by providing broader oversight within multiple geographical areas in a timely manner, (2) engagement by professionals with the appropriate expertise who are most familiar with the issue of interest, (3) determination of the most appropriate target audience (AFS, the public, decision makers, etc.) and mode of response when informing and educating WDAFS members on emerging environmental issues, and (4) assistance by various AFS Units and other organizations in developing the appropriate actions to address resource concerns.
Five screening considerations are needed before addressing potential environmental issues to determine the best course of action. These considerations include whether (1) the topic is pertinent to fisheries within the geographic boundaries of the Division or Chapter, (2) the actions taken are likely to influence the decision process, (3) the Unit members are supportive of advancing the action, (4) the Unit is willing to provide contact information for those scientists directly involved in the environmental review, and (5) those scientists are willing to impart accurate, unbiased, science-based information prior to determining the appropriate mode of response. Completing those five steps is crucial to ensuring the most suitable course of action.
Within AFS, multiple options are available to all members interested in developing advocacy positions. Actions may include drafting comment letters, resolutions, position and/or policy papers, and legislative briefings; developing an educational forum; or potentially pursuing litigation (Poole et al. 2017, this issue). An independent review panel may be solicited in some situations. The selected action should take into consideration the intended audience. The best and most effective approach for one action may not be the most appropriate for another. The following advocacy examples demonstrate how the WDAFS and its respective Chapters have engaged in issues involving lower Snake River dams, a proposed Intake Diversion Dam on the lower Yellowstone River in Montana, and amendments to the Federal Power Act.
Aquatic scientists from the Oregon and Idaho Chapters of AFS shared a resolve to restore Snake River salmon and steelhead Oncorhynchus mykiss, and were concerned about retaliation from their employers for advocating science-based positions. Those AFS members have used the WDAFS to escalate science based positions on fisheries rehabilitation objectives. Their communication and collaborations have produced a number of WDAFS resolutions and reviews pertinent to the recovery of Columbia River basin fish runs and fisheries over the course of almost 20 years. In 1999, when the WDAFS resolved to rehabilitate Snake River salmon and steelhead in their native ecosystem, one biologically required action involved breaching the lower Snake River dams. Several years later, a special WDAFS committee was formed to review the 2004 Biological Opinion on the Federal Columbia River Power System. In 2010, this same group evaluated the Adaptive Management Implementation Plan (AMIP) issued by the federal government in September 2009 as an addition to the 2008 Biological Opinion for the Federal Columbia River Power System (WDAFS 2010). The intent of the AMIP review was to inform WDAFS members and to benefit the parties involved in litigating the 2008 Biological Opinion, thereby increasing the opportunity for recovery of salmon and steelhead in the Columbia River basin (WDAFS 2010). All of those actions were completed under the auspices of the WDAFS, enabling AFS members closest to this polarizing topic to respond without fear of reprisal.
Most recently, WDAFS members combined previous resolutions by the Idaho and Oregon Chapters of AFS (ICAFS 1999; ORAFS 2000), as well as the 1999 WDAFS resolution related to the lower Snake River dams into a 2011 resolution (WDAFS 2011). The 2011 resolution stated that the four lower Snake River dams and reservoirs are a significant threat to the continued existence of remaining Snake River salmon, steelhead, Pacific Lamprey Entosphenus tridentatus, and White Sturgeon Acipenser transmontanus (WDAFS 2011). The WDAFS membership approved the resolution through electronic voting, declaring that the lower Snake River must be returned to a free-flowing condition by comprehensive planning and implementation using appropriate techniques and management practices in a timely manner (WDAFS 2011). The WDAFS provided the 2011 Snake River resolution to federal and state agencies, tribes, and elected or appointed officials and posted it on the WDAFS website (wdafs.org). Further, a press release was prepared by the WDAFS, alerting the media and the general public to the WDAFS's 2011 efforts to recover the fisheries of the Columbia River basin. Those endeavors by Chapter and WDAFS members over the past two decades have resulted in positive publicity for the fishes of the lower Snake River and the Columbia River basin overall.
Another example of a WDAFS Unit's engagement in environmental issues is the Montana Chapter's (MTAFS) participation in the environmental review process for the Intake Diversion Dam modification project on the lower Yellowstone River. The Intake Diversion Dam is a 1900s-era low-head, rock weir dam that raises the river water elevation to divert water from the Yellowstone River through the recently reconstructed headworks to a main irrigation canal. The dam has effectively impeded passage for several native fishes in all but the highest flow water years. The proposed modifications would harden the dam with concrete and raise its elevation by approximately 2 ft. The MTAFS's involvement began with a simple solicitation from its Resource Management Concerns Committee (RMCC) for issues of interest in 2013. Several biologists expressed concerns that the diversion dam modifications did not account for the migratory needs and biology of the federally listed Pallid Sturgeon Scaphirhynchus albus and other native fishes. Concerns generated by the RMCC included (1) contingencies for fish passage success were not addressed, (2) biological criteria were not incorporated into the design, and (3) long-term agency accountability for fish passage success was not considered (Campbell 2013). After identifying those concerns, the RMCC wrote a letter regarding the Intake Diversion Dam supplemental environmental assessment. The letter was submitted in April 2014 to the U.S. Bureau of Reclamation and the U.S. Army Corps of Engineers, the two lead agencies for the environmental assessment (MTAFS 2014). Under the National Environmental Policy Act, those public comments became part of the project record, and the decision-making agency was required to acknowledge (at a minimum) and address substantive comments.
Nearly a year later, the MTAFS was approached by an environmental organization intending to litigate the project. This group requested that the MTAFS provide fisheries expertise regarding critical issues and concerns of the project. An additional goal of the RMCC was to ensure that their comments and concerns emphasized the MTAFS support for irrigators' water rights and did not undermine the local biologist's ability to work in this small community.
The RMCC organized a panel for the 2015 MTAFS annual meeting to discuss the potential impacts of the Intake Diversion Dam modification on Pallid Sturgeon. The panel provided the MTAFS membership with the scientific background on the species, project progress, the RMCC's work, and options for the next steps from people who understood the legal process. The RMCC worked with the MTAFS' Executive Committee (EXCOM) to develop motions for the MTAFS business meeting to request a vote as to whether, and to what extent, the MTAFS should become involved in the lawsuit.
The discussion at the 2015 MTAFS business meeting was animated, and addressed many of the issues brought up in this advocacy series. The MTAFS membership voted to participate in a supporting role in the litigation, and directed the EXCOM to take necessary actions in support of the case, consistent with those MTAFS positions documented previously. The MTAFS remained an active participant through several stages in the process, including commenting on the final environmental impact statement, issued in October 2016 (BLM and USACE 2016). The key elements that allowed the membership to feel comfortable in this endeavor were: (1) helpful and timely information on the issue and the biology from respected peers, (2) an opportunity for all members to be heard through a poll to determine whether there was interest in participating in the environmental review of Intake Diversion Dam, (3) limitations set by the RMCC as to the extent of involvement and issues to be addressed, and (4) transparent and open lines of communication provided through full discussion at the MTAFS annual meeting.
The WDAFS's third example is the draft legislation to amend the Federal Power Act by the U.S. Congress in 2015. The amendments included language that would accelerate pending hydropower projects through the approval process. The new language also included changes in the conditioning process and timelines, and shifted decision making regarding aquatic resources from state and other federal agencies to the Federal Energy Regulatory Commission (FERC). Those amendments would have removed checks and balances provided by agencies tasked with managing potentially affected resources, such as fisheries, water, and wildlife, and transfer these roles to FERC, the agency mandated to permit energy projects. If enacted, the legislation would allow hydroelectric operators to avoid complying with the Endangered Species Act, the Clean Water Act, and other federal and tribal land management laws.
This proposed legislation garnered the attention of AFS fisheries professionals across the United States. The WDAFS and AFS have a long history with hydropower projects, dams, and their environmental consequences. The respected professional expertise and wealth of knowledge of aquatic scientists within the WDAFS and AFS were solicited by several nongovernmental organizations seeking to address proposed changes within the hydropower legislation evaluation process. The WDAFS's EXCOM and the AFS officers and executive director opted to develop their own respective comments, separate from the remarks of the groups that had approached the WDAFS and AFS. The WDAFS approach alleviated any potential negative repercussions to the members of AFS Chapters who were closely tied to hydropower projects, retaining a unified voice from the WDAFS. Letters were submitted by AFS and the WDAFS to the House Energy and Commerce Committee and the Senate Energy and Natural Resources Committee in May 2015. In the interim, the WDAFS and AFS learned that other entities also voiced their concerns, including the Association of Fish and Wildlife Agencies and several western states. Though each organization and state approached its review of the draft legislation differently, several critical components of the proposed laws were highlighted consistently, including: (1) the increased level of evidence required from resource management agencies to demonstrate the need for fish passage and evaluation of conditions prior to dam construction and the role of FERC making those decisions, (2) the proposed shortening of the licensing timeline, resulting in reduced data collection, and (3) the evaluation of dam operation and impacts on fish populations being conducted by energy specialists, rather than fisheries scientists. Collaboration by the WDAFS, AFS, other professional organizations, nongovernmental organizations, and western states were successful in changing some language within the draft hydropower legislation to benefit aquatic resources.
The WDAFS and Chapters, working together or independently, have assisted their members in developing effective avenues to address the lower Snake River dams, the proposed Intake Diversion Dam on the Yellowstone River, and proposed hydropower amendments to the Federal Power Act, providing pertinent information while reducing the potential for retribution from their employers. Consequentially, those actions, including the development and organization of letters, resolutions, educational panels, and policy statements, brought environmental concerns across the West to the attention of a broader audience. Participants in the efforts mentioned have received feedback from judges and government representatives that contributions from AFS Chapters and Divisions have greater professional authority than individual comments because of the scientific reputation of AFS. This reputation is well earned, and applying our collective knowledge to improving resource decisions is a valid way for AFS to promote and demonstrate the use of "best available science." The WDAFS website provides its members with examples of pathways to take to address their environmental concerns. Writing a letter or a resolution may not seem like an effective action, yet the connections and discussions leading up to those documents often result in additional achievements and increased awareness of important projects and issues. The dispersal of scientific-based information is what leads to positive action and change. American Fisheries Society Units are an excellent conduit for vetting, evaluating, advocating for, and directing appropriate scientific responses to current policy events. We encourage you to engage your respective AFS leaders in supporting and promoting our aquatic biota and their habitats.
We appreciate the critical reviews and comments of three anonymous reviewers and Bob Hughes, Guest Editor.
BLM (U.S. Bureau of Reclamation) and USACE (U.S. Army Corps of Engineers). 2016. Lower Yellowstone intake diversion dam fish passage project, Montana. USBOR and USACE, final environmental impact statement, Billings, Montana. Available: https://usbr.gov/gp/ mtao/loweryellowstone/EIS/2016feis.pdf. (December 2016).
Campbell, G. 2013. Letter to U.S. Fish and Wildlife Service: Lower Yellowstone intake dam modification, fish passage improvement. U.S. Bureau of Reclamation, Great Plains Regional Office, GP-4200, ENV-6.00, Billings, Montana.
ICAFS (Idaho Chapter of the American Fisheries Society). 1999. Resolution on the role of dams and Snake River salmon and steelhead recovery. IDAFS, Gillraker Gazette 19(2). Available: http://idahoafs.org/ newsletters/1999-05.pdf. (March 2016).
MTAFS (Montana Chapter of the American Fisheries Society). 2014. Letter on the Yellowstone River intake diversion dam supplemental environmental assessment. Available: http://fisheries.org/docs/wp/Intake-dam_Comments_Montana-Chapter-AFS-2014.pdf. (May2017).
ORAFS (Oregon Chapter of the American Fisheries Society). 2000. Resolution on Snake River salmon and steelhead recovery. ORAFS, Portland, Oregon. Available: orafs.org/wp-content/uploads/2012/07/Resolution-2000-Snake-River.pdf. (March 2016).
Poole, T., T. E. Bigford, and O. Mulvey-McFerron. 2017. Shaping AFS advocacy based on history and need. Fisheries 42:357–360.
WDAFS (Western Division of the American Fisheries Society). 2010. Review of the 2009 adaptive management implementation plan for the 2008 biological opinion regarding the federal Columbia River power system. Available: wdafs.org/download/resolutions/WDAFS%20Review%20of%20AMIP.pdf (Accessed March 2016).
WDAFS (Western Division of the American Fisheries Society). 2011. Resolution on the role of dams and conservation of Snake River salmon, steelhead, Pacific Lamprey, and White Sturgeon. Available: wdafs.org/download/resolutions/Western%20Division%20AFS%20Snake%20River%20Resolution%202011%20Final.pdf. (March 2016).
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This measure returns responsibility for determining the boundaries of the California's legislative districts to the State Legislature, taking it out of the hands of a bipartisan commission recently established by voters.
The new body, the Citizens Redistricting Commission, was established in 2008 when voters passed Proposition 11. It is currently responsible for overseeing the state-level 'redistricting' process—a constitutionally-mandated adjustment of the boundary lines of State Assembly and State Senate districts every ten years to reflect population changes in the census.
The commission - to be named later this year - will consist of 14 registered voters (5 Democrats, 5 Republicans, and 4 independents). They will be selected from a list of applicants, after a thorough vetting process by the State Legislature. Their work on redistricting is scheduled to begin in 2011.
A YES vote: Returns the responsibility for determining the boundaries of State Assembly, State Senate, and Board of Equalization districts back to the State Legislature.
A NO vote: Leaves the responsibility for determining the boundaries of State Assembly, State Senate, and Board of Equalization districts with the Citizens Redistricting Commission.
Every ten years, the State Constitution requires state legislative districts to be redrawn to reflect changes in the state's population. Supporters of this measure want this process to be put back in the hands of a democratically-elected body, the Legislature. They say state representatives will do a better job, because they may be removed from office, if voters disapprove of the way they have redrawn legislative districts—something that cannot be said of the Citizens Redistricting Commission.
