scholarly journals Grounding, Quantifiers, and Paradoxes

2021 ◽  
Author(s):  
Francesco A. Genco ◽  
Francesca Poggiolesi ◽  
Lorenzo Rossi
Keyword(s):  
Contemporary Literature ◽  
Formal System ◽  
The Other ◽  
Hard Problem ◽  
First Order ◽  
Explanatory Relation ◽  
Arbitrary Objects

AbstractThe notion of grounding is usually conceived as an objective and explanatory relation. It connects two relata if one—the ground—determines or explains the other—the consequence. In the contemporary literature on grounding, much effort has been devoted to logically characterize the formal aspects of grounding, but a major hard problem remains: defining suitable grounding principles for universal and existential formulae. Indeed, several grounding principles for quantified formulae have been proposed, but all of them are exposed to paradoxes in some very natural contexts of application. We introduce in this paper a first-order formal system that captures the notion of grounding and avoids the paradoxes in a novel and non-trivial way. The system we present formally develops Bolzano’s ideas on grounding by employing Hilbert’s ε-terms and an adapted version of Fine’s theory of arbitrary objects.

scholarly journals Thematic Maps for the Variation of Bearing Capacity of Soil Using SPTs and MATLAB

Geosciences ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 329
Author(s):  
Mahdi O. Karkush ◽  
Mahmood D. Ahmed ◽  
Ammar Abdul-Hassan Sheikha ◽  
Ayad Al-Rumaithi
Keyword(s):  
Bearing Capacity ◽  
Mean Squared Error ◽  
Ground Level ◽  
The Other ◽  
Thematic Maps ◽  
First Order ◽  
Squared Error ◽  
Order Polynomial ◽  
Interpolation Polynomials ◽  
Penetration Tests

The current study involves placing 135 boreholes drilled to a depth of 10 m below the existing ground level. Three standard penetration tests (SPT) are performed at depths of 1.5, 6, and 9.5 m for each borehole. To produce thematic maps with coordinates and depths for the bearing capacity variation of the soil, a numerical analysis was conducted using MATLAB software. Despite several-order interpolation polynomials being used to estimate the bearing capacity of soil, the first-order polynomial was the best among the other trials due to its simplicity and fast calculations. Additionally, the root mean squared error (RMSE) was almost the same for the all of the tried models. The results of the study can be summarized by the production of thematic maps showing the variation of the bearing capacity of the soil over the whole area of Al-Basrah city correlated with several depths. The bearing capacity of soil obtained from the suggested first-order polynomial matches well with those calculated from the results of SPTs with a deviation of ±30% at a 95% confidence interval.

Neural computation of motion in the fly visual system: quadratic nonlinearity of responses induced by picrotoxin in the HS and CH cells

1995 ◽  
Vol 74 (6) ◽  
pp. 2665-2684 ◽  
Author(s):  
Y. Kondoh ◽  
Y. Hasegawa ◽  
J. Okuma ◽  
F. Takahashi
Keyword(s):  
Mean Square Error ◽  
Order Term ◽  
Mirror Image ◽  
Second Order ◽  
The Other ◽  
Linear Component ◽  
Mean Square ◽  
Nonlinear Component ◽  
First Order ◽  
Order Kernel

