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11.5: Positive operators


Recall that self-adjoint operators are the operator analog for real numbers. Let us now define the operator analog for positive (or, more precisely, nonnegative) real numbers.

Definition 11.5.1. An operator (Tin mathcal{L}(V)) is called positive (denoted (Tge 0)) if (T=T^*) and (inner{Tv}{v} ge 0) for all (vin V).

If (V) is a complex vector space, then the condition of self-adjointness follows from the condition (inner{Tv}{v} ge 0) and hence can be dropped.

Example 11.5.2. Note that, for all (T in mathcal{L}(V)), we have (T^*Tge 0) since (T^*T) is self-adjoint and (inner{T^*Tv}{v}=inner{Tv}{Tv} ge 0).

Example 11.5.3. Let (Usubset V) be a subspace of (V) and (P_U) be the orthogonal projection onto (U).

Then (P_Uge 0). To see this, write (V=U oplus U^ot) and (v=u_v+u_v^ot) for each (vin V), where (u_v in U) and (u_v^ot in U^ot). Then (inner{P_U v}{w} = inner{u_v}{u_w+u_w^ot} = inner{u_v}{u_w} = inner{u_v+u_v^ot}{u_w} = inner{v}{P_U w}) so that (P_U^*=P_U). Also, setting (v=w) in the above string of equations, we obtain (inner{P_U v}{v}=inner{u_v}{u_v} ge 0), for all (vin V). Hence, (P_Uge 0).

If (lambda) is an eigenvalue of a positive operator (T) and (vin V) is an associated eigenvector, then (inner{Tv}{v} = inner{lambda v}{v} = lambda inner{v}{v} ge 0). Since (inner{v}{v}ge 0) for all vectors (vin V), it follows that (lambdage 0). This fact can be used to define (sqrt{T}) by setting

egin{equation*}
sqrt{T} e_i = sqrt{lambda_i} e_i,
end{equation*}

where (lambda_i) are the eigenvalues of (T) with respect to the orthonormal basis (e=(e_1,ldots,e_n)). We know that these exist by the Spectral Theorem.


JavaScript has the following types of operators. This section describes the operators and contains information about operator precedence.

JavaScript has both binary and unary operators, and one special ternary operator, the conditional operator. A binary operator requires two operands, one before the operator and one after the operator:

A unary operator requires a single operand, either before or after the operator:

Assignment operators

An assignment operator assigns a value to its left operand based on the value of its right operand. The simple assignment operator is equal ( = ), which assigns the value of its right operand to its left operand. That is, x = y assigns the value of y to x .

There are also compound assignment operators that are shorthand for the operations listed in the following table:

Compound assignment operators
Name Shorthand operator Meaning
Assignment x = y x = y
Addition assignment x += y x = x + y
Subtraction assignment x -= y x = x - y
Multiplication assignment x *= y x = x * y
Division assignment x /= y x = x / y
Remainder assignment x %= y x = x % y
Exponentiation assignment x **= y x = x ** y
Left shift assignment x <<= y x = x << y
Right shift assignment x >>= y x = x >> y
Unsigned right shift assignment x >>>= y x = x >>> y
Bitwise AND assignment x &= y x = x & y
Bitwise XOR assignment x ^= y x = x ^ y
Bitwise OR assignment x |= y x = x | y
Logical AND assignment x &&= y x && (x = y)
Logical OR assignment x ||= y x || (x = y)
Logical nullish assignment x ??= y x ?? (x = y)

Return value and chaining

Like most expressions, assignments like x = y have a return value. It can be retrieved by e.g. assigning the expression or logging it:

The return value matches the expression to the right of the = sign in the “Meaning” column of the table above. That means that (x = y) returns y , (x += y) returns the resulting sum x + y , (x **= y) returns the resulting power x ** y , and so on.

In the case of logical assignments, (x &&= y) , (x ||= y) , and (x ??= y) , the return value is that of the logical operation without the assignment, so x && y , x || y , and x ?? y , respectively.

Note that the return values are always based on the operands’ values before the operation.