Opponents of this measure believe allowing legislators to draw the boundaries of their own districts is a conflict of interest. In the past, legislators who oversee the redistricting process have often redrawn the districts to the advantage of whatever party is in power in Sacramento, or to protect incumbents. This has led to the creation of sprawling districts that criss-cross city and county lines and stretch over unrelated regions. It has also led, in recent years, to 99 percent of incumbents being reelected.
The Citizens Redistricting Commission, created by Proposition 11, may not draw districts in favor of incumbents, political candidates, or political parties. It is required to maintain the geographic integrity of cities, counties, neighborhoods, and communities of interest. Proposition 27 would eliminate these new redistricting standards—and return the power of redistricting to the lawmakers who rely on those same districts to be elected. | {
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es el cuarto kata de la serie de katas Heian del estilo Shotokan de karate. Fue creada por Ankō Itosu a principios del s. XX.
Historia
Este kata, como el resto de la serie Heian fue adaptado por Ankō Itosu del kata Kankū Dai a principios del siglo XX.
Estructura
Es el primer kata de Heian que introduce patadas en gran número.
Contiene 27 movimientos y dos kiai.
Diagrama (embusen)
El embusen de este kata es muy sencillo, al igual que el resto de las Heian. Prácticamente se asemeja a una I mayúscula.
Posiciones (dachi)
Kokutsu dachi
Zenkutsu dachi
Kosa dachi
Defensas (uke)
Ude uke
Yuji uke
Morote uke
Shuto uke
Kakiwake uke
Ataques directos (tsuki)
Oi tsuki
Gyaku tsuki
Ataques indirectos (uchi)
Uraken uchi
Enpi uchi
Shuto uchi
Morote kubi osae
Patadas (geri)
Yoko geri
Mae geri
Hiza geri
Puntos importantes
Enpi uchi
Existe la tendencia a golpear con la mano de delante al codo cuando se realiza el enpi uchi, sin embargo la técnica consiste en lo contrario, golpeando con el enpi uchi ayudándose de la potencia de la cadera (la cual hay que girar hacia delante para ganar potencia).
Aplicaciones (bunkai)
Morote kubi osae
Esta técnica es muy gráfica, pues consiste en agarrar con ambas manos el cuello del adversario y, al mismo tiempo que se bajan las manos se levanta la rodilla (hiza geri), golpeando con esta la cabeza del adversario.
Véase también
Equivalencias entre estilos
Este kata también se encuentra presente en otros estilos de karate, con distinto nombre y algunas diferencias en su ejecución.
Heian Yondan: Shotokan.
Pinan Yondan: Shitō-ryū, Shōrin-ryū, Wadō-ryū, Gensei-ryū, Kyokushin kaikan, Ryukyu Kempo, Shindō jinen-ryū, Shukokai.
Pyung ahn sa dan: Tang Soo Do (karate coreano).
Pinan sono yon: Kyokushinkai.
Referencias
Enlaces externos
Vídeos
Webs
Heian Yondan. Embusen, dibujo y vídeo
Katas de karate Shotokan | {
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module RubyWarrior
module Units
class Captive < Base
def initialize
bind
end
def max_health
1
end
def character
"#{R18n.t.captive.first_letter}"
end
end
end
end
| {
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{"url":"http:\/\/etheses.bham.ac.uk\/597\/","text":"eTheses Repository\n\n# Catalytic supercritical water oxidation of nitrogen-containing organic compounds\n\nHernandes, Mauricio Julio Angeles (2010)\nPh.D. thesis, University of Birmingham.\n\n Click on the icons below to preview their contents ... PDF (6Mb) IS_Decl_Angeles10PhD.pdfPDF (167Kb)Restricted to Repository staff only\n\n## Abstract\n\nThe results of the catalytic oxidation in supercritical water of two non-biodegradable and highly toxic nitrogen-containing organic compounds (DBU and quinoline) are presented. The reactions were studied in a tubular xed-bed reactor over three catalysts: Pt\/Al$$_2$$O$$_3$$, CuO\/Al $$_2$$O$$_3$$ and MnO$$_2$$\/CuO. The effect of operating conditions, namely temperature, pressure, oxygen concentration and initial concentration of the organic compounds were studied to evaluate their influence on its removal. Reaction rates were calculated from the experimental data collected. In addition, the selectivities and stabilities of the catalysts were investigated. Before conducting the experimental study the isothermal and isobaric operation of the reactor was veried together with the complete decomposition of hydrogen peroxide to oxygen and water in the preheating section and the reproducibility of experimental data was verified. Absence of external concentration gradients was determined experimentally for each reaction. The results showed that temperature was the main controlling variable of the catalytic oxidation. On the contrary, the effect of pressure depended on the catalyst used. Increasing the concentration of the organic compound did not aect their oxidation. Meanwhile, oxygen concentration above a stoichiometric ratio of two did not considerably improve the reaction. A power-law kinetic model was proposed to quantify the oxidation reaction. Three Langmuir-Hinshelwood-Hougen-Watson reaction rates were also explored to the experimental data. In the absence of a specic reaction mechanism the kinetic data were best represented by the power-law kinetic model. CO2 was the main carbon product of the reaction with small amounts of inorganic carbon species dissolved in the liquid effluent. Meanwhile, NH$$_4$$, NO$$_3$$ and NO$$_2$$ ions were the only nitrogen species detected in the liquid effluent. Pt\/Al$$_2$$O$$_3$$ proved to be the most effective catalyst because it promoted faster reactions rates, had higher selectivity towards CO2 and produced lower nitrogen species. Surface analysis of the spent catalysts identied that the loss of activity was due to the 23 reduction of surface area. Leaching of active metals and chemical changes on the surface of the active metals and support of the catalyst were found for CuO\/Al $$_2$$O$$_3$$ and MnO $$_2$$\/CuO. To conclude, it was demonstrated that catalytic supercritical water oxidation is a feasible and effective alternative for the destruction of contaminants in water. The thesis also includes suggestions for further research to continue the development of this technology and consolidate the process at industrial scale.\n\nType of Work: School of Chemical Engineering thesis. Santos, Regina and Leeke, Gary Colleges (2008 onwards) > College of Engineering & Physical Sciences School of Chemical Engineering TP Chemical technology University of Birmingham 597\nThis unpublished thesis\/dissertation is copyright of the author and\/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis\/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.\n\nRepository Staff Only: item control page","date":"2016-08-31 04:15:06","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.33666926622390747, \"perplexity\": 3352.6966101966927}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-36\/segments\/1471983577646.93\/warc\/CC-MAIN-20160823201937-00123-ip-10-153-172-175.ec2.internal.warc.gz\"}"} | null | null |
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Home › Perspectives › Malaysia's Energy Ecosystem: Braving The Pandemic to Keep The Lights On
Malaysia's Energy Ecosystem: Braving The Pandemic to Keep The Lights On
This Article Was Written By Energy Watch
| 01.09.21 | 8:20 PM
Datuk Ir. Baharin Din is a towering figure within the energy industry with three decades worth of experience. Most recently, he was appointed the new President and Chief Executive Officer (CEO) of Tenaga Nasional Berhad (TNB) earlier this February.
His appointment comes at a time when the energy and power sector of the country is wading into uncharted waters, amid a global pandemic and economic recession. For too long, Malaysia has been extremely reliant on fossil fuel energy for electricity generation. Now, as the tide shifts in favour of renewables, the urgent need to invest in energy transition has been made clearer. Malaysia is focusing on its power generation plan with a target of 40% renewable energy (RE) in its installed capacity by 2035.
As such, Datuk Ir. Baharin has plenty on his plate, ensuring Malaysians continue enjoying a reliable supply of electricity and futureproofing the company to insulate it against any probable future shocks in the long term. Speaking to Energy Watch recently, he said, "A financially stable TNB can be a cornerstone in Malaysia's effort to rebuild and reshape its economy in the process towards economy recovery post Covid-19 crisis."
A financially stable TNB can be a cornerstone in Malaysia's effort to rebuild and reshape its economy in the process towards economy recovery post Covid-19 crisis.
Datuk Ir. Baharin's primary order of business will be to drive TNB's aspiration of being a leading provider of sustainable energy solutions in Malaysia and internationally. The target set is to achieve 8,300MW of power from renewable energy both domestically and internationally. This will help contribute to the nation's broader goals of deriving 31% of its energy within the national installed capacity mix from renewable energy by 2025. Currently, TNB's (RE) generation capacity stands at 3402MW which means that it is just over 41% of the way through towards attaining this goal which is expected to be achieved in the next four years.
However, TNB, with Datuk Ir. Baharin in charge, have been confident and optimistic in realising this vision. Under his stewardship, TNB has been operating with a renewed sense of urgency as the utility giant aims to progress further towards a zero-carbon future.
Already, TNB is working with strategic partners in Europe and Singapore to tap into the burgeoning renewables market in the region and expand its renewable energy footprint through acquisitions and greenfield developments. Initial projections indicate that by 2025, with the retirement of four gas plants totaling 1,484 MW, renewable energy will contribute to 45% of TNB's total generation capacity.
While energy transition represents a crucial priority for TNB, now more than ever, its focus is on contributing to the welfare of the country amid a raging global pandemic. Datuk Ir. Baharin has found a balance in managing energy transition goals and Covid-19 relief efforts, at a time when many are struggling with the effects of a pandemic induced economic recession.
This commitment is displayed through four focus areas – which are, saving lives, protecting the vulnerable, keeping the lights on, and driving economic recovery.
With regards to saving lives and protecting the vulnerable, TNB has channeled aid through its Corporate Social Responsibility (CSR) arm to roll out initiatives such as Program Baiti Jannati and Golongan Asnaf. In total, TNB contributed RM1.2 million (24 homes), adding to the RM1.45 million contribution (31 homes) made in 2020 and distributed basic necessities and pocket money to 9,918 asnaf, with a total contribution worth RM420,000.
In its efforts to keep the lights on for the people during these tough times, TNB continues to provide their services throughout the spate of lockdowns. By ensuring smooth operation of its power stations through dedicated technical teams, TNB ensures that its customers receive an uninterrupted and stable supply of electricity.
In 2020, our contributions towards Covid relief to the community amounted to RM300 million. This included RM250 million in bill discounts from KWIE and RM43 million committed to reskilling Malaysians.
Another effort in this regard is the Diskaun Prihatin carried out in partnership with the government. RM50 million worth of electricity discounts have been channeled to the rakyat to date. They have also pledged to not disconnect electricity supply for overdue customers until the end of June 2021 and offered residential customers options to settle their bills in interest-free monthly installments.
On a wider scale, TNB has also worked to support the National Recovery Plan (NRP) in driving economic recovery by ensuring a reliable supply of electricity at the five new mega vaccination centres (PPV) in Klang Valley, facilitating a smooth vaccination process. On top of that, they have been focused on keeping more than 40 vaccine storage facilities and over 400 vaccination centres running without a single disruption in power.
"In 2020, our contributions towards Covid relief to the community amounted to RM300 million. This included RM250 million in bill discounts from KWIE and RM43 million committed to reskilling Malaysians." said Datuk Ir. Baharin.
From an economic standpoint, Datuk Ir. Baharin has elevated TNB's importance within the national post-COVID-19 economic recovery agenda framework.
Collectively these areas (TNB's six-pronged game-changing strategy) deliver a massive impact to the economy between 2021 and 2030 by contributing an estimated RM120 billion in Gross Domestic Product (GDP), benefitting local vendors and providing up to 4.5 million in skilled employment opportunities.
This has been achieved through a proposed six-pronged game-changing strategy including, Catalysing the Economy through Grid of the Future, Building a Global Solar Manufacturing Hub, Raising National Competitiveness through Energy Efficiency, Electrifying Mobility for Malaysia, Advancing Connectivity for our Digital Economy and Reskilling Malaysia by embracing future of work. Collectively these areas deliver a massive impact to the economy between 2021 and 2030 by contributing an estimated RM120 billion in Gross Domestic Product (GDP), benefitting local vendors and providing up to 4.5 million in skilled employment opportunities.
Within these six areas, several are low hanging fruits, attainable in the short to medium term which TNB has been focusing on.
The first area is to catalyse the economy through the Grid of the Future with the aim of transforming Malaysia's traditional grid into a world-class automated and digitally enabled grid, capable of providing maximum efficiency and reliability to consumers. This is necessary to ramp up energy transition and pave the way for a decentralised energy system. TNB aims to invest RM27 billion in "Grid of the Future" technologies which is expected to contribute RM20 billion to the national GDP and create over 300,000 jobs from 2021-2023.
Next, is to build a global solar manufacturing hub in the country to drive the growth of the solar manufacturing sector. TNB is looking to invest up to 1,400MW in large scale solar (LSS) and 75MW in distributed solar generation in Malaysia which would contribute to the country's 31% renewable energy target in generation mix by 2025. This is expected to generate RM6 billion in GDP and 47,000 jobs over the next two years.
TNB is also committed to reskilling the Malaysian workforce through the TNB Integrated Learning Solution (ILSAS).
On the international investment front, TNB has found preliminary success in its global ESG efforts. This has helped kickstart the launch of Vantage RE Ltd, a RE investment and active asset management company. It is tasked with owning, operating, and managing a portfolio of RE assets in the United Kingdom and throughout Europe.
Within a broader scope, Datuk Ir. Baharin's aspirations are for TNB to embrace and trailblaze sustainable energy initiatives, as well as becoming a leading provider of sustainable energy in the region and possibly the world. TNB's transformation agenda, outlined in its "Reimagining TNB" strategy outlines future generation sources, Grid of the Future technologies, and consumer experience enhancement as the three pillars of achieving this ambition.
