In 1994 Herbelin started and partially achieved the programme of showing that, for intuitionistic implicational logic, there is a Curry-Howard interpretation of sequent calculus into a variant of the λ-calculus, specifically a variant which manipulates formally “applicative contexts” and inverts the associativity of “applicative terms”. Herbelin worked with a fragment of sequent calculus with c...

In this paper we give two new combinatorial proofs of the classification of rational tangles using the calculus of continued fractions. One proof uses the classification of alternating knots. The other proof uses colorings of tangles. We also obtain an elementary proof that alternating rational tangles have minimal number of crossings. Rational tangles form a basis for the classification of kno...

LJQ is a focused sequent calculus for intuitionistic logic, with a simple restriction on the first premiss of the usual left introduction rule for implication. In a previous paper we discussed its history (going back to about 1950, or beyond) and presented its basic theory and some applications; here we discuss in detail its relation to call-by-value reduction in lambda calculus, establishing a...

We present a case of a patient with xanthogranulomatous pyelonephritis (XGP) presenting with a large (18 × 12 cm) left-sided flank mass with worsening left flank pain. CT abdomen/pelvis demonstrated a left kidney with parenchyma replaced by multiple large hypodense collections containing fluid and gas, a left staghorn calculus, and a communication between the kidney and large flank collection. ...

This paper aims at investigating the superiority of power allocation strategies, based on calculus of variations in a point-to-point two-way relay-assisted channel incorporating the amplify and forward strategy. Single and multilayer coding strategies for two cases of having and not having the channel state information (CSI) at the transmitters are studied, respectively. Using the notion of cal...

Haemophilus species are known to colonize the upper respiratory tract and can cause infections. However Haemophilus influenzae has been rarely described as a cause of genitourinary tract infection. We report a 44-year-old nonimmunocompromised Japanese man with bacteremic pyelonephritis caused by a nontypable H. influenzae associated with a left ureteral calculus. The organism was isolated from ...

Cardiovascular magnetic resonance (CMR) is an accurate tool for the determination of right and left ventricular volumes and ejection fractions. However, the current standard short-axis technique is time-consuming and thus, often not practicable for routine daily use, because papillary muscles and trabeculations have to be marked and their volumes subtracted from the total ventricular volume. To...

The calculus of constructions can be extended with an infinite hierarchy of universes and cumulative subtyping. Subtyping is usually left implicit in the typing rules. We present an alternative version of the calculus of constructions where subtyping is explicit. We avoid problems related to coercions and dependent types by using the Tarski style of universes and by adding equations to reflect ...

We introduce a new concept of complete integrability in the framework of noncommutative geometry. It involves a gauged bi-differential calculus over an associative (and not necessarily commutative) algebra A. Basically, this is an N0-graded left A-module with two covariant exterior derivatives acting on it which, as a consequence of certain (e.g., nonlinear differential) equations, are flat and...

BACKGROUND Renal vein thrombosis (RVT) with flank pain, and hematuria, is often mistaken with renal colic originating from ureteric or renal calculus. Especially in young and otherwise healthy patients, clinicians are easily misled by clinical presentation and calcified RVT. CASE PRESENTATION A 38-year-old woman presented with flank pain and hematuria suggestive of renal calculus on ultrasoun...