When chaining these expressions, each assignment is evaluated right-to-left. Consider these examples:

  • w = z = x = y is equivalent to w = (z = (x = y)) or x = y z = y w = y
  • z += x *= y is equivalent to z += (x *= y) or tmp = x * y x *= y z += tmp (except without the tmp ).

Destructuring

For more complex assignments, the destructuring assignment syntax is a JavaScript expression that makes it possible to extract data from arrays or objects using a syntax that mirrors the construction of array and object literals.

Comparison operators

A comparison operator compares its operands and returns a logical value based on whether the comparison is true. The operands can be numerical, string, logical, or object values. Strings are compared based on standard lexicographical ordering, using Unicode values. In most cases, if the two operands are not of the same type, JavaScript attempts to convert them to an appropriate type for the comparison. This behavior generally results in comparing the operands numerically. The sole exceptions to type conversion within comparisons involve the === and !== operators, which perform strict equality and inequality comparisons. These operators do not attempt to convert the operands to compatible types before checking equality. The following table describes the comparison operators in terms of this sample code:

Comparison operators
Operator Description Examples returning true
Equal ( == ) Returns true if the operands are equal. 3 == var1

Note: => is not an operator, but the notation for Arrow functions.

Arithmetic operators

An arithmetic operator takes numerical values (either literals or variables) as their operands and returns a single numerical value. The standard arithmetic operators are addition ( + ), subtraction ( - ), multiplication ( * ), and division ( / ). These operators work as they do in most other programming languages when used with floating point numbers (in particular, note that division by zero produces Infinity ). For example:

In addition to the standard arithmetic operations ( + , - , * , / ), JavaScript provides the arithmetic operators listed in the following table:

Bitwise operators

A bitwise operator treats their operands as a set of 32 bits (zeros and ones), rather than as decimal, hexadecimal, or octal numbers. For example, the decimal number nine has a binary representation of 1001. Bitwise operators perform their operations on such binary representations, but they return standard JavaScript numerical values.

The following table summarizes JavaScript's bitwise operators.

Bitwise logical operators

Conceptually, the bitwise logical operators work as follows:

  • The operands are converted to thirty-two-bit integers and expressed by a series of bits (zeros and ones). Numbers with more than 32 bits get their most significant bits discarded. For example, the following integer with more than 32 bits will be converted to a 32 bit integer:
  • Each bit in the first operand is paired with the corresponding bit in the second operand: first bit to first bit, second bit to second bit, and so on.
  • The operator is applied to each pair of bits, and the result is constructed bitwise.

For example, the binary representation of nine is 1001, and the binary representation of fifteen is 1111. So, when the bitwise operators are applied to these values, the results are as follows:

Note that all 32 bits are inverted using the Bitwise NOT operator, and that values with the most significant (left-most) bit set to 1 represent negative numbers (two's-complement representation).

x evaluates to the same value that -x - 1 evaluates to.

Bitwise shift operators

The bitwise shift operators take two operands: the first is a quantity to be shifted, and the second specifies the number of bit positions by which the first operand is to be shifted. The direction of the shift operation is controlled by the operator used.

Shift operators convert their operands to thirty-two-bit integers and return a result of either type Number or BigInt : specifically, if the type of the left operand is BigInt , they return BigInt otherwise, they return Number .

The shift operators are listed in the following table.

Bitwise shift operators
Operator Description Example
Left shift
( << )
This operator shifts the first operand the specified number of bits to the left. Excess bits shifted off to the left are discarded. Zero bits are shifted in from the right. 9<<2 yields 36, because 1001 shifted 2 bits to the left becomes 100100, which is 36.
Sign-propagating right shift ( >> ) This operator shifts the first operand the specified number of bits to the right. Excess bits shifted off to the right are discarded. Copies of the leftmost bit are shifted in from the left. 9>>2 yields 2, because 1001 shifted 2 bits to the right becomes 10, which is 2. Likewise, -9>>2 yields -3, because the sign is preserved.
Zero-fill right shift ( >>> ) This operator shifts the first operand the specified number of bits to the right. Excess bits shifted off to the right are discarded. Zero bits are shifted in from the left. 19>>>2 yields 4, because 10011 shifted 2 bits to the right becomes 100, which is 4. For non-negative numbers, zero-fill right shift and sign-propagating right shift yield the same result.