Internally, these aspirations have been reflected in the company's alignment and integration of its corporate strategy with sustainable strategies on ESG issues as well as contributions to the United Nation Sustainable Development Goals (UN SDGs). The four UN SDGs most relevant to TNB's value creation in business are, Goal 7 (Affordable and Clean Energy), Goal 8 (Decent Work and Economic Growth), Goal 13 (Climate Action), and Goal 17 (Partnerships for the Goals).
In line with this, TNB has pledged to not invest in any Greenfield coal plants internationally. With regards to domestic coal, the organization will adhere to the guidelines within the New Economic Policy (NEP) and ensure that its revenue from coal generation plants does not exceed 25% of its total group revenue.
Taking it a step further, TNB has strived to elevate its governance of ESG to its highest management committee via the Sustainability Development Committee (SDC). The SDC is responsible for managing sustainability risks and opportunities as well as monitoring the effectiveness and performance of related initiatives. It oversees evaluating and advising on the strategic direction and implementation of sustainable measures and is directly answerable to the Board of Directors (BOD).
The future holds great things to come for TNB under Datuk Ir. Baharin, with a focus on "saving lives, protecting the vulnerable, keeping the lights on, and driving economic recovery."
The positives of these four areas extend beyond the three indicators driving the NRP which relate to Covid-19 transmission figures, public healthcare capacity and the national vaccination drive.
It is estimated that the renewable energy industry generates 2.5x to 3x more employment per dollar of investment than fossil fuel technologies. Through RE developments, TNB will be looking forward to playing a key role in the country's recovery from the pandemic by creating a viable path towards a low carbon economy.
Datuk Ir. Baharin lauded TNB's priorities in its long standing philanthropic, education and socio-economic programmes, which benefit local communities, especially the underserved.
As the nation heads on the path of economic recovery, electricity demand is expected to improve. Nevertheless, the careful planning and execution of industry reforms will still serve as a fundamental catalyst in attracting high value, high tech businesses that create multiplier effects within the energy sector. This would go a long way in helping the economic goals of the nation to transition towards a high-income nation with a digitally skilled workforce.
Meanwhile, having refreshed its 10-year strategic plan, TNB is expected to be devoting time, energy, and effort on the ongoing energy transition plan. This would ensure that in time to come, TNB would be ready to deploy its capacities and provide sustainable energy solutions to Malaysians. On the investment front, effective energy transition will pave the way and open doors to fruitful investments that will contribute positively to the national economy. It is estimated that the renewable energy industry generates 2.5x to 3x more employment per dollar of investment than fossil fuel technologies. Through RE developments, TNB will be looking forward to playing a key role in the country's recovery from the pandemic by creating a viable path towards a low carbon economy.
As one of the largest power utility firms in Southeast Asia, TNB has demonstrated incredible flexibility to change in accordance with the nuances of energy shifts experienced the world over. However, it has not lost sight on its commitment to the rakyat, evidenced by the continued steady supply of electricity as well as a host of Covid-19 relief measures rolled out to help Malaysians. Under Datuk Ir. Baharin's astute leadership, TNB has proven that it is an integral asset to the public. It only stands to play a more significant role in the lives of all Malaysians as the country recuperates from the effects of the pandemic.
*All data and figures listed in the article are updated as of April 2021.
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,694 |
Absolute Organic Maple Syrup is 100% organic maple syrup with no preservatives or additives added and you sure can taste the difference! This wonderful maple syrup has a lovely taste and is a fantastic sweetener.
Maple Syrup is a really good natural sweetener can be used in a range of cooking, raw treats, splashed over yummy pancakes or added to smoothies. Maple syrup is graded according to how light the syrup is. As a general rule the lighter the syrup the higher the grade & the darker the color, the stronger the pure maple flavor. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,929 |
\section{Introduction}
\label{intro}
The family of space-times admitting two shear-free geodesic null
congruences contains significant and well-known solutions of the
Einstein equations. Hence, in the Schwarzschild and Kerr black holes
these congruences define the outgoing and ingoing propagation of
light in the radial direction. We find a similar situation in their
charged counterparts, the Reissner-Nordstr\"om and Kerr-Newman
solutions. Moreover, all the other vacuum Petrov-Bel type D
solutions and their charged counterparts also belong to this family.
But this family contains other interesting space-times. Indeed, we
have shown elsewhere \cite{fsD} that in every type D metric with a
vanishing Cotton tensor the two principal planes define an umbilical
2+2 structure, and that this geometric property states,
equivalently, that the two principal null directions determine
shear-free geodesic congruences. It is worth remarking that the
umbilical condition can be stated in terms of the {\em canonical
2--form} $U$, volume element of the time-like plane defined by the
two congruences \cite{fsD}.
On the other hand, some first integrals of the geodesic equation are
closely linked with this property. Thus, conformal and Killing
tensors of type 2+2 and non-null Killing-Yano tensors can only exist
in space-times admitting two shear-free geodesic null congruences
\cite{hm-1,diru-1,fsY,cfsKT}.
A shear-free geodesic null congruence determines a Debever principal
null direction of the Weyl tensor, but is not, necessarily, a
multiple Debever direction. Consequently, all the Petrov-Bel types,
excepting type N, are compatible with an umbilical 2+2 structure.
What restrictions does this condition impose on the Weyl and Ricci
tensors? In order to give an answer to this question one needs to
study the integrability conditions of the umbilical equation.
These integrability conditions were presented in spinorial formalism
by Dietz and R\"{u}diger \cite{diru-1} and they obtained some
complementary restrictions on the type D space-times. Here, we
develop this question in a plain tensorial way that allows us to
analyze, not only all the compatible Petrov-Bel types, but also the
restrictions on the Ricci tensor.
Our results can easily be summarized if one takes into account that
when $U$ defines an umbilical structure, its first derivatives can
be collected in a complex vector $\chi$ \cite{fsD,fsY}. Then the
covariant derivative $\nabla \chi$ contains all the information on
the second derivatives of $U$. We show that the Ricci tensor is
determined, up to two functions, by $U$, $\chi$ and the symmetric
part of $\nabla \chi$, and we give its explicit expression. On the
other hand we give a general expression for the Weyl tensor in terms
of the $U$, $\chi$, $\mathop{\rm d}\nolimits \chi$ and the scalar curvature. Moreover
we study the characterization of the different Petrov-Bel types and
we show that the 2--forms $U$ and $\mathop{\rm d}\nolimits \chi$ determine the
canonical 2--forms associated with the Weyl tensor geometry.
From our study a result easily follows: if a non conformally flat
space-time admits a non-null Maxwell field whose principal
directions define shear-free geodesic null congruences, then the
metric is type D and these directions are the double Deveber
directions of the Weyl tensor. This property has allowed elsewhere
\cite{fsY} to obtain the intrinsic characterization of the
space-times admitting Killing-Yano or conformal Killing-Yano
tensors, and to give an algorithm that determines these first
integrals of the geodesic equation.
It is known that a type D vacuum solution admitting a Killing tensor
also admits a Killing-Yano tensor \cite{collinson,ste}. On the other
hand, all the type D vacuum solutions admit a 2+2 conformal Killing
tensor \cite{walker-p} and, from our results here and \cite{fsY},
they also admit a conformal Killing-Yano tensor. Can these results
be generalized to the non vacuum case? Here we show that {\em every
type D solution with a 2+2 conformal Killing tensor also admits a
conformal Killing-Yano tensor}.
This paper is organized as follows. In section 2 we introduce the
notation and summarize some previous results needed in this work. In
section 3 we present the integrability conditions for the umbilical
equation and we obtain the restrictions that these conditions impose
on the Ricci and Weyl tensors. The compatible Petrov-Bel types are
considered in section 4 and we show that the Weyl canonical
bivectors are determined by $U$ and its differential concomitants.
Finally, section 5 is devoted to analyzing type D space-times in
detail and we recover some known result and provide new ones.
\section{Notation and previous results}
\label{sec-notation}
Let $(V_4,g)$ be an oriented space-time of signature $\{ -, +,+,+
\}$. The metric $G$ on the space of 2--forms is $G=\frac{1}{2} g
\wedge g$, $\wedge$ denoting the double-forms exterior product, $(A
\wedge B)_{\alpha \beta \mu \nu} = A_{\alpha \mu} B_{\beta \nu} +
A_{\beta \nu} B_{\alpha \mu} - A_{\alpha \nu} B_{\beta \mu} -
A_{\beta \mu} B_{\alpha \nu}$. If $F$ and $H$ are 2--forms, $(F,H)$
denotes the product with $G$:
$$
(F,H) \equiv G(F,H) = \frac14 G_{\alpha \beta \lambda \mu} F^{\alpha
\beta} H^{\lambda \mu} = \frac12 F_{\alpha \beta} H^{\alpha \beta}\,
,
$$
A self--dual 2--form is a complex 2--form ${\cal F}$ such that
$*{\cal F}= \textrm{i}{\cal F}$, where $*$ is the Hodge dual
operator. We can associate biunivocally with every real 2--form $F$
the self-dual 2--form ${\cal F}=\frac{1}{\sqrt{2}}(F-\textrm{i}*F)$.
For short, we here refer to a self--dual 2--form as a {\it SD
bivector}. The endowed metric on the 3-dimensional complex space of
the SD bivectors is ${\cal G}=\frac{1}{2}(G-\textrm{i} \; \eta)$,
$\eta$ being the metric volume element of the space-time. The
orthogonal complement of the SD bivectors space is the space of the
anti-self-dual 2--forms, which are those satisfying $*F = -
\textrm{i}F$.
If $F$ is a 2--form and $P$ and $Q$ are double-2--forms, $P(F)$ and
$P \circ Q$ denote, respectively, the 2--form and the double-2--form
given by:
$$
P(F)_{\alpha \beta} \equiv \frac12 P_{\alpha \beta}^{\ \ \mu \nu}
F_{\mu \nu}, \qquad (P \circ Q)_{\alpha \beta \rho \sigma} \equiv
\frac12 P_{\alpha \beta}^{\ \ \mu \nu} Q_{\mu \nu \rho \sigma}
$$
Every double-2--form, and in particular the Weyl tensor $W$, can be
considered as an endomorphism on the space of the 2--forms. The
restriction of the Weyl tensor on the SD bivectors space is the {\em
self-dual Weyl tensor} and it is given by:
$$
{\cal W} \equiv {\cal G} \circ W \circ {\cal G} = \frac12(W - \mathop{\textrm{i}}\nolimits
*W)
$$
For short we here refer to a p-dimensional distribution (set of
vector fields generated by p independent vector fields) as a
p--plane. The generalized second fundamental form $Q_v$ of a
non-null p--plane $V$ is the (2,1)-tensor:
\begin{equation}
Q_v(x,y) = h(\nabla_{v(x)}v(y)) \, , \qquad \forall \; \; x,y
\end{equation}
where $v$ is the projector on $V$. Let us consider the invariant
decomposition of $Q_v$ into its antisymmetric part $A_v$ and its
symmetric part $S_v \equiv S_v^T + {1 \over p}v \otimes \mathop{\rm tr}\nolimits S_v$,
where $S_v^T$ is a traceless tensor:
\begin{equation} \label{Q2}
Q_v = A_v + \frac{1}{p} v \otimes \mathop{\rm tr}\nolimits S_v + S_v^T
\end{equation}
The p-plane $V$ is a {\em foliation} if, and only if, $A_v =0$, and,
similarly, $V$ is said to be {\em minimal, umbilical or geodesic} if
$\mathop{\rm tr}\nolimits S_v=0$, $S_v^T =0$ or $S_v =0$, respectively.
A p+q almost-product structure is defined by a p-plane $V$ and its
orthogonal complement q-plane $H$. The almost-product structures can
be classified by taking into account the invariant decomposition of
the covariant derivative of the so called structure tensor $\Pi$
\cite{nav} or, equivalently, according to the foliation, minimal or
umbilical character of each plane \cite{fsD,olga}. We will say that
a structure is integrable when both, $V$ and $H$ are a foliation. We
will say that the structure is minimal (umbilical) if both, $V$ and
$H$ are minimal (umbilical).
On the space-time, a 2+2 almost-product structure is defined by a
time-like plane $V$ and its space-like orthogonal complement $H$.
Let $v$ and $h= g-v$ be the respective projectors and let $\Pi =
v-h$ be the {\it structure tensor}. A 2+2 space-time structure is
also determined by the {\it canonical} unitary 2-form $U$, volume
element of the time-like plane $V$. Then, the respective projectors
are $v=U^2$ and $h = -(*U)^2$, where $U^2 = U \cdot U$. Here, if $A$
and $B$ are two 2--tensors, we denote $A \cdot B$ the tensor with
components $(A \cdot B)_{\alpha \beta} = A_{\alpha}^{\ \mu} B_{\mu
\beta}$.
In working with 2+2 structures it is useful to introduce the
canonical SD bivector ${\cal U} \equiv \frac{1}{\sqrt{2}} (U - {\rm
{i}} *U )$ associated with $U$, that satisfies $2{\cal U}^2 = g$
and, consequently, it is unitary, $({\cal U},{\cal U}) = -1$. If
$\perp$ denotes the projector on the space of the SD bivectors which
are orthogonal to ${\cal U}$, and ${\cal G}_{\perp}$ is the
restriction of the metric on this space, for a 2--form $F$ and a
double-2--form $P$, we have:
\begin{equation}
{\cal G}_{\perp} = {\cal U} \otimes {\cal U} + {\cal G} \, , \qquad
F_{\perp} \equiv {\cal G}_{\perp}(F) \, , \qquad P_{\perp} \equiv
{\cal G}_{\perp} \circ P \circ {\cal G}_{\perp}
\end{equation}
If $A$ and $B$ are two 2--tensors, $[A,B]$ and $\{A,B\}$ denote the
commutator and anti-commutator, respectively:
$$
[A,B] = A \cdot B - B \cdot A \, ,\qquad \{A,B\} = A \cdot B + B
\cdot A
$$
With this notation a straightforward calculation leads to:
\begin{lemma} \label{lemma-real-U}
A real symmetric tensor $E$ is determined, up to two scalars $e_1$
and $e_2$, by the commutator $[{\cal U}, E]$, where ${\cal U}$ is a
unitary SD bivector. More precisely:
\begin{equation} \label{real-U}
E = \frac{1}{4}(e_1 \, g + e_2 \, \Pi) + {\cal U} \cdot \Big( [{\cal
U} , E] + \{ {\cal U} , \bar{\cal U} \cdot [\overline{{\cal U} , E}
] \} \Big)
\end{equation}
where $\Pi$ is the structure tensor associated with ${\cal U}$,
$\Pi= 2{\cal U} \cdot \bar{{\cal U}}$, and $\bar{\ }$ stands for
complex conjugate.