1. A computational model accounting for motion detection in the fly was examined by comparing responses in motion-sensitive horizontal system (HS) and centrifugal horizontal (CH) cells in the fly's lobula plate with a computer simulation implemented on a motion detector of the correlation type, the Reichardt detector. First-order (linear) and second-order (quadratic nonlinear) Wiener kernels from intracellularly recorded responses to moving patterns were computed by cross correlating with the time-dependent position of the stimulus, and were used to characterize response to motion in those cells. 2. When the fly was stimulated with moving vertical stripes with a spatial wavelength of 5-40 degrees, the HS and CH cells showed basically a biphasic first-order kernel, having an initial depolarization that was followed by hyperpolarization. The linear model matched well with the actual response, with a mean square error of 27% at best, indicating that the linear component comprises a major part of responses in these cells. The second-order nonlinearity was insignificant. When stimulated at a spatial wavelength of 2.5 degrees, the first-order kernel showed a significant decrease in amplitude, and was initially hyperpolarized; the second-order kernel was, on the other hand, well defined, having two hyperpolarizing valleys on the diagonal with two off-diagonal peaks. 3. The blockage of inhibitory interactions in the visual system by application of 10-4 M picrotoxin, however, evoked a nonlinear response that could be decomposed into the sum of the first-order (linear) and second-order (quadratic nonlinear) terms with a mean square error of 30-50%. The first-order term, comprising 10-20% of the picrotoxin-evoked response, is characterized by a differentiating first-order kernel. It thus codes the velocity of motion. The second-order term, comprising 30-40% of the response, is defined by a second-order kernel with two depolarizing peaks on the diagonal and two off-diagonal hyperpolarizing valleys, suggesting that the nonlinear component represents the power of motion. 4. Responses in the Reichardt detector, consisting of two mirror-image subunits with spatiotemporal low-pass filters followed by a multiplication stage, were computer simulated and then analyzed by the Wiener kernel method. The simulated responses were linearly related to the pattern velocity (with a mean square error of 13% for the linear model) and matched well with the observed responses in the HS and CH cells. After the multiplication stage, the linear component comprised 15-25% and the quadratic nonlinear component comprised 60-70% of the simulated response, which was similar to the picrotoxin-induced response in the HS cells. The quadratic nonlinear components were balanced between the right and left sides, and could be eliminated completely by their contralateral counterpart via a subtraction process. On the other hand, the linear component on one side was the mirror image of that on the other side, as expected from the kernel configurations. 5. These results suggest that responses to motion in the HS and CH cells depend on the multiplication process in which both the velocity and power components of motion are computed, and that a putative subtraction process selectively eliminates the nonlinear components but amplifies the linear component. The nonlinear component is directionally insensitive because of its quadratic non-linearity. Therefore the subtraction process allows the subsequent cells integrating motion (such as the HS cells) to tune the direction of motion more sharply.

scholarly journals Ganglioside incorporation and release by the isolated perfused rat liver

1991 ◽  
Vol 274 (2) ◽  
pp. 581-585 ◽  
Author(s):  
S C Kivatinitz ◽  
A Miglio ◽  
R Ghidoni
Keyword(s):  
Rat Liver ◽  
The Other ◽  
Regulatory Role ◽  
Isolated Perfused Rat Liver ◽  
Order Kinetic ◽  
Perfused Rat Liver ◽  
Ganglioside Gm1 ◽  
First Order ◽  
Pseudo First Order

The fate of exogenous ganglioside GM1 labelled in the sphingosine moiety, [Sph-3H]GM1, administered as a pulse, in the isolated perfused rat liver was investigated. When a non-recirculating protocol was employed, the amount of radioactivity in the liver and perfusates was found to be dependent on the presence of BSA in the perfusion liquid and on the time elapsed after the administration of the ganglioside. When BSA was added to the perfusion liquid, less radioactivity was found in the liver and more in the perfusate at each time tested, for up to 1 h. The recovery of radioactivity in the perfusates followed a complex course which can be described by three pseudo-first-order kinetic constants. The constants, in order of decreasing velocity, are interpreted as: (a) the dilution of the labelled GM1 by the constant influx of perfusion liquid; (b) the washing off of GM1 loosely bound to the surface of liver cells; (c) the release of gangliosides from the liver. Process (b) was found to be faster in the presence of BSA, probably owing to the ability of BSA to bind gangliosides. The [Sph-3H]GM1 in the liver underwent metabolism, leading to the appearance of products of anabolic (GD1a, GD1b) and catabolic (GM2, GM3) origin; GD1a appeared before GM2 and GM3 but, at times longer than 10 min, GM2 and GM3 showed more radioactivity than GD1a. At a given time the distribution of the radioactivity in the perfusates was quite different from that of the liver. In fact, after 60 min GD1a was the only metabolite present in any amount, the other being GM3, the quantity of which was small. This indicates that the liver is able to release newly synthesized gangliosides quite specifically. When a recirculating protocol was used, there were more catabolites and less GD1a than with the non-recirculating protocol. A possible regulatory role of ganglioside re-internalization on their own metabolism in the liver is postulated.