Logical operators

Logical operators are typically used with Boolean (logical) values when they are, they return a Boolean value. However, the && and || operators actually return the value of one of the specified operands, so if these operators are used with non-Boolean values, they may return a non-Boolean value. The logical operators are described in the following table.

Logical operators
Operator Usage Description
Logical AND ( && ) expr1 && expr2 Returns expr1 if it can be converted to false otherwise, returns expr2 . Thus, when used with Boolean values, && returns true if both operands are true otherwise, returns false .
Logical OR ( || ) expr1 || expr2 Returns expr1 if it can be converted to true otherwise, returns expr2 . Thus, when used with Boolean values, || returns true if either operand is true if both are false, returns false .
Logical NOT ( ! ) !expr Returns false if its single operand that can be converted to true otherwise, returns true .

Examples of expressions that can be converted to false are those that evaluate to null, 0, NaN, the empty string (""), or undefined.

The following code shows examples of the && (logical AND) operator.

The following code shows examples of the || (logical OR) operator.

The following code shows examples of the ! (logical NOT) operator.

Short-circuit evaluation

As logical expressions are evaluated left to right, they are tested for possible "short-circuit" evaluation using the following rules:

  • false && anything is short-circuit evaluated to false.
  • true || anything is short-circuit evaluated to true.

The rules of logic guarantee that these evaluations are always correct. Note that the anything part of the above expressions is not evaluated, so any side effects of doing so do not take effect.

Note that for the second case, in modern code you can use the new Nullish coalescing operator ( ?? ) that works like || , but it only returns the second expression, when the first one is "nullish", i.e. null or undefined . It is thus the better alternative to provide defaults, when values like '' or 0 are valid values for the first expression, too.

String operators

In addition to the comparison operators, which can be used on string values, the concatenation operator (+) concatenates two string values together, returning another string that is the union of the two operand strings.

The shorthand assignment operator += can also be used to concatenate strings.

Conditional (ternary) operator

The conditional operator is the only JavaScript operator that takes three operands. The operator can have one of two values based on a condition. The syntax is:

If condition is true, the operator has the value of val1 . Otherwise it has the value of val2 . You can use the conditional operator anywhere you would use a standard operator.

This statement assigns the value "adult" to the variable status if age is eighteen or more. Otherwise, it assigns the value "minor" to status .

Comma operator

The comma operator ( , ) evaluates both of its operands and returns the value of the last operand. This operator is primarily used inside a for loop, to allow multiple variables to be updated each time through the loop. It is regarded bad style to use it elsewhere, when it is not necessary. Often two separate statements can and should be used instead.

For example, if a is a 2-dimensional array with 10 elements on a side, the following code uses the comma operator to update two variables at once. The code prints the values of the diagonal elements in the array:

Unary operators

A unary operation is an operation with only one operand.

Delete

The delete operator deletes an object's property. The syntax is:

where object is the name of an object, property is an existing property, and propertyKey is a string or symbol referring to an existing property.

The fourth form is legal only within a with statement, to delete a property from an object, and also for properties of the global object.

If the delete operator succeeds, it removes the property from the object. Trying to access it afterwards will yield undefined . The delete operator returns true if the operation is possible it returns false if the operation is not possible.

Deleting array elements

Since arrays are just objects, it's technically possible to delete elements from them. This is however regarded as a bad practice, try to avoid it. When you delete an array property, the array length is not affected and other elements are not re-indexed. To achieve that behavior, it is much better to just overwrite the element with the value undefined . To actually manipulate the array, use the various array methods such as splice .

Typeof

The typeof operator is used in either of the following ways:

The typeof operator returns a string indicating the type of the unevaluated operand. operand is the string, variable, keyword, or object for which the type is to be returned. The parentheses are optional.