\end{lemma}
There are some first order differential concomitants of $U$ that
determine the geometric properties of the structure \cite{fsD}.
Moreover, the first order differential properties of a 2+2 structure
admit a kinematical interpretation \cite{cf}. Now we summarize some
of these results needed in the following sections. If $i_{\xi}$
denotes the interior product with a vector field $\xi$, and $\delta$
the exterior codifferential, $\delta = *d*$, we have the following
lemma \cite{fsD}:
\begin{lemma} \label{lem-umb}
Let us consider the 2+2 structure defined by the canonical
2--form $U$. The three following conditions are equivalent: \\
(i) The structure is umbilical\\
(ii) The canonical SD bivector ${\cal U}=\frac{1}{\sqrt{2}} (U -
{\rm i} *U)$ satisfies:
\begin{equation}
\Sigma[U] \equiv \nabla {\cal U} - i_{\xi} {\cal U} \otimes {\cal U}
- i_{\xi}{\cal G}=0 \, , \qquad \xi \equiv \delta {\cal U}
\label{umb}
\end{equation}
(iii) The principal directions of $U$ determine shear-free geodesic
null congruences.
\end{lemma}
In the following we refer to (\ref{umb}) as the {\em umbilical
equation}.
On the other hand, let us define the 1--forms:
\begin{equation} \label{Phi-Psi}
\begin{array}{l}
\Phi \equiv \Phi[U] \equiv *U(\delta*U) - U(\delta U) \\[1mm]
\Psi \equiv \Psi[U] \equiv *U(\delta U) + U(\delta *U)
\end{array}
\end{equation}
where, for a 2-tensor $A$ and a vector $x$, $A(x)_{\mu} = A_{\mu
\nu} x^{\nu}$. Then, we have the following result \cite{fsD}:
\begin{lemma} \label{lem-m-i}
Let $U$ be the canonical 2--form of a 2+2 almost product
structure. Then it holds:\\
(i) The structure is minimal if, and only if, $U$ satisfies
$\, \Phi[U]=0$.\\
(ii) The structure is integrable if, and only if, $U$ satisfies $\,
\Psi[U] =0$.
\end{lemma}
These characterizations of a minimal and an integrable structure,
and the kinematic interpretation of these geometric properties given
in \cite{cf} lead to call the $\Phi$ and $\Psi$ given in
(\ref{Phi-Psi}) the {\em expansion vector} and the {\em rotation
vector} of the structure, respectively.
Every non-null 2-form $F$ can be written in the form $F =
e^{\phi}[\cos \psi U + \sin \psi *U]$, where the {\it geometry} $U$
is a unitary and simple 2--form that determines the 2+2 associated
structure (principal planes), $\phi$ is the {\it energetic index}
and $\psi$ is the {\it Rainich index}. When $F$ is solution of the
source-free Maxwell equations, $\delta F =0$, $\delta *F =0$, one
says that its intrinsic geometry $U$ defines a {\it Maxwellian
structure}. In terms of the intrinsic elements $(U,\phi,\psi)$,
Maxwell equations become \cite{rai,cff}:
\begin{equation} \label{maxwell-rainich}
\mathop{\rm d}\nolimits \phi = \Phi[U] \, , \qquad \qquad \mathop{\rm d}\nolimits \psi = \Psi[U]
\end{equation}
Then, from (\ref{maxwell-rainich}) the Rainich theorem \cite{rai}
follows:
\begin{lemma}
A unitary 2-form $U$ defines a Maxwellian structure if, and only if,
the expansion and the rotation are closed 1--forms, namely $U$
satisfies:
\begin{equation}\label{max2}
\mbox{\rm d} \Phi[U] = 0 \, , \qquad \qquad \mbox{\rm d} \Psi[U] =
0
\end{equation}
\end{lemma}
When the Maxwell-Minkowski energy tensor $T$ associated with a
non-null 2--form is divergence--free, the underlying 2+2 structure
is said to be {\em pre-Maxwellian} \cite{debever}. The conservation
of $T$ is equivalent to the first of the Maxwell-Rainich equations
(\ref{maxwell-rainich}) \cite{fsY}. Consequently: {\em a 2+2
structure is pre-Maxweelian if, and only if, the canonical 2--form
satisfies the first equation in (\ref{max2}).}
We can collect the expansion vector $\Phi$ and the rotation vector
$\Psi$ in a complex vector with a simple expression in terms of the
canonical SD bivector ${\cal U}$. Indeed, if we define $\chi \equiv
\chi[U] = i_{\xi} {\cal U}$, $\xi \equiv \delta{\cal U}$, we have:
\begin{equation} \label{chi}
\chi = \frac12 (\Phi[U] + \mathop{\textrm{i}}\nolimits \Psi[U])
\end{equation}
Then, conditions (\ref{max2}) that characterize a Maxwellian
structure can be written as:
\begin{equation} \label{maxwellian-chi}
\mathop{\rm d}\nolimits \chi = 0
\end{equation}
It is worth remarking that in (\ref{maxwellian-chi}) there are just
five independent complex equations (or in (\ref{max2}) ten real
ones). This fact has been pointed out in \cite{cff} and is a
consequence of the integrability condition $\delta \delta {\cal U} =
0$. Indeed this identity states, equivalently, that the complex
2--form $\mathop{\rm d}\nolimits \chi$ is orthogonal to ${\cal U}$:
\begin{equation} \label{max-5}
(\mathop{\rm d}\nolimits \chi, {\cal U}) = 0
\end{equation}
condition that in real formalism becomes:
$$( \mathop{\rm d}\nolimits \Phi, U ) + ( \mathop{\rm d}\nolimits \Psi ,*U) =0 \label{r-1} \, , \qquad
(\mathop{\rm d}\nolimits \Phi , *U) - (\mathop{\rm d}\nolimits \Psi, U) =0 $$
\section{Integrability conditions for umbilical 2+2-structures}
\label{sec-integrability}
As a consequence of lemma \ref{lem-umb} the Riemann tensor of the
space-times admitting two shear-free geodesic null congruences must
be submitted to the integrability conditions of the umbilical
equation (\ref{umb}). We can obtain these conditions from the Ricci
identities for the SD bivector ${\cal U}$:
\begin{equation} \label{u1}
\nabla_{\alpha} \nabla_{\beta} \, {\cal U}_{\mu \nu} -
\nabla_{\beta} \nabla_{\alpha} \, {\cal U}_{\mu \nu} = {\cal
U}_{\mu}^{\ \lambda} \, R_{\lambda \nu \beta \alpha} - {\cal
U}_{\nu}^{\ \lambda} \, R_{\lambda \mu \beta \alpha}
\end{equation}
The umbilical equation implies that the covariant derivative of the
canonical 2--form ${\cal U}$ is determined by the complex vector
$\xi \equiv \delta {\cal U}$. Indeed, (\ref{umb}) may equivalently
be written as
\begin{equation} \label{u2}
\nabla {\cal U} = i_{\xi} {\cal G}_{\perp} \, , \qquad \xi \equiv
\delta {\cal U} \, .
\end{equation}
If one simplifies (\ref{u1}) by using (\ref{u2}), one obtains:
\begin{proposition} \label{pro-integra-con}
Under the umbilical condition {\rm (\ref{u2})} the Ricci identities
{\rm (\ref{u1})} take the form:
\begin{equation} \label{integra-con-1}
(Riem - K \wedge g) \circ {\cal G}_{\perp} = 0
\end{equation}
\begin{equation} \label{T-xi-chi}
K \equiv T \cdot {\cal U} \, , \qquad T \equiv \nabla \xi - \chi
\otimes \xi
\end{equation}
where $\xi = \delta {\cal U}$ and $\chi = i_{\xi}{\cal U}$.
\end{proposition}
Taking into account the usual decomposition of the Riemann tensor,
we can write (\ref{integra-con-1}) as equations for the Weyl and
Ricci tensors. Indeed, by considering the self-dual and the
anti-self-dual parts in the first pair of indexes of this equation,
we obtain:
\begin{theorem} \label{theo-integra-con-2}
Let ${\cal W}$, $Ric$ and $R$ be the self-dual Weyl tensor, the
Ricci tensor and the scalar curvature of a space-time admitting an
umbilical structure ${\cal U}$. The integrability conditions for the
umbilical equation {\rm (\ref{umb})} may be written as:
\begin{eqnarray}
{\cal W}_{\perp} & = & \Omega {\cal G}_{\perp} \, , \qquad
\Omega \equiv - \left[\frac{R}{12} + (A, {\cal U} )\right] \label{i-c-1} \\
{\cal W}({\cal U})_{\perp} & = & -A_{\perp} \label{i-c-2}\\[2mm]
[{\cal U}, Ric] & = & 2 \, {\cal U} \cdot S \cdot {\cal U} - S
\label{i-c-3}
\end{eqnarray}
where $A$ and $S$ are the antisymmetric and symmetric parts of the
tensor $T$ given in {\rm (\ref{T-xi-chi})}:
$$A= \frac{1}{2} (T - T^{t}), \qquad S=\frac{1}{2} ( T + T^{t} )$$
\end{theorem}
The integrability conditions (\ref{i-c-1}) and (\ref{i-c-2}) can be
used to obtain an expression for the Weyl tensor whereas the third
one (\ref{i-c-3}) offers an expression for the Ricci tensor. Below
we give explicit expressions of these two irreducible parts of the
Riemann tensor, and we show that they are determined up to two
scalars by $U$ and its derivatives. This fact is a consequence of
the Codazzi relations, which give all the mixed components of the
curvature tensor as a concomitant of the second fundamental forms of
an arbitrary $p+q$ structure. Thus, only the total projections of
the curvature tensor on the two planes are not determined by the
second fundamental forms. In the case of a 2+2 structure these
projections have one sole component. Thus, if $v(t)$ and $h(t)$
denote the total projection of a tensor $t$ on the planes $V$ and
$H$, respectively, we have:
\begin{equation} \label{curvaturas}
v(Riem) = - X \, U \otimes U , \qquad h (Riem) = Y \, *U \otimes *U
\end{equation}
Let us note that the two scalars $X$ and $Y$ are the Gauss
curvatures of the respective 2--plane when the structure is a
product one, that is, when the space-time metric breaks down into
two bi-dimensional metrics, $g = v_{ij}(x^k) \mathop{\rm d}\nolimits x^i \mathop{\rm d}\nolimits x^j +
h_{AB}(x^C) \mathop{\rm d}\nolimits x^A \mathop{\rm d}\nolimits x^B$, $i,j,k = 0,1$ and $A,B,C= 2,3$.
Before obtaining the Ricci and Weyl tensors, we study some
integrability restrictions on the structure $U$ that are independent
of the curvature tensor. The third integrability equation
(\ref{i-c-3}) can be written in the form:
\begin{equation} \label{def-P}
[{\cal U}, Ric ] = [{\cal U} , L] \, , \qquad L \equiv [S , {\cal
U}]
\end{equation}
Thus, the tensor $L$ determines the commutator $[{\cal U}, Ric ]$.
But lemma \ref{lemma-real-U} implies that this commutator fixes the
Ricci tensor up to two scalars. More precisely, considering that
(\ref{i-c-3}) implies $\bar{{\cal U}} \times [\bar{{\cal U}} , Ric ]
= \bar{L}$, and taking $E = Ric$ in expression (\ref{real-U}), we
have:
\begin{equation} \label{ricci-1}
\begin{array}{lll}
Ric & = & \frac{1}{4}( R \ g + r \Pi) + {\cal U} \times [{\cal U} ,
L] + {\cal U} \times \{ {\cal U},
\bar{L} \} = \\[2mm]
& = & \frac{1}{4}( R \ g + r \Pi) + \frac{1}{2} ( L + \bar{L}) +
{\cal U} (L - \bar{L} ) {\cal U}
\end{array}
\end{equation}
The Ricci tensor being real, the imaginary part of the last term in
the above expression must vanish. Then, one obtains:
\begin{equation} \label{integra-con-3-a}
v (\mbox{\rm{Im}}[ L]) =0 , \qquad h ( \mbox{\rm{Im}} [L]) = 0
\end{equation}
A straightforward calculation allows us to obtain its real and
imaginary parts from the definition (\ref{def-P}) of $L$:
\begin{eqnarray} \label{re-P}
4 \mbox{\rm{Re}}[ L] & = & M - U \cdot M \cdot U + *U \cdot M
\cdot *U - U \cdot N \cdot *U - *U \cdot N \cdot U \\
4 \mbox{\rm{Im}}[ L] & = & N - U \cdot N \cdot U + *U \cdot N \cdot
*U + U \cdot M \cdot *U + *U \cdot M \cdot U \label{im-P}
\end{eqnarray}
$M$ and $N$ being the symmetric tensors:
\begin{equation} \label{M-N}
M \equiv {\cal L}_{\Phi} g - \Phi \otimes \Phi + \Psi \otimes \Psi
\, , \qquad N \equiv {\cal L}_{\Psi} g - \Phi
\stackrel{\sim}{\otimes} \Psi
\end{equation}
where ${\cal L}_{s}$ denotes the Lie derivative with respect to a
vector field $s$ and, for two arbitrary tensors, $A
\stackrel{\sim}{\otimes} B = A \otimes B + B \otimes A$. We can make
the integrability conditions (\ref{integra-con-3-a}) more explicit.
