Quantitative Algebras and a Classification of Metric Monads

Quantitative algebras are $\Sigma$-algebras acting on metric spaces, where operations are nonexpanding. We prove that for finitary signatures $\Sigma$ there is a bijective correspondence between varieties of quantitative algebras and strongly finitary monads on the category $\mathsf{Met}$ of metric spaces. For uncountable cardinals $\lambda$ there is an analogous bijection between varieties of $\lambda$-ary quantitative algebras and strongly $\lambda$-accessible monads. Moreover, we present a bijective correspondence between $\lambda$-varieties of $\Sigma$-algebras as introduced by Mardare, Panangaden and Plotkin and enriched, surjections-preserving $\lambda$-accesible monads on $\mathsf{Met}$. Finally, a bijective correspondence between generalized $\lambda$-ary varieties and enriched $\lambda$-accessible monads on $\mathsf{Met}$ in general is presented

SELEKTIVNOST PLIJENA U SOMA (Silurus glanis) I AFRIČKOG SOMA (Clarias gariepinus)

The experiments aimed at prey selectivity in two Siluriformes predators. African catfish, Clarias gariepinus, and wels, Silurus glanis, were performed under laboratory conditions. Prey fish (12-22% TL of predator) were submitted to one.year.old African catfish (~220 g) and wels (~150 g) originating from intensive culture, ie with no previous experience with live fish food. In African catfish, negative selectivity (avoidance) was shown for Nile tilapia (Oreochromis niloticus) and topmouth gudgeon (Pseudorasbora parva) whilst rudd(Scardinius erythrophthalmus) and sunbleak (Leucaspius delineatus) were preferred (positive selectivity). The intensity and efficiency of African catfish predation were quite low because its feeding strategy is based rather on prey searching than hunting. Prey fish, wounded and/or dead from its clumsy attacks, were sonsumed preferably overnight. Not one successful attack of African catfish on healthy prey fish was registered. The SGR and FCR of clarias fed live fish were 0.39%. day-1 and 4.73 respectively. In wels, strong negative selectivity (avoidance) was proved for roach (Rutilus rutilus) and topmouth gungeon, and lower avoidance for Prussian carp (Carassius auratus gibelio) and chub (Leuciscus cephalus). Asp (Aspius aspius) were found to be low preferred but high preference was shown for sunbleak, rudd and bitterling (Rhodeus sericeus). Both catfishes preferred smaller prey fish during the 10.day experimental period whilst those which remained non-consumed belonged to the mean or above-mean size categories.Istraživanja su bila usmjerena na selektivnost plijena u dvije vrste grabežljivaca siluriformes - afričkog soma (Clarius gariepinus) i soma (Silurus glanis). Istraživanja su provedena u laboratorijskim uvjetima. Riba plijen (12-22% TL grabežljivaca) poslužila je jednogodišnjem afričkom somu (~220 g) i somu (~150 g) porijeklom iz intenzivnog uzgoja bez prethodnog iskustva u prehrani živim ribama. Afrički je som pokazao negativnu seletivnost (izbjegavanje) prema nilskoj tilapiji (Oreochromis niloticus) i amurskom čebačoku (Pseudorasbora parva), a crvenperka (Scardinius erythrophthalmus) i bjelica (Leucaspius delineatus) bile su preferirane (pozitivna selektivnost). Intenzitet i efikasnost proždrljivosti afričkog soma bila je posve niska, jer je njegova hranidbena strategija u osnovi zapravo na selektivnosti traženja, a ne lova. Plijen, ozlijeđen ili mrtav u tijeku neefikasnog lova, bio je bolje konzumiran za vrijeme noći. Ni jedan uspješan napad afričkog soma na zdravi plijen nije registriran. U soma je bila dokazana jaka negativna selektivnost (uklanjanje) za bodorku (Rutilus rutilus) i amurski čebačok (Pseudorasbora parva), a slabije izbjegavanje za babušku (Carassius auratus gibelio) i klena (Leuciscus cephalus). Bolen (Aspius aspius) nisko je preferiran, dok je visoka preferiranost pokazana za bjelicu (Leucaspius delineatus), crvenperku (Scardinius erythrophthalmus) i gavčicu (Rhodeus sericeus). Obje vrste soma preferirale su manji plijen za vrijeme desetodnevnog eksperimentalnog razdoblja, dok su oni koji su ostali nekonzumirani pripadali kategoriji srednjih ili većih riba

SELEKTIVNOST PLIJENA U SOMA (Silurus glanis) I AFRIČKOG SOMA (Clarias gariepinus)