Suppose you define the following variables:

The typeof operator returns the following results for these variables:

For the keywords true and null , the typeof operator returns the following results:

For a number or string, the typeof operator returns the following results:

For property values, the typeof operator returns the type of value the property contains:

For methods and functions, the typeof operator returns results as follows:

For predefined objects, the typeof operator returns results as follows:

The void operator is used in either of the following ways:

The void operator specifies an expression to be evaluated without returning a value. expression is a JavaScript expression to evaluate. The parentheses surrounding the expression are optional, but it is good style to use them.

Relational operators

A relational operator compares its operands and returns a Boolean value based on whether the comparison is true.

The in operator returns true if the specified property is in the specified object. The syntax is:

where propNameOrNumber is a string, numeric, or symbol expression representing a property name or array index, and objectName is the name of an object.

The following examples show some uses of the in operator.

Instanceof

The instanceof operator returns true if the specified object is of the specified object type. The syntax is:

where objectName is the name of the object to compare to objectType , and objectType is an object type, such as Date or Array .

Use instanceof when you need to confirm the type of an object at runtime. For example, when catching exceptions, you can branch to different exception-handling code depending on the type of exception thrown.

For example, the following code uses instanceof to determine whether theDay is a Date object. Because theDay is a Date object, the statements in the if statement execute.

Operator precedence

The precedence of operators determines the order they are applied when evaluating an expression. You can override operator precedence by using parentheses.

The following table describes the precedence of operators, from highest to lowest.

A more detailed version of this table, complete with links to additional details about each operator, may be found in JavaScript Reference.


11.5: Positive operators

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Feature Papers represent the most advanced research with significant potential for high impact in the field. Feature Papers are submitted upon individual invitation or recommendation by the scientific editors and undergo peer review prior to publication.

The Feature Paper can be either an original research article, a substantial novel research study that often involves several techniques or approaches, or a comprehensive review paper with concise and precise updates on the latest progress in the field that systematically reviews the most exciting advances in scientific literature. This type of paper provides an outlook on future directions of research or possible applications.

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to authors, or important in this field. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.


11.5: Positive operators

All articles published by MDPI are made immediately available worldwide under an open access license. No special permission is required to reuse all or part of the article published by MDPI, including figures and tables. For articles published under an open access Creative Common CC BY license, any part of the article may be reused without permission provided that the original article is clearly cited.

Feature Papers represent the most advanced research with significant potential for high impact in the field. Feature Papers are submitted upon individual invitation or recommendation by the scientific editors and undergo peer review prior to publication.

The Feature Paper can be either an original research article, a substantial novel research study that often involves several techniques or approaches, or a comprehensive review paper with concise and precise updates on the latest progress in the field that systematically reviews the most exciting advances in scientific literature. This type of paper provides an outlook on future directions of research or possible applications.

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to authors, or important in this field. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.


Bit Shift Operators

These operators are used for performing shift operations on binary values.

Bit-shit operatiorsDetails
And Known as the Bitwise AND Operator. It copies a bit to result if it is found in both operands.
Or Known as the Binary OR Operator. It copies a bit if found in either operand.
Xor The Binary XOR Operator. For copying a bit if set in one of the operands rather than both.
Not It is known as the Binary Ones Complement Operator. It is a unary operator that 'flips' the bits.

Let us demonstrate how to use these operators using an example:

Step 1) Create a new console application. If you don't know how to do it, visit our previous tutorial on Data Types and Variables.

Step 2) Add the following code:

Step 3) Run the code by clicking the Start button. You should get the following window:

Here is a screenshot of the code:

  1. Creating a module named Module1.
  2. Creating the main sub-procedure.
  3. Creating an integer variable w with a value of 50.
  4. Creating an integer variable x with a value of 11.
  5. Creating an integer variable y with a value of 0.
  6. Applying the bitwise And operator to the values of variables w and x and assigning the result to variable y.
  7. Printing some text and the result of the above operation on the console.
  8. Applying the bitwise Or operator to the values of variables w and x and assigning the result to variable y.
  9. Printing some text and the result of the above operation on the console.
  10. Applying the bitwise Xor operator to the values of variables w and x and assigning the result to variable y.
  11. Printing some text and the result of the above operation on the console.
  12. Applying the bitwise Not operator to the value of variable w and assigning the result to variable y.
  13. Printing some text and the result of the above operation on the console.
  14. Pause the console to wait for user input via the keyboard.
  15. End the sub-procedure.
  16. End the module.