Indeed, by using (\ref{im-P}) we can easily write these equations
as:
$$
[v(N), U] = 0 \, , \qquad [h[N], *U] = 0
$$
But, taking into account that the sole symmetric tensor in $V$
(resp. $H$) which commutes with $U$ (resp. $*U$) is proportional to
$v$ (resp. $h$), we have:
\begin{proposition} \label{pro-integra-con-3}
The canonical 2--form $U$ of an umbilical structure satisfies the
integrability conditions:
\begin{equation}
v ( \ {\cal L}_{\Psi} g - \Phi \stackrel{\sim}{\otimes} \Psi \ ) =
\lambda \ v \label{r3} \, , \qquad h ( \ {\cal L}_{\Psi} g - \Phi
\stackrel{\sim}{\otimes} \Psi \ ) = \mu \ h
\label{integra-con-3-b}
\end{equation}
where $\Phi$ and $\Psi$ are given in {\rm (\ref{Phi-Psi})}, and
$\lambda$ and $\mu$ are two scalars that can be obtained by taking
the trace.
\end{proposition}
\subsection{The Ricci tensor}
Taking its real part, the expression (\ref{ricci-1}) of the Ricci
tensor becomes:
\begin{equation} \label{ricci-2}
Ric = \frac{1}{4}( R \ g + r \Pi) + \mbox{\rm{Re}}[L] - U \cdot
\mbox{\rm{Im}}[ L ] \cdot *U - *U \cdot \mbox{\rm{Im}} [L] \cdot U
\end{equation}
where the scalar curvature $R$ and the trace $r$ with the structure
tensor $\Pi$ depend on the scalars $X$ and $Y$ and the $U$
derivatives as:
\begin{equation} \label{R-r-1}
R = 2 (X+Y) + \Phi^2 - \Psi^2 - 2 \delta \Phi \, , \quad \qquad r =
2(X-Y)
\end{equation}
Finally, if we substitute (\ref{re-P}) and (\ref{im-P}) in the
expression (\ref{ricci-2}), we obtain:
\begin{theorem} \label{theo-ricci}
If a space-time admits an umbilical structure $U$, the Ricci tensor
takes the expression:
\begin{equation}
Ric = \frac{1}{4}( \hat{R} \ g + \hat{r} \Pi) + \frac12 ( M - U
\cdot N \cdot *U - *U \cdot N \cdot U) \label{ricci-3}
\end{equation}
$M$ and $N$ depending on the expansion and rotation vectors $\Phi$
and $\Psi$ as (\ref{M-N}), and
$$
\begin{array}{lll}
2 \hat{R} & \equiv & 4 (X+Y) + 3 \Phi^2 - 3 \Psi^2 - 2 \delta
\Phi\\[1mm]
2 \hat{r} & \equiv & 4 (X-Y) + \Pi(\Phi, \Phi) - \Pi(\Psi, \Psi) +
2 \delta_{\Pi} \Phi
\end{array}
$$
where $\delta_{\Pi} \Phi \equiv - \Pi^{\alpha \beta} \nabla_{\alpha}
\Phi_{\beta}$.
\end{theorem}
This proposition shows that the Ricci tensor is determined, up to
the scalars $X$ and $Y$ given in (\ref{curvaturas}), by $U$, $\chi$
and ${\cal L}_{\chi} g$.
\subsection{The Weyl tensor}
As a consequence of theorem \ref{theo-integra-con-2}, the self-dual
Weyl tensor ${\cal W}$ is determined by the scalar $\Omega$ and the
self-dual 2--form ${\cal Z} \equiv A_{\perp}$. Indeed, (\ref{i-c-1})
gives the orthogonal components of ${\cal W}$, (\ref{i-c-2}) gives
the mixed components and the ${\cal U} \otimes {\cal U}$ component
is determined by the traceless condition. On the other hand, from
the expression (\ref{T-xi-chi}) of $T$ we can obtain:
\begin{eqnarray}
2 (A,{\cal U}) & = & \delta \chi - \chi^2 \\
{\cal Z} \equiv A_{\perp} & = & \frac{1}{2} \mathop{\rm d}\nolimits \xi_{\perp} =
[\nabla \chi , {\cal U} ]_{\perp} = \frac{1}{2} [ \mathop{\rm d}\nolimits \chi , {\cal
U}]_{\perp} = \frac{1}{2} [ \mathop{\rm d}\nolimits \chi , {\cal U}] \label{zeta}
\end{eqnarray}
and, consequently, we have:
\begin{theorem} \label{theo-weyl}
If a space-time admits an umbilical structure ${\cal U}$, the
self-dual Weyl tensor takes the expression:
\begin{equation} \label{weyl-auto-a}
{\cal W} = 3 \Omega \, {\cal U} \otimes {\cal U} + \Omega \, {\cal
G} + {\cal U} \stackrel{\sim}{\otimes} {\cal Z}
\end{equation}
where
\begin{equation}
\Omega = \frac12 (\chi^2 - \delta \chi) - \frac{R}{12} \, , \qquad
{\cal Z} = \frac{1}{2} [ \mathop{\rm d}\nolimits \chi , {\cal U}] \label{weyl-auto-b}
\end{equation}
Moreover, the Weyl tensor invariants are
$$a \equiv \mathop{\rm tr}\nolimits {\cal W}^2 = 2 (3 \Omega^2 - ({\cal Z},{\cal Z})) \, , \qquad b
\equiv \mathop{\rm tr}\nolimits {\cal W}^3 = 3 \Omega (({\cal Z},{\cal Z}) - 2 \Omega^2)
$$ and the Weyl tensor eigenvalues
\begin{equation} \label{valpro}
\Omega, \qquad \frac{1}{2} \Big( - \Omega \pm \sqrt{9 \Omega^2 - 4
({\cal Z},{\cal Z})} \Big)
\end{equation}
\end{theorem}
This theorem shows that the Weyl tensor is determined by the scalar
curvature $R$, and by $U$, $\chi$ and $\mathop{\rm d}\nolimits\chi$. This fact and
theorem \ref{theo-ricci}, which gives the Ricci tensor, show that
the Riemann tensor is determined, up to the scalars $X$ and $Y$, by
the the first and second derivatives of $U$, in accordance with our
comment before expression (\ref{curvaturas}).
From expressions (\ref{weyl-auto-a}) and (\ref{weyl-auto-b}) we can
obtain the real Weyl tensor. Indeed, if we substitute $\chi$ in
terms of the expansion and rotation vectors $\Phi$ and $\Psi$, and
we take the real part of (\ref{weyl-auto-a}), we obtain:
\begin{proposition} \label{pro-weyl-2}
If a space-time admits an umbilical structure $U$ the Weyl tensor
takes the expression:
$$
W= 3 \Omega_1 (U \otimes U - *U \otimes *U) + 3 \Omega_2 \, U
\stackrel{\sim}{\otimes} *U + \Omega_1 \, G + \Omega_2 \, \eta + U
\stackrel{\sim}{\otimes} Z - *U \stackrel{\sim}{\otimes} *Z
$$
where
\begin{eqnarray} \label{Z-real}
Z & = & \frac14 ([\mathop{\rm d}\nolimits \Phi , U] + [\mathop{\rm d}\nolimits \Psi , *U]) ,\\
\Omega_1 & \equiv & \frac{1}{24} ( \Phi^2 - \Psi^2 - 2 \delta \Phi)
- \frac16 (X+Y) \, , \quad \Omega_2 \equiv \frac14 ( (\Phi,\Psi) -
\delta \Psi) \label{v-propi-real-im}
\end{eqnarray}
\end{proposition}
\section{The compatible Petrov-Bel types}
\label{petrov}
The algebraic classification of the Weyl tensor $W$ can be obtained
by studying the traceless linear map defined by the self--dual Weyl
tensor ${\cal W}$ on the SD bivectors space. In terms of the
invariants $a$ and $b$ the characteristic equation reads $\,
x^{3}-\frac{1}{2} ax -\frac{1}{3} b =0 \, $. Then, Petrov-Bel
classification follows taking into account both the eigenvalue
multiplicity and the degree of the minimal polynomial. The
algebraically regular case (type I) occurs when $6b^2 \not= a^3$ and
so the characteristic equation admits three different roots. If
$6b^2 = a^3 \not= 0$, there is a double root and a simple one and
the minimal polynomial distinguishes between types D and II.
Finally, if $a=b=0$ all the roots are equal and so zero, and the
Weyl tensor is of type O, N or III, depending on the degree of the
minimal polynomial. A fully tensorial algorithm has been presented
in \cite{fms} enabling us to determine the Petrov-Bel type.
On the other hand, let us remember that we have defined a Debever SD
bivector as one whose principal directions are Debever principal
null directions of the Weyl tensor \cite{fms}. As the principal
directions of ${\cal U}$ are null shear--free geodesics, they are
Debever principal directions and, consequently, ${\cal U}$ is always
a unitary Debever SD bivector.
In the previous section we have obtained the Weyl tensor of a metric
admitting a 2+2 umbilical structure as well as the invariants of
the Weyl tensor. These invariants depend on $\Omega$ and $({\cal
Z},{\cal Z})$ as given in theorem \ref{theo-weyl}. Then, a
straightforward calculation leads to:
$$ a^3 - 6 b^2 = - 2 ({\cal Z},{\cal Z})(9 \Omega^2 - 4 ({\cal Z},{\cal Z}))$$
Then, the algorithm given in \cite{fms} works and we can obtain the
algebraic type of the Weyl tensor in terms of ${\cal Z}$ and
$\Omega$:
\begin{theorem} \label{theo-types}
If a space-time admits a 2+2 umbilical structure, then the
canonical SD bivector ${\cal U}$ is a unitary Debever SD bivector.
Thus,
the space-time cannot be of Petrov-Bel type N. Moreover:\\[1mm]
i) It is of type O if, and only if, $\ \Omega =0 , \quad {\cal Z}
=0 $.\\[1mm]
ii) It is of type III if, and only if, $\ \Omega = 0 ,
\quad {\cal Z} \neq 0, \quad ({\cal Z},{\cal Z}) =0$.\\[1mm]
iii) It is of type D if, and only if, $\ \Omega \neq 0 , \quad
{\cal Z} =0 $.\\[1mm]
iv) It is of type II if, and only if, $\ \Omega \neq 0 \neq {\cal
Z}, \quad
({\cal Z},{\cal Z})(9 \Omega^2 - 4 ({\cal Z},{\cal Z})) = 0$.\\[1mm]
v) It is of type I if, and only if, $\ ({\cal Z},{\cal Z})(9
\Omega^2 - 4 ({\cal Z},{\cal Z})) \neq 0 $.
\end{theorem}
Now we analyze the relationship between the geometry of the Weyl
tensor and the geometrical elements defined by ${\cal U}$ and its
derivatives. We show that both SD bivectors ${\cal U}$ and ${\cal
Z}$ are closely related to the principal null directions or Debever
directions.
For every Petrov-Bel type, we briefly summarize the geometrical
elements that the Weyl tensor outlines. We use the notation and
results used in the aforementioned paper \cite{fms}, where an
exhaustive approach to this topic can be found. We compare the
canonical form of the Weyl tensor of every type with the expression
of the Weyl tensor obtained in theorem \ref{theo-weyl}.
\subsection{Petrov-Bel type III}
The self-dual Weyl tensor of a type III space-time takes the
canonical expression \cite{fms}:
$${\cal W} = {\cal U} \stackrel{\sim}{\otimes} {\cal H} $$
where ${\cal H}$ is the null eigen-bivector and ${\cal U}$ the
canonical unitary SD bivector. The two Debever directions are the
principal directions of the canonical SD bivector ${\cal U}$, the
triple one being the common null principal direction to ${\cal H}$
and ${\cal U}$.
From theorem \ref{theo-types}, a type III space-time with an
umbilical structure is characterized by $\Omega =0$ and $({\cal
Z},{\cal Z})= 0$, that is, ${\cal Z}$ is a null SD bivector. Then,
the expression for the Weyl tensor in theorem \ref{theo-weyl}
becomes
$${\cal W} = {\cal U} \stackrel{\sim}{\otimes} {\cal Z} $$
Consequently, we find that ${\cal U}$ coincides with the canonical
unitary SD bivector and ${\cal Z}$ with the null eigen-bivector.
This way, we can conclude
\begin{proposition}
If a type III space-time admits a 2+2 umbilical structure ${\cal
U}$, then the Debever SD bivectors are ${\cal U}$ and ${\cal Z}$,
that is, the Debever directions are the principal directions of
${\cal U}$, the triple one being the fundamental direction of the
null SD bivector ${\cal Z}$.
\end{proposition}
\subsection{Petrov-Bel type D}
Theorem \ref{theo-types} states that a type D space-time admits a
2+2 umbilical structure ${\cal U}$ if, and only if, $\Omega \neq 0$
and ${\cal Z} =0$. Then, expression (\ref{weyl-auto-a}) of the Weyl
tensor becomes:
$$
{\cal W} = 3 \Omega \, {\cal U} \otimes {\cal U} + \Omega \, {\cal
G}
$$
Thus, ${\cal U}$ is the principal SD bivector of the Weyl tensor
with associated eigenvalue $\Omega$. Then the principal null
directions of ${\cal U}$ are the Debever directions of the Weyl
tensor. Consequently, we conclude:
\begin{proposition}
If a type D space-time admits a 2+2 umbilical structure ${\cal U}$,
then ${\cal U}$ is the principal SD bivector of the Weyl tensor,
that is, the two double Debever directions are the principal
directions of ${\cal U}$.
