Witness to a passing

Counterexamples to witness conjectures

Consider the class of exp-log constants, which is constructed from the integers using the field operations, exponentiation and logarithm. Let z be such an exp-log constant and let n be its size as an expression. Witness conjectures attempt to give bounds $(n) for the number of decimal digits which need to be evaluated in order to test whether z equals zero. For this purpose, it is convenient to...

On humanizing the expert witness: a proposed narrative approach to expert witness qualification.

Before expert witnesses may testify in court, it is necessary that they be qualified to render an expert opinion. The qualification process has three steps: first, the expert’s training, education, experience, and other indices of qualification are elicited on direct examination by the retaining attorney. Second, a proffer is made to the court of the witness as an expert; the proffer may be cha...

Recalling a Witness

type ref t = id:N{witnessed (has_a_t id t)} let has (id:N) (H h _) = match h id with Used _ _ (Untyped _)→⊤ | _→⊥ abstract type uref = id:N{witnessed (has id)}type uref = id:N{witnessed (has id)} To enforce these invariants on state-manipulating operations, we define a preorder rel on heap, that constrains the heap evolution. It states that every Used identifier remains Used; every Typed refere...

Witness to a thousand stories: a look at insurance data.

Material witness: A quick fix.

M AERIA L W TN SS Delicately patterned microand nanostructures can be produced without the need for laborious fabrication, by relying on physical forces to organize materials spontaneously into intricate forms. The capacity of soft materials such as surfactants and block copolymers to self-organize into regular patterns has been long recognized1–3, and superlattices and other ordered arrays in ...