Enablement

  • The following query performs a left outer join of tables T1 and T2. Include both tables in the FROM clause, separated by a comma. Apply the outer join operator to all columns of T2 in predicates that also reference T1.The previous query is equivalent to the following one, which uses the outer join operator:
  • The following query performs a right outer join of tables T1 and T2. Include both tables in the FROM clause, separated by a comma, and apply the outer join operator to all columns of T1 in predicates that also reference T2.The previous query is equivalent to the following one, which uses the outer join operator:

A set of predicates that are separated by AND operators is known as an . If there are no AND operators in a WHERE clause, the set of predicates in the WHERE clause is considered to be the only AND-factor.


USDA Awards Over $11.5 Million to Help Small and Mid-Sized Farms on National Ag Day

WASHINGTON, March 23, 2021 – The U.S. Department of Agriculture (USDA) announced today an $11.5 million research investment to help ensure America’s small and medium-sized farms become more profitable and improve the quality of life in American farm communities.

“Few groups are as resilient and as determined as American farm families,” said Agriculture Secretary Tom Vilsack. “Under the Biden-Harris Administration, USDA is committed to creating a fairer, more equitable system for farms of all sizes to compete and remain profitable. This investment in innovative research will give these family farms the tools they need to be more sustainable, profitable and productive as they face agricultural and economic challenges. When American farmers have a chance to compete, they have a greater chance at succeeding.”

USDA’s National Institute of Food and Agriculture (NIFA) awarded 24 grants to 20 universities and organizations through their Agriculture and Food Research Initiative (AFRI), the nation’s leading and largest competitive grants program for agricultural sciences. These research efforts focus on alternative crop enterprises, marketing, and scaling up fruit and vegetable production to overcome marketing constraints.

By focusing on these key elements, small and medium-sized farm operators can increase their competitiveness in local markets and can provide greater access to food for their communities. This is extremely critical as we build back a stronger, more equitable food and farming system.


Floor Division (//) Operator

Floor Division (//) Operator in Python can be only used with binary forms. This Operator is used between two operands to get the quotient as the result of Python program and show it as output. Now, the difference is that the Floor Division operator ignoes the numbers after decimal point in the quotient and put a zero after decimal.

Syntax and Semantics of Floor Division Operator:

SyntaxExample
(int, int)-> int25//5 returns 5
(float, float)-> float10.5//5.0 returns 2.0
(int, float)-> float11//2.5 returns 4.0
(float, int)-> float4.0//3 returns 1.0

Modulo (%) Operator

Modulo (%) Operator is used between two operands to perform division and obtain the reminder as output from the program.

Syntax and Semantic of Modulo Operator:

SyntaxExample
(int, int)-> int25%4 returns 1
(float, float)-> float2.5%1.2 returns 0.10
(int, float)-> float13%2.0 returns 1.0
(float, int)-> float1.5%2 returns 1.5

Exponent ** Operator

Exponent ** Operator is used to calculate the power or exponent of a number. To compute X y (X raised to y power), the expression is written as X**y in Python. The exponent operator is also called Power operator.


Despite Positive Occupancy Signs, Operators Still Face Structural Financial Challenges

The last year has been difficult for skilled nursing providers but there are plenty of signs for optimism coming out of the pandemic according to George Mesires, Co-Leader, Senior Living & Care practice Faegre Drinker Biddle & Reath LLP.

Skilled Nursing News got the chance to chat with Mesires about what he is seeing in the market and how the pandemic is impacting the law firm’s clients in skilled nursing and senior care.

This interview has been edited for length and clarity.

You told me that despite all the challenges skilled nursing has faced, it has demonstrated resilience, and you’re cautiously optimistic about the future. Why is that?