\end{proposition}
\subsection{Petrov-Bel type II}
A type II Weyl tensor has a unitary eigenbivector associated with
the simple eigenvalue $- 2 \rho$ and just a null one ${\cal H}$
corresponding to the double eigenvalue $\rho$. The double Debever
principal null direction $l$ is the fundamental direction of ${\cal
H}$ and, moreover, there exist two simple Debever directions
$l_{\pm}$. Thus, three unitary Debever SD bivectors $\{ {\cal V} ,
{\cal V}_{\pm} \}$ can be considered, ${\cal V}$ having $l_{\pm}$ as
principal directions, and ${\cal V}_{\pm}$ having $l$ and $l_{\pm}$,
respectively, as principal directions. In terms of these Debever SD
bivectors the Weyl tensor takes these two alternative canonical
expressions \cite{fms}:
\begin{equation} \label{tipo2}
{\cal W} = \rho {\cal G} + \frac{3}{2} \rho \ {\cal V}_{+} \stackrel
{\sim}{\otimes} {\cal V}_{-} = \ - 2 \rho {\cal G} + {\cal H}
\stackrel{\sim}{\otimes} {\cal V}
\end{equation}
As theorem \ref{theo-types} states, type II can occur in two
different ways, when ${\cal Z}$ is a null SD bivector, $({\cal Z},
{\cal Z}) = 0$, or when $9 \Omega^2 - 4 ({\cal Z},{\cal Z}) = 0$,
both $\Omega$ and ${\cal Z}$ being non zero.
In the first case, expressions (\ref{valpro}) give us the double
eigenvalue $\rho = \Omega$. Moreover, from theorem \ref{theo-weyl}
we obtain that ${\cal W} ({\cal Z}) = \Omega {\cal Z}$ and so,
${\cal Z}$ is the canonical null SD bivector. This way ${\cal Z}$
determines the double Debever principal null direction. Moreover, in
this case the expression (\ref{weyl-auto-a}) of the Weyl tensor
becomes:
$$
{\cal W} = \Omega {\cal G} + \frac{3}{2} \Omega \ {\cal U}
\stackrel{\sim}{\otimes} \left[ {\cal U} + \frac{2}{3 \Omega} {\cal
Z} \right]
$$
By comparing this expression with the first in (\ref{tipo2}) we
conclude that in this case ${\cal U} + \frac {2}{3 \Omega} {\cal Z}$
and ${\cal U}$ are the unitary Debever SD bivectors ${\cal
V}_{\pm}$.
In the second case, ${\cal Z}$ is a non null SD bivector, and
expressions (\ref{valpro}) imply that the double eigenvalue is $\rho
= - \frac{1}{2} \Omega$. Then the SD bivector $\frac{3}{2} \Omega \
{\cal U} + {\cal Z} $ is null, and the expression
(\ref{weyl-auto-a}) of the Weyl tensor can be written as:
$$
{\cal W} - \Omega {\cal G} = {\cal U} \stackrel{\sim}{\otimes} \left
[ \frac{3}{2} \Omega \ {\cal U} + {\cal Z} \right]
$$
Thus, we have $\frac{3}{2} \Omega \ {\cal U} + {\cal Z} $ coincides
with the ${\cal H}$ of (\ref{tipo2}) and, consequently, it is the
canonical null SD bivector. These results are summarized as follows:
\begin{proposition}
Let ${\cal U}$ be the canonical SD bivector of an umbilical
structure in a type II space-time. It holds:
i) If $({\cal Z}, {\cal Z}) = 0$, then ${\cal Z}$ is the canonical
null SD bivector and thus the fundamental direction of ${\cal Z}$ is
the double Debever direction. This one is also the common principal
directions of the Debever SD bivectors ${\cal U}$ and ${\cal U} +
\frac{2}{3 \Omega} {\cal Z}$. The other two principal directions of
these SD bivectors determine the two simple Debever directions.
ii) If $9 \Omega^2 - 4 ({\cal Z},{\cal Z}) = 0$, then ${\cal U}$ is
the Debever SD bivector whose principal directions are the two
simple Debever directions, and the double one is the fundamental
direction of the null SD bivector $\frac{3}{2} \Omega \ {\cal U} +
{\cal Z}$
\end{proposition}
\subsection{Petrov-Bel type I}
In an algebraically general space-time the Weyl tensor has three
different eigenvalues $\rho_i$, and an orthonormal frame $\{ {\cal
U}_i \}$ of eigenbivectors of the Weyl tensor can be built. On the
other hand, four simple Debever principal null directions exist that
define six unitary Debever SD bivectors $\{ {\cal V}_{i \pm} \}$. If
we choose a value of the index $i$, say $i=3$, the Weyl tensor can
be written as \cite{fms} \cite{fsI}:
\begin{equation} \label{tipo1}
{\cal W} = \rho_3 \ {\cal G} + \frac{\rho_2 - \rho_1}{2} \ {\cal
V}_{3+} \stackrel{\sim}{\otimes} {\cal V}_{3-}
\end{equation}
As a consequence of theorem \ref{theo-types}, when the space-time
admits an umbilical structure, the type I case can be characterized
by the scalar condition $({\cal Z},{\cal Z})(9 \Omega^2 - 4 ({\cal
Z},{\cal Z})) \neq 0$ . Then, the expression (\ref{weyl-auto-a}) of
the Weyl tensor can be written as (\ref{tipo1}) by taking:
\begin{eqnarray}
\rho_3 & \equiv & \Omega \, , \qquad \rho_2 -\rho_1 \equiv 2
\sqrt{ 9 \Omega^2 - 4 ({\cal Z},{\cal Z})} \\[2mm]
{\cal V}_{3+} & \equiv & {\cal U} \, ,\qquad {\cal V}_{3-} \equiv
\frac{1}{\sqrt{ 9 \Omega^2 -4 ({\cal Z},{\cal Z})}} ( 3 \Omega
{\cal U} + 2 {\cal Z} )
\end{eqnarray}
Thus, we can state:
\begin{proposition}
Let ${\cal U}$ be an umbilical structure in a type I space-time.
Then the four Debever principal null directions are the principal
directions of the Debever SD bivectors ${\cal U}$ and $3 \Omega
{\cal U} + 2{\cal Z}$.
\end{proposition}
The expression (\ref{tipo1}) is not adapted to the Weyl
eigenbivectors; however, these can be obtained by means of the
projectors given in \cite{fms}. Indeed, using (\ref{weyl-auto-a})
and the expression (\ref{valpro}) of the eigenvalues, we obtain:
\begin{proposition}
In a type I space-time with an umbilical structure ${\cal U}$, the
orthonormal basis of eigenbivectors $\{{\cal U}_i\}$ associated with
the eigenvalues {\rm (\ref{valpro})} are, respectively:
$$
{\cal U}_3 \propto {\cal U} \cdot {\cal Z} \, ,\qquad {\cal U}_1
\propto (3\Omega - \alpha) {\cal U} + 2 {\cal Z} \, , \qquad {\cal
U}_2 \propto (3\Omega + \alpha) {\cal U} + 2 {\cal Z} \, ,
$$
where $\alpha \equiv \sqrt{ 9 \Omega^2 -4 ({\cal Z},{\cal Z})}$.
\end{proposition}
\section{Type D space-times admitting two shear-free geodesic null congruences}
\label{sec-typeD}
In theorem \ref{theo-types} we have shown that the Petrov-Bel type D
space-times admitting two geodesic shear-free null congruences, that
is, an umbilical structure, are those non conformally flat
space-times satisfying ${\cal Z} = 0$. Then, from the expression
$2{\cal Z} = [\mathop{\rm d}\nolimits \chi, {\cal U}]$ (see (\ref{zeta})) and condition
(\ref{maxwellian-chi}) which characterizes a Maxwellian structure,
we obtain the following:
\begin{proposition} \label{pro-max-typeD}
If a non conformally flat space-time admits an umbilical and
Maxwellian structure, then the Weyl tensor is Petrov-Bel type D and
the structure is aligned with the Weyl principal structure.
\end{proposition}
This result has been used elsewhere \cite{fsY} to characterize the
type D space-times admitting a non-null Killing-Yano or conformal
Killing-Yano tensor.
Nevertheless, type D space-times exist with an umbilical and non
Max\-wellian structure. In order to obtain complementary conditions
that guarantee the Maxwellian character of the principal structure
one should consider this lemma:
\begin{lemma}
The complex 2--form $\mathop{\rm d}\nolimits \chi$ admits the following decomposition
in its self-dual and anti-self-dual parts:
\begin{equation} \label{chi-dual-anti}
\mathop{\rm d}\nolimits \chi = ([\mathop{\rm d}\nolimits \chi, {\cal U}] + \{\mathop{\rm d}\nolimits \chi, {\cal U} \})
\cdot{\cal U}
\end{equation}
\end{lemma}
The decomposition (\ref{chi-dual-anti}) is valid for an arbitrary
complex two form, the first term being a self-dual 2--form. The
second term contains, generically, the ${\cal U}$-component but, for
the 2--form $\mathop{\rm d}\nolimits \chi$, this component vanishes as a consequence of
(\ref{max-5}).
From lemma above, theorem \ref{theo-types} and expression
(\ref{zeta}) one finds: {\em a space-time with two shear-free
geodesic null congruences is type D, if and only if, the 2--form
$\mathop{\rm d}\nolimits \chi$ is anti-self dual}, as stated by Dietz and R\"{u}diger
\cite{diru-1}. Then, if this anti-self-dual part vanishes, the
umbilical principal structure of a type D space-time becomes
Maxwellian. But the nullity of a self-dual or anti-self-dual 2--form
is equivalent to the nullity of its real (or imaginary) part. Thus,
we can state:
\begin{proposition} \label{pro-max-iff}
In a non conformally flat space-time, an umbilical structure ${\cal
U}$ is Maxwellian ($\mathop{\rm d}\nolimits \chi = 0$)
if, and only if, two (and then all) of the following conditions hold:\\[1mm]
(i) The space-time is Petrov-Bel type D (and the structure is the
principal one).\\[1mm]
(ii) The structure is pre-Maxwellian (i.e. the expansion 1--form is
closed, $\ \mathop{\rm d}\nolimits \Phi = 0$).\\[1mm]
(iii) The rotation 1--form is closed, $\ \mathop{\rm d}\nolimits \Psi = 0$.\\[1mm]
(iv) $ \{\mathop{\rm d}\nolimits \chi, {\cal U}\} = 0$ (i.e. $\mathop{\rm d}\nolimits \Phi = *\mathop{\rm d}\nolimits \Psi$).
\end{proposition}
Now we analyze in detail the last condition (iv) in the proposition
above. Under the umbilical condition, the anti-self-dual part of
$\mathop{\rm d}\nolimits \chi$ is $\{S,{\cal U}\}$ as a consequence of the expression
of the tensor $S$ given in theorem \ref{theo-integra-con-2} and the
definition of $\chi$. Then, from the integrability condition
(\ref{i-c-3}), we can state:
\begin{lemma}
Let ${\cal U}$ be the canonical SD bivector of an umbilical
structure and $S$ the tensor defined in theorem
\ref{theo-integra-con-2}. The
following statements are equivalent:\\[1mm]
i) $\mathop{\rm d}\nolimits \chi$ is a self-dual 2-form (i.e. $ \{\mathop{\rm d}\nolimits \chi, {\cal U}\}
= 0$)\\[1mm]
ii) $[ Ric , {\cal U}] = 2S $.
\end{lemma}
As a direct consequence of this lemma and proposition
\ref{pro-max-iff} we obtain:
\begin{corollary} \label{cor-max-ricci}
In a non conformally flat space-time, let ${\cal U}$ be the
canonical SD bivector of an umbilical structure and $S$ the tensor
defined in theorem \ref{theo-integra-con-2}. The
following statements are equivalent:\\[1mm]
i) ${\cal U} $ defines a maxwellian structure.\\[1mm]
ii) The space-time is Petrov-Bel type D and $[ Ric , {\cal U}] =
2S$.
\end{corollary}
Despite this result, the Maxwellian character of an umbilical
structure does not restrict, generically, the algebraic type of the
Ricci tensor. Nevertheless, the Maxwellian condition can restrict
the Ricci tensor if we impose complementary conditions. Thus, we
analyze elsewhere \cite{fsKV} the important role played by tensor
$S$ in generalizing to other energy contents the commutative group
of symmetries that the type D vacuum solutions admit, and we will
show in \cite{fsKV} that in this case the Ricci tensor becomes
algebraically special. In this study corollary \ref{cor-max-ricci}
will play a significative role.
On the other hand, some conditions on the Ricci tensor can impose
strong restrictions on the Weyl principal structure of a type D
space-time. Indeed, we have shown elsewhere \cite{fsD} that, for
vacuum solutions or when the Cotton tensor vanishes, the principal
structure of a type D space-time is umbilical and Maxwellian.
Moreover, in this case, the Weyl eigenvalues are real if, and only
if, the structure is integrable \cite{fsD}. Generalizing this kind
of results to other energy contents is underway and involves
analyzing the Bianchi identities for a type D Weyl tensor and a
Ricci restricted by the umbilical integrability conditions.
Nevertheless, we can obtain some simple results which do not depend
on the Ricci tensor. Thus, from proposition \ref{pro-max-iff} and
the expression (\ref{v-propi-real-im}) of the imaginary part of the
Weyl eigenvalue, we have:
\begin{proposition} \label{pro-in-real}
If a Petrov-Bel type D space-time admits an umbilical and integrable
structure, then the Weyl tensor has real eigenvalues and the
structure is the principal one and Maxwellian.\\[1mm]
Moreover, a function $\phi$ exists such that $\mathop{\rm d}\nolimits \phi = \Phi$ and
the metric tensor is conformal to a product one, the conformal
factor being $e^{-2\phi}$.
\end{proposition}
The second statement of this proposition is a direct consequence of
the changes that a conformal transformation produces on the
differential properties of a structure. A summary of this subject
can be found in \cite{fsD}.