On the role of Ramsey quantifiers in first order arithmetic

1982 ◽  
Vol 47 (2) ◽  
pp. 423-435 ◽  
Author(s):  
James H. Schmerl ◽  
Stephen G. Simpson
Keyword(s):  
Formal System ◽  
Intended Meaning ◽  
Completeness Proof ◽  
First Order ◽  
Uncountable Cardinal ◽  
Consistent Extension ◽  
Witness Set ◽  
Order Arithmetic ◽  
Infinite Set

The purpose of this paper is to study a formal system PA(Q2) of first order Peano arithmetic, PA, augmented by a Ramsey quantifier Q2 which binds two free variables. The intended meaning of Q2xx′φ(x, x′) is that there exists an infinite set X of natural numbers such that φ(a, a′) holds for all a, a′ Є X such that a ≠ a′. Such an X is called a witness set for Q2xx′φ(x, x′). Our results would not be affected by the addition of further Ramsey quantifiers Q3, Q4, …, Here of course the intended meaning of Qkx1 … xkφ(x1,…xk) is that there exists an infinite set X such that φ(a1…, ak) holds for all k-element subsets {a1, … ak} of X.Ramsey quantifiers were first introduced in a general model theoretic setting by Magidor and Malitz [13]. The system PA{Q2), or rather, a system essentially equivalent to it, was first defined and studied by Macintyre [12]. Some of Macintyre's results were obtained independently by Morgenstern [15]. The present paper is essentially self-contained, but all of our results have been directly inspired by those of Macintyre [12].After some preliminaries in §1, we begin in §2 by giving a new completeness proof for PA(Q2). A by-product of our proof is that for every regular uncountable cardinal k, every consistent extension of PA(Q2) has a k-like model in which all classes are definable. (By a class we mean a subset of the universe of the model, every initial segment of which is finite in the sense of the model.)

scholarly journals Pancreatic secretion and pressure biomechanics in pancreatic acinus

2020 ◽  
Vol 19 (1) ◽  
pp. 6-12
Author(s):  
G. Ya. Kostyuk ◽  
O. G. Kostyuk ◽  
M. V Burkov ◽  
I. A. Golubovsky ◽  
M. P. Bulko ◽  
...  
Keyword(s):  
Flow System ◽  
Dynamic Pressure ◽  
Excretory Duct ◽  
The Other ◽  
Duct System ◽  
First Order ◽  
Pancreatic Acinus ◽  
Mercury Column ◽  
The Mathematical Model ◽  
Oddi Sphincter

The article highlights the mechanism of the mathematical model of acinus, the components of the formation of pressure in its cavity and the formation of pancreatic juice. It has been established that the mechanism for creating pressure in the acinus cavity is similar to the intraductal one. In this case, the question remains open about the causes of such high pressure, which is measured in several hundred millimeters of a mercury column, especially since, as histologically established, the pancreas and its ducts do not have muscle structures, and those rudiments of myofibrils, which are noted in some places of the flow system, of course, cannot ensure the development of such pressure. The increase in pressure in the cavity of the acinus is associated with the phenomenon of osmosis in its cells. Since cell membranes have the property of conductivity, as a result of osmosis, water through the membrane first passes from the blood to the cell, then from the cell through the membrane into the acinus cavity. In addition to the mechanism of osmosis through the membrane, in the cells of the acinus epithelium, there is a filtering mechanism through the pores of the layer of connective tissue to the lymph channel. It has now been established that, together with simple osmosis, the phenomenon of electroosmosis takes place in secreting cells and organs of excretion, not only accelerates the transfer of substances, but also increases the pressure on the other side of the membrane against the gradient by almost several first-order units. Thus, the outflow of fluid from the acinus cavity proceeds continuously, but only with a change in the speed of movement, it is determined by the pressure drop in the acinus – tubule – excretory duct system, the opening of the Oddi sphincter and the pulse of the cardiovascular wave, which creates dynamic pressure in the capillary. This whole mechanism, as a result, leads to the filling of the cavity of the acinus and the creation of a certain pressure in it.