First, I think, occupancy has troughed. Certainly, the rollout of the vaccine has made a tremendous difference in terms of fixing the occupancy problem, and setting a floor, and will [grow from] the steep drop-off [in occupancy levels] that we have seen.

With the rollout of the vaccine, the numbers on the uptake have been really promising. Hopefully, that loosens up a lot of [marketing] activity [such] that admission flow can get back to normal.

From a litigation perspective, what do you think skilled nursing operators need to be ready for as we work our way through this? How do you think they should prepare themselves?

I think there’s a general concern that operators and those around the space will face some sort of COVID-related liability. Today, the litigation has not been as rampant as some have thought or predicted, and that’s a very good thing.

There’s a patchwork of effort among the states to address some of the liability issues. From my perspective, it would be ideal if there could be a federal fix to that.

Generally, from an operator’s perspective, continued vigilance, the duty of care, and execution of best practices with infection control should carry the day.

You’ve done a lot of M&A and distress work in the past. Do you expect a lot of pain coming after the CARES Act funds eventually run out?

No doubt, some operators have been buoyed by CARES Act funding it’s a tremendous amount of money that went into the system.

After it runs out, there isn’t going to be that mask on any of the financial challenges that some operators were experiencing pre-pandemic. The pandemic obviously hastened financial challenges that some of the operators were [already] facing pre-pandemic. There will be a subset of weaker operators that are going to face the same challenges that they faced pre-pandemic, but just aggravated by the pandemic.

For instance, the labor issues that were preexisting will still be there, if not heightened. For those communities whose physical structure was aging, there’s still going to be a lot of deferred CapEx to be done. I do think that there will be a need to address some of the structural financial challenges for some operators — there is an incredible amount of capital on the sidelines. [With respect to ongoing M&A activity], for the communities that have been trading through the pandemic, the market has been quite strong.

Does it surprise you at times when you’re seeing some of the properties traded during the pandemic, how well they’ve traded?

No — I think the pandemic has underscored how important the operator is. We’re going to hear that refrain louder and more often now. Strong operators that run communities that are outperforming their peers in the market in this environment will be able to garner disproportionately strong returns.

There’s been a lot of attention on private equity in terms of who’s investing and whether they should be investing in skilled nursing. How do you view all this attention on private equity?

From a market participant standpoint, I view more participants and capital as a good thing for the industry. More participants lead to a more liquid market and generally leads to a healthier market environment.

That said, I do think that there’s significant headline risk, if you will, just based on the easy bipartisan political attraction that naming the private equity as the bad guy can have.

I do think that private equity and private equity-backed communities are going to face a lot of scrutiny from both parties across the aisle, which may make it a little unappetizing for some private equity groups that aren’t comfortable with that scrutiny.

If they’ve already taken on private equity, would you recommend your clients be ready to deal with the scrutiny going forward?

My view is that private equity-backed communities should be aware that they may face inquiry from state and federal regulatory bodies and legislators. That is just a risk. It’s certainly not, in my view, a significant impediment because the story at the end of the day is a compelling story that private equity has been a significant benefit to the industry.

In general, what types of problems are your clients really dealing with right now in the skilled nursing space?

I’ve looked at the different phases of the pandemic. At the outset of the pandemic, it was what I call operational triage. There was obviously a tremendous amount of focus that needed to be done on how to prep the communities to deal with the operations on a day-to-day basis to best face the pandemic. That involved acquiring PPE, setting up operational protocols, following all the best practices that were being articulated by the CDC and state regulatory authorities.

Those operational challenges then manifested themselves financially, whether it was on the revenue side or the expense side, both lines were adversely affected. I think lenders were patient, and have generally been patient, and have given operators the runway that they need to care for the health and well-being of residents.

Eventually, you’re going to see the lenders really start to take a look at their credit, and make sure that the financial institution is being best protected as well.

I think that’s the phase of where we are now, as there are some interactions and negotiations with lenders about how to deal with some of the issues that have occurred or some of the financial outliers that have been caused by the pandemic.

Outlook for skilled nursing — long or short?