It is worth remarking that all the degenerate static solutions as
well as their charged counterparts satisfy the hypothesis of the
proposition \ref{pro-in-real}. The canonical expression of the
metric as conformal to a product one has allowed us to obtain an
intrinsic and explicit labeling of both families of solutions
\cite{fsD,fsS}.
It has been known for years \cite{hm-1,diru-1} that the two null
eigenvectors of a conformal or a Killing tensor of type 2+2 as well
as the two principal directions of a non-null Killing-Yano or a
conformal Killing-Yano 2--form are shear-free geodesic null
congruences. More recently \cite{fsY,cfsKT} we have recovered this
property and have studied the complementary conditions, as equations
on the structure $U$ defined by these null directions, that
guarantee the existence of these first integrals of the geodesic
equation. For conformal Killing tensors and conformal Killing-Yano
tensors these complementary conditions are related with Maxwellian
properties of the structure. More precisely, we have
\cite{fsY,cfsKT}:
\begin{lemma} \label{lemma-ck-cky}
A 2+2 traceless symmetric tensor is a conformal Killing tensor if,
and only if, it defines an umbilical and pre-Maxwellian
structure.\\[1mm]
A non-null 2--form is a conformal Killing-Yano tensor if, and only
if, it defines an umbilical and Maxwellian structure.
\end{lemma}
It is known that the type D vacuum solutions which admit a Killing
tensor also admit a Killing-Yano tensor \cite{collinson,ste}, and
all the type D vacuum solutions admit a conformal Killing tensor
\cite{walker-p}. The last statement can be generalized to type D
solutions with a vanishing Cotton tensor and extended to conformal
Killing-Yano tensors as a consequence of the results in \cite{fsD}
and lemma \ref{lemma-ck-cky}. Moreover, from this lemma and
proposition \ref{pro-max-iff} we obtain an interesting result which
does not depend on the energy content:
\begin{theorem}
Every Petrov-Bel type D space-time that admits a 2+2 conformal
Killing tensor also admits a conformal Killing-Yano tensor.
\end{theorem}
{\bf Acknowledgements} This work has been partially supported by the
Spanish Ministerio de Educaci\'on y Ciencia, MEC-FEDER project
FIS2006-06062.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,434 |
{"url":"http:\/\/sp.marksharks.com\/ms\/g08\/s02\/solved_questions\/ncert\/NCERT_OTHERS_LESSON16\/index.html","text":"Lesson: Light\nTopic 1: Laws of Reflection\n\nQuestion: 1\n\nYou may have observed the image of the sun in the windows of distant buildings during sunset or sunrise. However, the same image is not seen in the windows of distant building at midday. Can you explain why?\n\nSolution:\n\nAs the sun is relatively low in the sky during sunrise or sunset, the rays of the sun strike the window and reach our eyes, which are at a similar height to the window. At midday, the sun is very high, so rays from the sun that strike the window reflect downward and so we are not able to see the reflection.\n\nQuestion: 2\n\nHow does a ray of light follow the first law of reflection if after reflection the individual rays for a number of incident parallel rays scatter in many different directions?\n\nSolution:\n\nAccording to the first law of reflection, the angle of incidence is equal to the angle of reflection. When a surface is rough, it can be considered to be a collection of numerous tiny plane mirrors oriented at different angles. Thus, individual reflected rays will scatter in different directions, but they can be considered to be following the first law of reflection individually.\n\nQuestion: 3\n\nMost magazines have glossy pages, whereas newspapers have a rougher surface. Would it be easier to read from rough pages or glossy pages? Explain your answer.\n\nSolution:\n\nIt is much easier to read from rough pages as they undergo diffused reflection. Glossy pages result in regular reflection and cause a glare on our eyes. The reader mostly sees an image of the light source which illuminates the page, rather than seeing the text and pictures on the page.\n\nQuestion: 4\n\nCan you see the objects in a dark room? Can you see objects outside a dark room? Explain.\n\nSolution:\n\nWe see objects only when light reflected by that object reaches our eyes. In a dark room, there is no light that can be reflected by any object and so we are unable to see objects. But if there is light outside the room, we can see those objects, since they will reflect light that will reach our eyes.\n\nQuestion: 5\n\nIn which direction will a ray of light falling along the normal to a mirror be reflected?\n\nSolution:\n\nA ray of light falling normally on a mirror means that it is falling on the mirror at\n\n${90}^{\\circ }$\u00a0to the mirror surface. Therefore, the incident ray and the reflected ray both make an angle of ${0}^{\\circ }$\u00a0with the normal as per the first law of reflection and the ray, upon reflection, retraces its path.\n\nQuestion: 6\n\nDefine reflection of light and state the laws of reflection.\n\nSolution:\n\nReflection is a phenomenon in which a ray of light falls on a surface and returns to the same medium in a different direction.\n\nThe laws of reflection are as follows:\n\n1. When a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection.\n2. The incident ray, reflected ray and the normal always lie in the same plane.\n\nQuestion: 7\n\nWhat is the angle of incidence?\n\nSolution:\n\nThe angle between the normal and the incident ray is called the angle of incidence.\n\nQuestion: 8\n\nWhat is the angle of reflection?\n\nSolution:\n\nThe angle between the normal and the reflected ray is called the angle of reflection.\n\nQuestion: 9\n\nExplain diffuse reflection?\n\nSolution:\n\nWhen a set of parallel rays undergoes reflection, but the reflected rays are not parallel to each other, the resulting reflection is known as diffuse reflection.\n\nQuestion: 10\n\nHow are we able to see an object which is not self-illuminating?\n\nSolution:\n\nAn object that is not self-illuminating reflects light that is incident on it. We are able to see these objects since our eyes receive light reflected from the object.\n\nTopic 2: Image Formation\n\nQuestion: 1\n\nYou might have noticed that emergency vehicles, such as ambulances often have text in the front written in reversed lettering. Why?\n\nSolution:\n\nVehicles drivers on a road normally view the ambulance in their rear-view mirrors, so whatever they see will be a mirror image. Thus, if the text on the front of an emergency vehicle is written in reversed lettering, the image seen by the driver in the rear-view mirror will appear in proper orientation.\n\nQuestion: 2\n\nList five characteristics of an image formed by a plane mirror.\n\nSolution:\n\nThe five characteristics of an image formed by a plane mirror are as follows:\n\n1. Image is erect.\n2. Image is virtual.\n3. Image distance from the mirror is equal to the object distance from the mirror.\n4. Image height is same as object height.\n5. Image is always formed behind the mirror.\n\nQuestion: 3\n\nList three uses of a plane mirror.\n\nSolution:\n\nThe three uses of a plane mirror are as follows:\n\n1. Plane mirrors are used as a looking glass.\n2. Plane mirrors are used to construct periscope which is used in submarines.\n3. Plane mirrors are also used to make kaleidoscope, a toy which produces beautiful patterns from coloured paper, pieces of glass or small coloured beads.\n\nQuestion: 4\n\nCan the image formed by a plane mirror be projected on a screen?\n\nSolution:\n\nNo, images formed by a plane mirror can never be projected onto a screen, as light rays do not actually reach the image. The image is a virtual image positioned behind the mirror.\n\nQuestion: 5\n\nThree objects A, B and C are placed in front of a plane mirror as shown. Can Priya see the images A, B, C on the mirror? Justify your answer.\n\nSolution:\n\nA plane mirror forms a virtual image behind the mirror. The image distance between the mirror and the image distance will always be equal to the distance between the mirror and the object. Priya can see the objects placed at points A and B but not the object placed at point C as per the image below. Object C is out of range of Priya\u2019s visibility.\n\nQuestion: 6\n\nThe image of an object is formed by two plane mirrors. One mirror is twice the size of the other. In which mirror will the image be bigger and why?\n\nSolution:\n\nThe image of an object will be the same size as the object, irrespective of the size of the plane mirror.\n\nQuestion: 7\n\nDefine lateral inversion?\n\nSolution:\n\nWhen an image is formed by a plane mirror, the left-to-right orientation of the object is reversed in the image. This is known as lateral inversion.\n\nTopic 3: Functioning of the Human Eye\n\nQuestion: 1\n\nHow you can take care of your eyes?\n\nSolution:\n\nWe should take the following measures to look after our eyes:\n\ni.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Wash our eyes two or three times a day\n\nii.\u00a0\u00a0\u00a0\u00a0\u00a0 Never touch our eyes with dirty hands\n\niii.\u00a0\u00a0\u00a0 Never rub our eyes\n\niv.\u00a0\u00a0\u00a0 Read books and watch television from an appropriate distance\n\nv.\u00a0\u00a0\u00a0\u00a0\u00a0 Consult an ENT specialist in case of redness or irritation\n\nQuestion: 2\n\nDescribe the construction of a kaleidoscope.\n\nSolution:\n\nA Kaleidoscope is made by joining three plane mirror strips to form a triangle.\u00a0 A piece of hollow cardboard tube is wrapped around the mirrors. On one side of the cardboard tube we place small pieces of plastic or glasses of different colours, wrapped between two transparent sheets. The other side is closed with a transparent plastic sheet. When we look through the plastic sheet, we see beautiful coloured patterns formed as a result of multiple reflections of the pieces on the mirrors.\n\nQuestion: 3\n\nWhy do we blink our eyelids?\n\nSolution:\n\nBlinking allows the eyelid to help keep the eye clean and protects our eyes from becoming dry. Another benefit of blinking is that it can stop foreign bodies from falling into our eyes.\n\nQuestion: 4\n\nWhat happens to your pupils as you enter a dark room from sunlight? Why?\n\nSolution:\n\nAs we enter a dark room from sunlight, we are unable to see things for a little while. This is because the pupils will have closed in the sunlight. As the pupils open in the dark room, more light enters the eye and we can see things again.\n\nQuestion: 5\n\nOnce a ray of light enters the eye, which part of the eye focuses the light ray on the retina?\n\nSolution:\n\nOnce light enters the eye, the lens focuses the light on the retina.\n\nQuestion: 6\n\nHow is a rainbow formed in nature? And in lab by a prism?\n\nSolution:\n\nIn nature, raindrops break sunlight into the combination of colours seen by the human eye. This is because every raindrop acts like a prism and breaks the light into rainbow colours. A prism does the same thing, breaking white light into its different constituent colours.\n\nQuestion: 7\n\nWhat causes the blind spot?\n\nSolution:\n\nAt the point in the eye where the optic nerve connects to the retina, we don't have rods or cones. This place is called the blind spot. Thus, images falling on this portion of the retina or the blind spot are not visible to us.","date":"2020-08-08 11:58:51","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 2, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2754024863243103, \"perplexity\": 775.1220958510789}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-34\/segments\/1596439737645.2\/warc\/CC-MAIN-20200808110257-20200808140257-00265.warc.gz\"}"} | null | null |
Q: IPython Permission Denied I'm encountering a problem starting an ipython notebook or an ipython console in spyder that results in the error message "Assertion failed: Permission denied (......\src\err.cpp:247) and (in ipython notebook) the kernel endlessly restarts.
I'm using Anaconda installation of python on Windows 7, and have the same problems with both ipython 1.1 and ipython 1.0. I did not have this problem when I ran ipython versions before 1.0, before I switched to Anaconda.
A google search finds another instance of this problem, which suggests that its due to interactions with PyZMQ and a firewall. I've tried adding specific exceptions for python and ipython to my firewall, and turning the firewall off completely, with no change. I can run ipython in command line, but neither the notebook or the console in spyder work (giving the error above.)
Any information about this would be helpful. I couldn't find any file err.cpp in any folder \src\ in my python installation, so I can't confirm what triggers the error has any relation to PyZMQ or firewalls. No change is made when turning off the firewall or elevating the command prompt. What else can I try?
A: I realise this is two years old, but I've just been able to sort out a similar problem, so it would have been good to see more answers to this.
In my case it wasn't the Windows Firewall or virus scanner, but that my employer's IT services group runs VNC over the same port that is hardcoded into 0MQ, as used by iPython in Anaconda.
Enough people complained that IT provided a script to move the VNC port for affected people, while also logging the change in their own records, so everybody is happy.
Try doing a "netstat -ab" from the command line, and check if anything is listening on port 5905, which iPython needs (at least as it is in early 2016, with Anaconda). You'll need to use "Run As Administrator" with cmd. If you can't do that just use "netstat -a". The difference is the b option will also list the process that has taken the port, and in our case we see vncserve.exe there. But -a is enough to see listening ports.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,146 |
These days, the last thing any company wants is to be put on blast by social media or a watchdog group with a good reputation and powerful following (like the ACLU).
Unfortunately for Amazon, the ACLU conducted an experiment using the company's new facial scanning software, Rekognition, to show just how dangerous it could be for law enforcement to be using facial scanning tech. In short, when the ACLU ran the faces of the members of the United States legislature through the software, it returned false positives for 28 members of Congress.
While the concept behind using facial recognition software seems great, there's certainly a problem when it comes to accuracy. For consumer purposes, such as unlocking that fancy iPhone X or Samsung, facial recognition is a viable alternative to other biometrics, like a fingerprint.
But when it comes to policing, there's still a long way to go before the tech is ready for deployment. Without some serious legal requirements/restriction placed on the use of this tech, as the ACLU experiment shows, there's certainly a very high risk that individuals will be misidentified using facial recognition tech, which could lead to severe consequences.
The ACLU is not alone, as recently even Microsoft joined in, in demanding that Congress act to regulate the use of facial recognition.
The ACLU test also showed what many have been warning against from the start: AI discriminates against minorities. The ACLU test's numbers showed that "nearly 40%" of the false positives occurred to the members of Congress that are people of color.