The experiments aimed at prey selectivity in two Siluriformes predators. African catfish, Clarias gariepinus, and wels, Silurus glanis, were performed under laboratory conditions. Prey fish (12-22% TL of predator) were submitted to one.year.old African catfish (~220 g) and wels (~150 g) originating from intensive culture, ie with no previous experience with live fish food. In African catfish, negative selectivity (avoidance) was shown for Nile tilapia (Oreochromis niloticus) and topmouth gudgeon (Pseudorasbora parva) whilst rudd(Scardinius erythrophthalmus) and sunbleak (Leucaspius delineatus) were preferred (positive selectivity). The intensity and efficiency of African catfish predation were quite low because its feeding strategy is based rather on prey searching than hunting. Prey fish, wounded and/or dead from its clumsy attacks, were sonsumed preferably overnight. Not one successful attack of African catfish on healthy prey fish was registered. The SGR and FCR of clarias fed live fish were 0.39%. day-1 and 4.73 respectively. In wels, strong negative selectivity (avoidance) was proved for roach (Rutilus rutilus) and topmouth gungeon, and lower avoidance for Prussian carp (Carassius auratus gibelio) and chub (Leuciscus cephalus). Asp (Aspius aspius) were found to be low preferred but high preference was shown for sunbleak, rudd and bitterling (Rhodeus sericeus). Both catfishes preferred smaller prey fish during the 10.day experimental period whilst those which remained non-consumed belonged to the mean or above-mean size categories.Istraživanja su bila usmjerena na selektivnost plijena u dvije vrste grabežljivaca siluriformes - afričkog soma (Clarius gariepinus) i soma (Silurus glanis). Istraživanja su provedena u laboratorijskim uvjetima. Riba plijen (12-22% TL grabežljivaca) poslužila je jednogodišnjem afričkom somu (~220 g) i somu (~150 g) porijeklom iz intenzivnog uzgoja bez prethodnog iskustva u prehrani živim ribama. Afrički je som pokazao negativnu seletivnost (izbjegavanje) prema nilskoj tilapiji (Oreochromis niloticus) i amurskom čebačoku (Pseudorasbora parva), a crvenperka (Scardinius erythrophthalmus) i bjelica (Leucaspius delineatus) bile su preferirane (pozitivna selektivnost). Intenzitet i efikasnost proždrljivosti afričkog soma bila je posve niska, jer je njegova hranidbena strategija u osnovi zapravo na selektivnosti traženja, a ne lova. Plijen, ozlijeđen ili mrtav u tijeku neefikasnog lova, bio je bolje konzumiran za vrijeme noći. Ni jedan uspješan napad afričkog soma na zdravi plijen nije registriran. U soma je bila dokazana jaka negativna selektivnost (uklanjanje) za bodorku (Rutilus rutilus) i amurski čebačok (Pseudorasbora parva), a slabije izbjegavanje za babušku (Carassius auratus gibelio) i klena (Leuciscus cephalus). Bolen (Aspius aspius) nisko je preferiran, dok je visoka preferiranost pokazana za bjelicu (Leucaspius delineatus), crvenperku (Scardinius erythrophthalmus) i gavčicu (Rhodeus sericeus). Obje vrste soma preferirale su manji plijen za vrijeme desetodnevnog eksperimentalnog razdoblja, dok su oni koji su ostali nekonzumirani pripadali kategoriji srednjih ili većih riba

Minimization via duality

We show how to use duality theory to construct minimized versions of a wide class of automata. We work out three cases in detail: (a variant of) ordinary automata, weighted automata and probabilistic automata. The basic idea is that instead of constructing a maximal quotient we go to the dual and look for a minimal subalgebra and then return to the original category. Duality ensures that the minimal subobject becomes the maximally quotiented object

Sound and complete axiomatizations of coalgebraic language equivalence

Coalgebras provide a uniform framework to study dynamical systems, including several types of automata. In this paper, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are sound and complete with respect to behavioral equivalence can be extended to a coarser coalgebraic language equivalence, which arises from a generalised powerset construction that determinises coalgebras. We show that soundness and completeness are established by proving that expressions modulo axioms of a calculus form the rational fixpoint of the given type functor. Our main result is that the rational fixpoint of the functor $FT$, where $T$ is a monad describing the branching of the systems (e.g. non-determinism, weights, probability etc.), has as a quotient the rational fixpoint of the "determinised" type functor $\bar F$, a lifting of $F$ to the category of $T$-algebras. We apply our framework to the concrete example of weighted automata, for which we present a new sound and complete calculus for weighted language equivalence. As a special case, we obtain non-deterministic automata, where we recover Rabinovich's sound and complete calculus for language equivalence.Comment: Corrected version of published journal articl

Non-Deterministic Kleene Coalgebras

In this paper, we present a systematic way of deriving (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of systems. This generalizes both the results of Kleene (on regular languages and deterministic finite automata) and Milner (on regular behaviours and finite labelled transition systems), and includes many other systems such as Mealy and Moore machines

The groupoidal analogue Theta~ to Joyal's category Theta is a test category

We introduce the groupoidal analogue \tilde\Theta to Joyal's cell category \Theta and we prove that \tilde\Theta is a strict test category in the sense of Grothendieck. This implies that presheaves on \tilde\Theta model homotopy types in a canonical way. We also prove that the canonical functor from \Theta to \tilde\Theta is aspherical, again in the sense of Grothendieck. This allows us to compare weak equivalences of presheaves on \tilde\Theta to weak equivalences of presheaves on \Theta. Our proofs apply to other categories analogous to \Theta.Comment: 41 pages, v2: references added, Remark 7.3 added, v3: metadata update

Experimental breeding station for edible insects

Práce má za úkol seznámit o možnostech a podmínkách chovu jedlého hmyzu. Cílem bylo navrhnout experimentální zařízení umožňující měření a regulaci chovných podmínek jmenovitě teploty a vlhkosti v chovném prostředí a přísun krmiva a tekutin. Toto zařízení bylo sestaveno a experimentálními měřeními ověřena funkčnost splněním různých parametrů.The arcticle was supported by project no. FEKT-S-20-6215, New approaches in the use of modern micro- and nanoelectronics.The task of this work is to introduce the possibilities and conditions of breeding edible insects. The goal was to design an experimental device enabling the measurement and regulation of breeding conditions, namely temperature and humidity in the breeding environment and the supply of feed and fluids. This device was assembled and functionality verified by experimental measurements by meeting various parameters