Quasi-selective ultrafilters and asymptotic numerosities

We isolate a new class of ultrafilters on N, called "quasi-selective" because they are intermediate between selective ultrafilters and P-points. (Under the Continuum Hypothesis these three classes are distinct.) The existence of quasi-selective ultrafilters is equivalent to the existence of "asymptotic numerosities" for all sets of tuples of natural numbers. Such numerosities are hypernatural numbers that generalize finite cardinalities to countable point sets. Most notably, they maintain the structure of ordered semiring, and, in a precise sense, they allow for a natural extension of asymptotic density to all sequences of tuples of natural numbers.Comment: 27 page

Euclidean integers, Euclidean ultrafilters, and Euclidean numerosities

We introduce a "Euclidean" notion of size (numerosity) for "Punktmengen", i.e. sets of points of Euclidean (finitely dimensional) spaces over any "line" L, namely one that maintains the Cantorian defiitions of order, addition and multiplication, while preserving the ancient principle that "the whole is greater than the part" (a set is (strictly) larger than its proper subsets). These numerosities satisfy the five Euclid's common notions, thus enjoying a very good arithmetic, since they constitute the nonnegative part of the ordered ring of the Euclidean integers, here introduced by suitably assigning a transfinite sum to (ordinally indexed) kappa-sequences of integers (so generating a semiring of nonstandard natural numbers). Most relevant is the natural set theoretic definition of the set-preordering <: given any two sets X, Y of any cardinality, one has X<Y if and only if there exists a proper superset of X that is equinumerous to Y . Extending this "superset property" from countable to uncountable sets has been one of the main open question in this area from the beginning of the century

Extended LaSalle's invariance principle for full-range cellular neural networks

In several relevant applications to the solution of signal processing tasks in real time, a cellular neural network (CNN) is required to be convergent, that is, each solution should tend toward some equilibrium point. The paper develops a Lyapunov method, which is based on a generalized version of LaSalle's invariance principle, for studying convergence and stability of the differential inclusions modeling the dynamics of the full-range (FR) model of CNNs. The applicability of the method is demonstrated by obtaining a rigorous proof of convergence for symmetric FR-CNNs. The proof, which is a direct consequence of the fact that a symmetric FR-CNN admits a strict Lyapunov function, is much more simple than the corresponding proof of convergence for symmetric standard CNNs

Convergence of Neural Networks with a Class of Real Memristors with Rectifying Characteristics

The paper considers a neural network with a class of real extended memristors obtained via the parallel connection of an ideal memristor and a nonlinear resistor. The resistor has the same rectifying characteristic for the current as that used in relevant models in the literature to account for diode-like effects at the interface between the memristor metal and insulating material. The paper proves some fundamental results on the trajectory convergence of this class of real memristor neural networks under the assumption that the interconnection matrix satisfies some symmetry conditions. First of all, the paper shows that, while in the case of neural networks with ideal memristors, it is possible to explicitly find functions of the state variables that are invariants of motions, the same functions can be used as Lyapunov functions that decrease along the trajectories in the case of real memristors with rectifying characteristics. This fundamental property is then used to study convergence by means of a reduction-of-order technique in combination with a Lyapunov approach. The theoretical predictions are verified via numerical simulations, and the convergence results are illustrated via the applications of real memristor neural networks to the solution of some image processing tasks in real time

Complete Stability of Neural Networks With Extended Memristors

The article considers a large class of delayed neural networks (NNs) with extended memristors obeying the Stanford model. This is a widely used and popular model that accurately describes the switching dynamics of real nonvolatile memristor devices implemented in nanotechnology. The article studies via the Lyapunov method complete stability (CS), i.e., convergence of trajectories in the presence of multiple equilibrium points (EPs), for delayed NNs with Stanford memristors. The obtained conditions for CS are robust with respect to variations of the interconnections and they hold for any value of the concentrated delay. Moreover, they can be checked either numerically, via a linear matrix inequality (LMI), or analytically, via the concept of Lyapunov diagonally stable (LDS) matrices. The conditions ensure that at the end of the transient capacitor voltages and NN power vanish. In turn, this leads to advantages in terms of power consumption. This notwithstanding, the nonvolatile memristors can retain the result of computation in accordance with the in-memory computing principle. The results are verified and illustrated via numerical simulations. From a methodological viewpoint, the article faces new challenges to prove CS since due to the presence of nonvolatile memristors the NNs possess a continuum of nonisolated EPs. Also, for physical reasons, the memristor state variables are constrained to lie in some given intervals so that the dynamics of the NNs need to be modeled via a class of differential inclusions named differential variational inequalities

Physical Implementation of a Tunable Memristor-based Chua's Circuit

Nonlinearity is a central feature in demanding computing applications that aim to deal with tasks such as optimization or classification. Furthermore, the consensus is that nonlinearity should not be only exploited at the algorithm level, but also at the physical level by finding devices that incorporate desired nonlinear features to physically implement energy, area and/or time efficient computing applications. Chaotic oscillators are one type of system powered by nonlinearity, which can be used for computing purposes. In this work we present a physical implementation of a tunable Chua's circuit in which the nonlinear part is based on a nonvolatile memristive device. Device characterization and circuit analysis serve as guidelines to design the circuit and results prove the possibility to tune the circuit oscillatory response by electrically programming the device.Comment: Accepted by IEEE 48th European Solid State Circuits Conference (ESSCIRC 2022