From my perspective, I’m optimistic. At the end of the day and when the dust settles, I think folks are going to recognize that the best place for our frailest — and the most important constituent in that marketplace, the elderly — is going to be in a community that is custom-fit for them.

With the demographic tailwinds, with the demonstrated resilience, and with the marketplace’s ability to get through a 100-year event the way that it has, I think it’s going to attract more and more participants to the space in a similar way that the participants were attracted to it after the Great Recession.


Published May 24. 2020 6:55PM | Updated May 25. 2020 5:48PM

By Sten Spinella Day staff writer

As the paper's new politics and government reporter, I write about state and national issues with a focus on southeastern Connecticut. I particularly enjoy reporting on voting rights and how political trends play out at the local level. I've worked as a town reporter for The Day, covering Montville and Waterford from 2019-2021 as well as writing breaking news and general assignment stories.

As the paper's new politics and government reporter, I write about state and national issues with a focus on southeastern Connecticut. I particularly enjoy reporting on voting rights and how political trends play out at the local level. I've worked as a town reporter for The Day, covering Montville and Waterford from 2019-2021 as well as writing breaking news and general assignment stories.

Waterford — Millstone Power Station’s COVID-19 response, which faced criticism from some of its employees earlier this month, has now drawn the ire of the watchdog group Connecticut Coalition Against Millstone.

The group took issue with Millstone beginning the refueling of one of its two active nuclear reactors — a monthslong process that calls for bringing in 750 temporary workers — despite knowing of coronavirus cases among employees. Emails between Millstone/Dominion Energy and the state Department of Energy and Environmental Protection show the parties were aware of the first positive case by April 13, 11 days before the refueling started.

The group’s other chief complaint is that of 11 positive cases at Millstone, some are among਌ontrol room operators. This new information, gleaned from the coalition’s state Freedom of Information request for emails between DEEP and Millstone/Dominion and filed as a result of a May 3 story in The Day, had not been publicly announced.

𠇊s of April 24, 2020 or sooner, the State of Connecticut knew that some of the 11 Millstone employees who had just tested positive for COVID-19 are licensed operators who work in crews in the Unit 2 and 3 control rooms,” a May 18 news release from the coalition read. �ral and state regulators withheld this information from the public.”

Millstone’s pandemic management

Millstone spokesman Kenneth Holt said the lack of positive cases since April 29 is proof of the station’s proactive safety precautions.

“I think it’s clear that we are being successful in managing our response to the coronavirus,” Holt said. “That’s best exemplified by the fact that we haven’t had any new cases at Millstone since April 29th.”

Holt confirmed that about 500 tests have been conducted on Millstone workers.

Millstone has identified 11 positive cases among its employees, three of whom are control room operators. One isਊ Millstone employee who had traveled to New York and was in self-quarantine.

Holt said all 11 people who tested positive are back at work after testing negative multiple times. All of the cases were asymptomatic.

Coalition director Nancy Burton asserts that by not suspending the refueling, Millstone is exposing its employees and putting the general public at risk. But as Holt and DEEP Radiation Division Director Jeffrey Semancik said, as long as Millstone has an adequate number of licensed operators available, the refueling can go on as scheduled.

Holt said Millstone has a staff of 89 licensed operators.

“If we felt we couldn’t operate the reactors safely, we would shut them down,” Holt said. “That has not been the case. We’re talking about a small percentage of people who tested positive.”

Holt added that Millstone did contact tracing with the positive employees. Millstone must have, at minimum, two licensed operators in the control room 24/7, according to NRC spokesman Neil Sheehan. Plant operators at one facility cannot pick up and help out somewhere else — their certifications are for specific plants.

“There are typically three or four licensed operators in the control room, and the control room is easily large enough to allow for social distancing,” Sheehan wrote in an April 22 email to Burton.

Semancik said that if Millstone drops below its staffing requirements, it would have to report this to the Nuclear Regulatory Commission, and it would be a public notification.

“There is no set number of positive COVID-19 cases that would cause the NRC to step in and halt a refueling and maintenance outage,” Sheehan wrote in an email to The Day.