The Philosophy of African Logic

2017 ◽  
pp. 96-121
Author(s):  
Jonathan O. Chimakonam
Keyword(s):  
Formal System ◽  
Cultural Influence ◽  
Formal Logic ◽  
Cross Cultural ◽  
The Other ◽  
Prototype System ◽  
African Philosophy ◽  
System 2 ◽  
The One ◽  
Universal Applicability

The chapter aims to do two things: 1) a rigorous presentation of philosophy of African logic and 2) to do this from the perspective of Ezumezu (an African) logic. The chapter will proceed by defining the three aspects of Ezumezu logic namely: 1) as a formal system, 2) as methodology, and 3) as a philosophy of African logic. My inquiry in this work primarily is with the philosophy of African logic but it will also cut across formal logic and methodology in addition. In the first section, I will attempt to show how the cultural influence behind the formulation of the principles of African logic justifies such a system as relative on the one hand, and how the cross-cultural applications justify it as universal on the other. I believe that this is where African philosophical assessment of African logic ought to begin because most critics of the idea of African logic agitate that an African system of logic, if it is ever possible, must necessarily lack the tincture of universal applicability. Afterwards, I will narrow my inquiry down to the African philosophy appraisal of African logic with an example of Ezumezu system. This focus is especially critical because it purveys a demonstration of a prototype system of an African logic. In the section on some principles of Ezumezu logic, I will attempt to accomplish the set goal of this chapter by presenting and discussing some principles of Ezumezu logic which I had formulated in earlier works in addition to formulating a few additional ones. The interesting thing to note here is that these principles are/will all (be) articulated from the African background ontology. I will conclude by throwing further light on the merits, nature and promises of an African logic tradition.

On Axiomatizability of Non-Commutative Lp-Spaces

2007 ◽  
Vol 50 (4) ◽  
pp. 519-534
Author(s):  
C. Ward Henson ◽  
Yves Raynaud ◽  
Andrew Rizzo
Keyword(s):  
Hilbert Spaces ◽  
Normed Space ◽  
The Other ◽  
Space Structures ◽  
Operator Spaces ◽  
Infinite Dimensions ◽  
Schatten Classes ◽  
Lp Spaces ◽  
First Order ◽  
Order Language

AbstractIt is shown that Schatten p-classes of operators between Hilbert spaces of different (infinite) dimensions have ultrapowers which are (completely) isometric to non-commutative Lp-spaces. On the other hand, these Schatten classes are not themselves isomorphic to non-commutative Lp spaces. As a consequence, the class of non-commutative Lp-spaces is not axiomatizable in the first-order language developed by Henson and Iovino for normed space structures, neither in the signature of Banach spaces, nor in that of operator spaces. Other examples of the same phenomenon are presented that belong to the class of corners of non-commutative Lp-spaces. For p = 1 this last class, which is the same as the class of preduals of ternary rings of operators, is itself axiomatizable in the signature of operator spaces.