Memristor Circuits for Simulating Neuron Spiking and Burst Phenomena

Since the introduction of memristors, it has been widely recognized that they can be successfully employed as synapses in neuromorphic circuits. This paper focuses on showing that memristor circuits can be also used for mimicking some features of the dynamics exhibited by neurons in response to an external stimulus. The proposed approach relies on exploiting multistability of memristor circuits, i.e., the coexistence of infinitely many attractors, and employing a suitable pulse-programmed input for switching among the different attractors. Specifically, it is first shown that a circuit composed of a resistor, an inductor, a capacitor and an ideal charge-controlled memristor displays infinitely many stable equilibrium points and limit cycles, each one pertaining to a planar invariant manifold. Moreover, each limit cycle is approximated via a first-order periodic approximation analytically obtained via the Describing Function (DF) method, a well-known technique in the Harmonic Balance (HB) context. Then, it is shown that the memristor charge is capable to mimic some simplified models of the neuron response when an external independent pulse-programmed current source is introduced in the circuit. The memristor charge behavior is generated via the concatenation of convergent and oscillatory behaviors which are obtained by switching between equilibrium points and limit cycles via a properly designed pulse timing of the current source. The design procedure takes also into account some relationships between the pulse features and the circuit parameters which are derived exploiting the analytic approximation of the limit cycles obtained via the DF method

Non-Conventional Yeasts Whole Cells as Efficient Biocatalysts for the Production of Flavors and Fragrances

The rising consumer requests for natural flavors and fragrances have generated great interest in the aroma industry to seek new methods to obtain fragrance and flavor compounds naturally. An alternative and attractive route for these compounds is based on bio-transformations. In this review, the application of biocatalysis by Non Conventional Yeasts (NCYs) whole cells for the production of flavor and fragrances is illustrated by a discussion of the production of different class of compounds, namely Aldehydes, Ketones and related compounds, Alcohols, Lactones, Terpenes and Terpenoids, Alkenes, and Phenols

Study of Holtermanniella wattica, Leucosporidium creatinivorum, Naganishia adeliensis, Solicoccozyma aeria, and Solicoccozyma terricola for their lipogenic aptitude from different carbon sources

Background The ability of some microorganisms to accumulate lipids is well known; however, only recently the number of studies on microbial lipid biosynthesis for obtaining oleochemical products, namely biofuels and some building blocks for chemistry, is rapidly and spectacularly increased. Since 1990s, some oleaginous yeasts were studied for their ability to accumulate lipids up to 60\u201370% of their dry weight. Due to the vast array of engineering techniques currently available, the recombinant DNA technology was the main approach followed so far for obtaining lipid-overproducing yeasts, mainly belonging to the Yarrowia lipolytica. However, an alternative approach can be offered by worldwide diversity as source of novel oleaginous yeasts. Lipogenic aptitude of a number of yeast strains has been reviewed, but many of these studies utilized a limited number of species and/or different culture conditions that make impossible the comparison of different results. Accordingly, the lipogenic aptitude inside the yeast world is still far from being fully explored, and finding new oleaginous yeast species can acquire a strategic importance. Results Holtermanniella wattica, Leucosporidium creatinivorum, Naganishia adeliensis, Solicoccozyma aeria, and Solicoccozyma terricola strains were selected as a result of a large-scale screening on 706 yeasts (both Ascomycota and Basidiomycota). Lipid yields and fatty acid profiles of selected strains were evaluated at 20 and 25 \ub0C on glucose, and on glycerol, xylose, galactose, sucrose, maltose, and cellobiose. A variable fatty acid profile was observed in dependence of both temperature and different carbon sources. On the whole, L. creatinivorum exhibited the highest performances: total lipid yield (YL) >7 g/l on glucose and glycerol, % of intracellular lipids on cell biomass (YL/DW) >70% at 20 \ub0C on glucose, lipid coefficient (YL/Glu) around 20% on glucose, and daily productivity (YL/d) on glucose and sucrose >1.6 g/(l*d). Conclusions This study provides some meaningful information about the lipogenic ability of some yeast species. Variable lipid yields and fatty acid profiles were observed in dependence of both temperature and different carbon sources. L. creatinivorum exhibited the highest lipogenic performances

Geomorphology of the northwestern Kurdistan Region of Iraq: landscapes of the Zagros Mountains drained by the Tigris and Great Zab Rivers

We present the geomorphological map of the northwestern part of the Kurdistan Region of Iraq, where the landscape expresses the tectonic activity associated with the Arabia-Eurasia convergence and Neogene climate change. These processes influenced the evolution of landforms and fluvial pathways, where major rivers Tigris, Khabur, and Great Zab incise the landscape of Northeastern Mesopotamia Anticlinal ridges and syncline trough compose the Zagros orogen. The development of water and wind gaps, slope, and karsts processes in the highlands and the tilting of fluvial terraces in the flat areas are the main evidence of the relationship between tectonics, climate variations and geomorphological processes. During the Quaternary, especially after the Last Glacial Maximum, fluctuating arid and wet periods also influenced local landforms and fluvial patterns of the area. Finally, the intensified Holocene human occupation and agricultural activities during the passage to more complex societies over time impacted the evolution of the landscape in this part of Mesopotamia