SYLLABUS A range of topics for the course follows. 1. Algebraic theories: universal algebra; equational logic; soundness and completeness; theory translations and constructions. 2. Algebras: initial algebras; induction principle; recursive domain equations; free algebras. 3. Presheaves: cartesian closure; essential geometric morphisms; free cocompletions; Kan extensions; coends. 4. Simply typed...

A principled approach to the design of program verification and construction tools is applied to separation logic. The control flow is modelled by power series with convolution as separating conjunction. A generic construction lifts resource monoids to assertion and predicate transformer quantales. The data flow is captured by concrete store/heap models. These are linked to the separation algeb...

It is shown that continuity of a family of invariant (Haar) measures on a topological groupoid G is equivalent to the continuity of the implied convolution product f * g for all pairs of functions / and g. An example is given of a groupoid which admits no (continuous) Haar measure. It results, therefore, that the usual C*-algebra associated with a Haar measure on G cannot, in general, be constr...

In this paper, we address the parameterization problem for traffic envelopes needed for deterministic traffic regulation and service guarantees. A parameterized function is a good “substitute” for a traffic envelope if (i) the substitute is not smaller than the envelope and (ii) no other functions not smaller than the envelope are smaller than the substitute. Analogous to the least square appro...

Exact calculations of Feynman’s path integrals (defined on a time lattice) are mainly based on recurrence integral formulas in which the convolution of two functions having a common feature retains the same feature. Therefore, exactly soluble path integrals in quantum mechanics may be classified by their recurrence integral formula used in the calculation. According to this classification, ther...

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Abstract The Fourier algebra of the affine group real line has a natural identification, as Banach space, with space trace-class operators on $$L^2({{\mathbb {R}}}^\times , dt/ |t|)$$ L 2 ( R × ,</mml...

This article introduces YaConv , a new algorithm to compute convolution using GEMM microkernels from Basic Linear Algebra Subprograms library that is efficient for multiple CPU architectures. Previous approaches either create copy of each image element filter or reload these elements into cache call, leading redundant instances the in cache. Instead, loads once and maximizes reuse elements. The...

it is shown that every  almost linear bijection $h : arightarrow b$ of a unital $c^*$-algebra $a$ onto a unital$c^*$-algebra $b$ is a $c^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries  $u in a$, all $y in a$, and all $nin mathbb z$, andthat almost linear continuous bijection $h : a rightarrow b$ of aunital $c^*$-algebra $a$ of real rank zero onto a unital$c^*$-algebra...