The test, apart from trying to exert more pressure on Amazon to not sell facial recognition software or services to law enforcement, was meant to be a wake up call to the members of congress that facial recognition tech could impact them personally as well. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,191 |
#include "config.h"
#include "MediaStreamTrack.h"
#if ENABLE(MEDIA_STREAM)
#include "AllAudioCapabilities.h"
#include "AllVideoCapabilities.h"
#include "AudioStreamTrack.h"
#include "Dictionary.h"
#include "Event.h"
#include "ExceptionCode.h"
#include "ExceptionCodePlaceholder.h"
#include "MediaConstraintsImpl.h"
#include "MediaSourceStates.h"
#include "MediaStream.h"
#include "MediaStreamCenter.h"
#include "MediaStreamPrivate.h"
#include "MediaStreamTrackSourcesCallback.h"
#include "MediaStreamTrackSourcesRequest.h"
#include "MediaTrackConstraints.h"
#include "NotImplemented.h"
#include "VideoStreamTrack.h"
#include <wtf/Functional.h>
#include <wtf/NeverDestroyed.h>
namespace WebCore {
MediaStreamTrack::MediaStreamTrack(ScriptExecutionContext& context, MediaStreamTrackPrivate& privateTrack, const Dictionary* constraints)
: RefCounted()
, ActiveDOMObject(&context)
, m_privateTrack(privateTrack)
, m_eventDispatchScheduled(false)
, m_stoppingTrack(false)
{
suspendIfNeeded();
m_privateTrack->setClient(this);
if (constraints)
applyConstraints(*constraints);
}
MediaStreamTrack::MediaStreamTrack(MediaStreamTrack& other)
: RefCounted()
, ActiveDOMObject(other.scriptExecutionContext())
, m_privateTrack(*other.privateTrack().clone())
, m_eventDispatchScheduled(false)
, m_stoppingTrack(false)
{
suspendIfNeeded();
m_privateTrack->setClient(this);
}
MediaStreamTrack::~MediaStreamTrack()
{
m_privateTrack->setClient(nullptr);
}
void MediaStreamTrack::setSource(PassRefPtr<MediaStreamSource> newSource)
{
m_privateTrack->setSource(newSource);
}
const String& MediaStreamTrack::id() const
{
return m_privateTrack->id();
}
const String& MediaStreamTrack::label() const
{
return m_privateTrack->label();
}
bool MediaStreamTrack::enabled() const
{
return m_privateTrack->enabled();
}
void MediaStreamTrack::setEnabled(bool enabled)
{
m_privateTrack->setEnabled(enabled);
}
bool MediaStreamTrack::stopped() const
{
return m_privateTrack->stopped();
}
bool MediaStreamTrack::muted() const
{
return m_privateTrack->muted();
}
bool MediaStreamTrack::readonly() const
{
return m_privateTrack->readonly();
}
bool MediaStreamTrack::remote() const
{
return m_privateTrack->remote();
}
const AtomicString& MediaStreamTrack::readyState() const
{
static NeverDestroyed<AtomicString> ended("ended", AtomicString::ConstructFromLiteral);
static NeverDestroyed<AtomicString> live("live", AtomicString::ConstructFromLiteral);
static NeverDestroyed<AtomicString> newState("new", AtomicString::ConstructFromLiteral);
switch (m_privateTrack->readyState()) {
case MediaStreamSource::Live:
return live;
case MediaStreamSource::New:
return newState;
case MediaStreamSource::Ended:
return ended;
}
ASSERT_NOT_REACHED();
return emptyAtom;
}
void MediaStreamTrack::getSources(ScriptExecutionContext* context, PassRefPtr<MediaStreamTrackSourcesCallback> callback, ExceptionCode& ec)
{
RefPtr<MediaStreamTrackSourcesRequest> request = MediaStreamTrackSourcesRequest::create(context, callback);
if (!MediaStreamCenter::shared().getMediaStreamTrackSources(request.release()))
ec = NOT_SUPPORTED_ERR;
}
RefPtr<MediaTrackConstraints> MediaStreamTrack::getConstraints() const
{
// FIXME: https://bugs.webkit.org/show_bug.cgi?id=122428
notImplemented();
return 0;
}
RefPtr<MediaSourceStates> MediaStreamTrack::states() const
{
return MediaSourceStates::create(m_privateTrack->states());
}
RefPtr<MediaStreamCapabilities> MediaStreamTrack::getCapabilities() const
{
// The source may be shared by multiple tracks, so its states is not necessarily
// in sync with the track state. A track that is new or has ended always has a source
// type of "none".
RefPtr<MediaStreamSourceCapabilities> sourceCapabilities = m_privateTrack->capabilities();
MediaStreamSource::ReadyState readyState = m_privateTrack->readyState();
if (readyState == MediaStreamSource::New || readyState == MediaStreamSource::Ended)
sourceCapabilities->setSourceType(MediaStreamSourceStates::None);
return MediaStreamCapabilities::create(sourceCapabilities.release());
}
void MediaStreamTrack::applyConstraints(const Dictionary& constraints)
{
m_constraints->initialize(constraints);
m_privateTrack->applyConstraints(m_constraints);
}
void MediaStreamTrack::applyConstraints(PassRefPtr<MediaConstraints>)
{
// FIXME: apply the new constraints to the track
// https://bugs.webkit.org/show_bug.cgi?id=122428
}
RefPtr<MediaStreamTrack> MediaStreamTrack::clone()
{
if (m_privateTrack->type() == MediaStreamSource::Audio)
return AudioStreamTrack::create(*this);
return VideoStreamTrack::create(*this);
}
void MediaStreamTrack::stopProducingData()
{
// NOTE: this method is called when the "stop" method is called from JS, using
// the "ImplementedAs" IDL attribute. This is done because ActiveDOMObject requires
// a "stop" method.
// The stop method should "Permanently stop the generation of data for track's source", but it
// should not post an 'ended' event.
m_stoppingTrack = true;
m_privateTrack->stop(MediaStreamTrackPrivate::StopTrackAndStopSource);
m_stoppingTrack = false;
}
bool MediaStreamTrack::ended() const
{
return m_privateTrack->ended();
}
void MediaStreamTrack::addObserver(MediaStreamTrack::Observer* observer)
{
m_observers.append(observer);
}
void MediaStreamTrack::removeObserver(MediaStreamTrack::Observer* observer)
{
size_t pos = m_observers.find(observer);
if (pos != notFound)
m_observers.remove(pos);
}
void MediaStreamTrack::trackReadyStateChanged()
{
if (stopped())
return;
MediaStreamSource::ReadyState readyState = m_privateTrack->readyState();
if (readyState == MediaStreamSource::Live)
scheduleEventDispatch(Event::create(eventNames().startedEvent, false, false));
else if (readyState == MediaStreamSource::Ended && !m_stoppingTrack)
scheduleEventDispatch(Event::create(eventNames().endedEvent, false, false));
configureTrackRendering();
}
void MediaStreamTrack::trackMutedChanged()
{
if (stopped())
return;
if (muted())
scheduleEventDispatch(Event::create(eventNames().muteEvent, false, false));
else
scheduleEventDispatch(Event::create(eventNames().unmuteEvent, false, false));
configureTrackRendering();
}
void MediaStreamTrack::trackEnabledChanged()
{
if (stopped())
return;
setEnabled(m_privateTrack->enabled());
configureTrackRendering();
}
void MediaStreamTrack::configureTrackRendering()
{
if (stopped())
return;
// 4.3.1
// ... media from the source only flows when a MediaStreamTrack object is both unmuted and enabled
}
void MediaStreamTrack::trackDidEnd()
{
m_privateTrack->setReadyState(MediaStreamSource::Ended);
for (Vector<Observer*>::iterator i = m_observers.begin(); i != m_observers.end(); ++i)
(*i)->trackDidEnd();
}
void MediaStreamTrack::stop()
{
m_privateTrack->stop(MediaStreamTrackPrivate::StopTrackOnly);
}
void MediaStreamTrack::scheduleEventDispatch(PassRefPtr<Event> event)
{
{
MutexLocker locker(m_mutex);
m_scheduledEvents.append(event);
if (m_eventDispatchScheduled)
return;
m_eventDispatchScheduled = true;
}
callOnMainThread(bind(&MediaStreamTrack::dispatchQueuedEvents, this));
}
void MediaStreamTrack::dispatchQueuedEvents()
{
Vector<RefPtr<Event>> events;
{
MutexLocker locker(m_mutex);
m_eventDispatchScheduled = false;
events.swap(m_scheduledEvents);
}
if (!scriptExecutionContext())
return;
for (auto it = events.begin(); it != events.end(); ++it)
dispatchEvent((*it).release());
events.clear();
}
} // namespace WebCore
#endif // ENABLE(MEDIA_STREAM)
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,716 |
{"url":"https:\/\/quant.stackexchange.com\/questions\/18758\/how-do-i-loop-through-all-the-stocks-with-quantmod-and-ttr","text":"# how do I loop through all the stocks with quantmod and ttr?\n\nI just started with quantmod package. If I want to select stocks based on their recent performance, then I need to loop through all the stocks in, say, NYSE. So I need:\n\n1. get all the stock symbols\n2. select those symbols that do have data\n3. loop through them one by one(say, each time, download the stock data as $X$, and do some analysis. Then loop to next one, and set it as $X$)\n\nMy question is: how can I do these? Here is part of my thought:\n\n1. use stockSymbols() function in TTR package: AllSym <- stockSymbols(). The first column of AllSym are all the potential symbols.\n\n2. Use getSymbols(AllSym[i,1]) to loop all the stock i:\n\nQuestions here:\n\n1. Not all the symbols from TTR have data. Some may have error when using getSymbols. I actually do not care about this certain stock. So how can I continue with the loop? [How can I use the try function?]\n\n2. The getSymbols function will automatically make the stock symbols as the variables. How can I copy(or set) it to $X$(instead of something like $APPL$)?\n\n3. How can I loop trough the variables with their names saved as strings in a vector? For example, if we do use getSymbols function to get data with name as the stock symbol. How can I loop through those stocks?[Note that their variable name are stored in first column AllSym as string]\n\nThank you very much!\n\nTry the following:\n\nlibrary(quantmod) # also loads xts and TTR\n\n# Fetch all Symbols & store only the tickers to retrieve the data\nsymbols <- stockSymbols()\nsymbols <- symbols[,1]\n\n\nNext we will specify where to to store data\n\ndataset<- xts() # Only run once\n\nThe following code is the loop that will download OHLC data to your environment. It will then store the Adjusted Close of the downloaded companies and merge them in dataset\n\n# cool progress bar to see the % of completion\nn <- length(symbols)\npb <- txtProgressBar(min = 0, max = n, style=3)\n\n# Actual loop:\nfor(i in 1:length(symbols)) {\nsymbols[i]-> symbol\n# specify the \"from\" date to desired start date\ntryit <- try(getSymbols(symbol,from=\"2014-01-01\", src='yahoo'))\nif(inherits(tryit, \"try-error\")){\ni <- i+1\n} else {\n# specify the \"from\" date to desired start date\ndata <- getSymbols(symbol, from=\"2014-01-01\", src='yahoo')\nrm(symbol)\n}\nsetTxtProgressBar(pb, i)\n}\n\n\nIf the loop breaks, say on the 50th iteration, then just re run the last block of code by changing the following\n\n# cool progress bar to see the % of completion\nn <- length(symbols)\npb <- txtProgressBar(min = 0, max = n, style=3)\n\n# Actual loop:\n# IF IT BREAKS ON THE 50th ITERATION, it must be skipped, therefore change it to 51\nfor(i in 51:length(symbols)) {\nsymbols[i]-> symbol\n...\n\n\nKeep on doing it until symbols is exhausted. Remember that it will download all the data unto your environment & that all the Adjusted Close prices are to be found in dataset\n\n\u2022 Is there any way to keep the loop going without break? \u2013\u00a0Mehdi Zare Sep 13 '17 at 19:31\n\u2022 most likely with a try() function \u2013\u00a0Rime Sep 18 '17 at 8:45\n\u2022 Check out errors and exceptions documentation at docs.python.org\/3\/tutorial\/errors.html All it requires is a try: block and in the except: block just put pass unless you want to do something like print a statement and the stock that caused the error. \u2013\u00a0Shanemeister Apr 14 '18 at 17:06\n\nYou may refer this :\n\nuse the latest package in CRAN \"BatchGetSymbols\" for downloading OHLC data for multiple tickers in a single data frame.\n\nYou may not need to construct the loop for this.","date":"2019-06-25 07:30:55","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.25110846757888794, \"perplexity\": 3520.7288963185933}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-26\/segments\/1560627999814.77\/warc\/CC-MAIN-20190625072148-20190625094148-00047.warc.gz\"}"} | null | null |
<div class="row" style="margin-bottom: 70px;">
<div class="col-md-4 col-md-offset-1 border">
<h2 class="text-center">Profile Details</h2>
<p><span>Username: </span> {{currentUser.Username}}</p>
<p><span>Id: </span> {{currentUser.Id}}</p>
<p><span>Is Administrator: </span> {{currentUser.isAdmin ? 'Yes' : 'No'}}</p>
</div>
<div class="col-md-4 col-md-offset-2 border">
<h2 class="text-center">Change Password</h2>
<form name="changePasswordForm">
<label for="old-password">Old Password</label>
<input type="password" required="required" min-length="6" max-length="100" ng-model="data.OldPassword"
id="old-password" class="form-control"/>
<br/>
<label for="new-password">New Password</label>
<input type="password" required="required" min-length="6" max-length="100" ng-model="data.NewPassword"
id="new-password" class="form-control"/>
<br/>
<label for="reg-confirm-password">Confirm Password</label>
<input type="password" required="required" min-length="6" max-length="100"
ng-model="data.ConfirmPassword" id="reg-confirm-password" class="form-control"/>
<br/>
<button class="btn btn-primary"
ng-disabled="changePasswordForm.$invalid || data.NewPassword != data.ConfirmPassword"
ng-click="changePassword(data)">Change Password
</button>
</form>
</div>
</div> | {
"redpajama_set_name": "RedPajamaGithub"
} | 7,626 |
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