Dissection of the neuron network in the catfish inner retina. V. Interactions between NA and NB amacrine cells

1990 ◽  
Vol 63 (1) ◽  
pp. 120-130 ◽  
Author(s):  
H. M. Sakai ◽  
K. I. Naka
Keyword(s):  
White Noise ◽  
Small Amplitude ◽  
Amacrine Cell ◽  
Amacrine Cells ◽  
The Other ◽  
First Order ◽  
Membrane Noise ◽  
Current Pulses ◽  
Damped Oscillation ◽  
Order Kernel

1. Simultaneous intracellular recordings were made from two neighboring N amacrine cells, one an ON amacrine (NA) cell and the other an OFF amacrine (NB) cell. Extrinsic current was injected into one amacrine cell, and the resulting intracellular responses were recorded from the other amacrine cell. Test signals included 1) a single-frequency sinusoid, 2) a depolarizing or hyperpolarizing pulse, or 3) a white-noise modulated current. In some cell pairs, membrane noise was measured in the dark as well as under a steady background illumination. 2. Current pulses injected into a NA cell evoked a damped oscillation from a NB cell. The first-order kernel derived by cross-correlating the white-noise current injected into a NA cell against the evoked response from a NB cell was a large depolarization followed by a damped oscillation. The frequency of oscillations varied slightly from pair to pair but averaged 35 Hz. 3. Current pulses injected into a NB cell evoked a sign-inverting response (hyperpolarization) of very small amplitude from a NA cell. Similarly, the first-order kernel was a hyperpolarization of very small amplitude. 4. The power spectrum of the membrane noise recorded from NA and NB cells in the dark or during steady illumination often showed a peak at 35 Hz. Such membrane noise synchronizes synergistically among NA cells and among NB cells in the dark. In addition, the membrane fluctuations seen in NA and NB cells in the dark were out of phase. 5. Transmission between NA and NB cells was largely accounted for by a linear component; however, a very small but significant second- and third-order nonlinearity was also generated. 6. These results show that the interactions occurring between amacrine cells of opposite response polarity are much more complex than those between cells of the same response polarity and that the neural circuitry in the inner retina actively controls interactions between ON and OFF channels in the dark as well as in the presence of light stimuli.

New family of parasupercoherent states: entanglement, uncertainties, and statistical properties

2020 ◽  
Vol 98 (10) ◽  
pp. 953-958
Author(s):  
Amin Motamedinasab ◽  
Azam Anbaraki ◽  
Davood Afshar ◽  
Mojtaba Jafarpour
Keyword(s):  
Harmonic Oscillator ◽  
Arbitrary Order ◽  
Annihilation Operator ◽  
The Other ◽  
Mandel Parameter ◽  
First Order ◽  
New Family ◽  
Wide Range ◽  
New States ◽  
Minimum Uncertainty

The general parasupersymmetric annihilation operator of arbitrary order does not reduce to the Kornbluth–Zypman general supersymmetric annihilation operator for the first order. In this paper, we introduce an annihilation operator for a parasupersymmetric harmonic oscillator that in the first order matches with the Kornblouth–Zypman results. Then, using the latter operator, we obtain the parasupercoherent states and calculate their entanglement, uncertainties, and statistics. We observe that these states are entangled for any arbitrary order of parasupersymmetry and their entanglement goes to zero for the large values of the coherency parameter. In addition, we find that the maximum of the entanglement of parasupercoherent states is a decreasing function of the parasupersymmetry order. Moreover, these states are minimum uncertainty states for large and also small values of the coherency parameter. Furthermore, these states show squeezing in one of the quadrature operators for a wide range of the coherency parameter, while no squeezing in the other quadrature operator is observed at all. In addition, using the Mandel parameter, we find that the statistics of these new states are subPoissonian for small values of the coherency parameter.

The other hard problem: How to bridge the gap between symbolic and subsymbolic cognition

1998 ◽  
Vol 21 (1) ◽  
pp. 22-23
Author(s):  
Axel Cleeremans
Keyword(s):  
Implicit Learning ◽  
The Other ◽  
Hard Problem ◽  
Symbolic Cognition

The constructivist notion that features are purely functional is incompatible with the classical computational metaphor of mind. I suggest that the discontent expressed by Schyns, Goldstone & Thibaut about fixed-features theories of categorization reflects the growing impact of connectionism. Their perspective is similar to recent research on implicit learning, consciousness, and development. A hard problem remains, however: how to bridge the gap between subsymbolic and symbolic cognition.

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