Holt could not say whether Millstone has a threshold of positive cases where Dominion, by its own accord, would suspend the refueling.

“I’m sure there is in one in our plans, but it would be a lot more than 10,” Holt said.

“It’s more of a calculus based on the number people available in critical roles,” Holt wrote in a follow-up email. “We have a minimum number of people required to operate the reactor including licensed operators, shift technical advisors, health physics technicians, security officers and chemists. If we are unable to fully staff those positions, decisions need to be made about operation of the reactor.”

According to Semancik, DEEP doesn’t have the power to suspend refueling — that falls to the NRC or to Millstone/Dominion.

“The NRC has specific staffing requirements for licensed operators,” Semancik said. �ter that, it becomes a business decision. Do they have enough people to do the work or not? That’s really up to them.”

Pushing buttons

Beyond needing to maintain a certain staffing level, having control operators who tested positive raises other problems. The coalition’s FOI request revealed a particular concern by򠷮P.

“Millstone is an interesting case,” Semancik wrote in an April 26 email to Dominion contacts. “The control room must be staffed 24/7 by a limited number of licensed operators. While they try to maintain social distancing, there are space limits. They also have to manipulate switches that can’t be easily cleaned due to concerns about inadvertent actuation.”

In essence, there is fear of accidentally pressing an important button because of the necessity to constantly clean surfaces created by the pandemic.

Burton felt this reason enough to stop the refueling.

“It’s outrageous!” she said. “They’ve identified positive employees in the control room, and they have the power to create a catastrophe by pressing the wrong button.”

She also took exception to the discussion of social distancing in Semancik’s email.

“The NRC has been trying to assure us for months that this will not be a problem because they will honor principles and practices of social distancing,” Burton said. “The emails from Mr. Semancik absolutely blow those notions away.”

Holt acknowledged the “knobs, dials and switches that you wouldn’t want to flip accidentally.” But, he said, “That’s why we took steps to protect people in the control room, to limit access. We made hand sanitizer available to everyone so they could clean their hands.”

Burton and Holt have been on opposite sides of the issue of nuclear power for more than a decade, and they acknowledged the mention of the other’s name with a tired familiarity.਋urton said Holt is a mouthpiece for Dominion who will say anything to make sure the company’s bottom line stays healthy.

“Ms. Burton is entitled to her opinion about how we should run the plant, but we know how to operate a nuclear facility,” Holt said. “We’ve had plans in place to respond to the pandemic since 2006, regularly looked at and updated, based on the most current information available. If we did not think we could operate the plant safely, we would shut it down. We still feel we can safely operate, and we have."

Worldwide nuclear response to COVID

Sheehan noted refueling and maintenance outage work has taken place at numerous nuclear power plants across the country since the pandemic began.

Libbe HaLevy, an author, anti-nuclear activist and host of Nuclear Hotseat, a podcast centered on nuclear news, has been paying close attention to how the nuclear industry is handling the COVID-19 crisis in her broadcasts for months now.

She spoke to a situation in Newport, Mich., where򠈷 workers have tested positive for COVID-19 at DTE Energy’s Fermi-2 nuclear reactor, causing a temporary work stoppage during its refueling outage work. Every worker at the plant — more than 2,000 — were tested for the virus.

“They should have stopped the refueling before it started,” HaLevy said, referring to Millstone. 𠇊t Fermi, they knew they had one case. They should have done what was done in Japan at the Genkai Nuclear Plant, where they were doing follow-up work to build an anti-terrorism facility. One worker tested positive on April 14. Then, all civil engineering work at the plant halted that night. The company has not restarted the project and does not know when it will. That was the response in Japan after one positive. Here, there was one positive they knew about in Fermi before the refueling, they let it go ahead, and now they have 237 positives that we know about.”

HaLevy also faulted Millstone for touting its low number of positive cases despite the hundreds of employees, temporary or otherwise, who haven't been tested.

"How many licensed operators are cleared for Millstone?" HaLevy asked. "Out of those, how many have tested positive so far? And knowing that there's a latency period, how can the numbers go up if you don't test?"