The Principle Of Excluded Middle Then And Now: Aristotle And Principia Mathematica

The prevailing truth-functional logic of the twentieth century, it is argued, is incapable of expressing the subtlety and richness of Aristotle's Principle of Excluded Middle, and hence cannot but misinterpret it. Furthermore, the manner in which truth-functional logic expresses its own Principle of Excluded Middle is less than satisfactory in its application to mathematics. Finally, there are glimpses of the "realism" which is the metaphysics demanded by twentieth century logic, with the remarkable consequent that Classical logic is a particularly inept instrument to analyze those philosophies which stand opposed to the "realism" it demands

Glass and polycrystal states in a lattice spin model

We numerically study a nondisordered lattice spin system with a first order liquid-crystal transition, as a model for supercooled liquids and glasses. Below the melting temperature the system can be kept in the metastable liquid phase, and it displays a dynamic phenomenology analogous to fragile supercooled liquids, with stretched exponential relaxation, power law increase of the relaxation time and high fragility index. At an effective spinodal temperature Tsp the relaxation time exceeds the crystal nucleation time, and the supercooled liquid loses stability. Below Tsp liquid properties cannot be extrapolated, in line with Kauzmann's scenario of a `lower metastability limit' of supercooled liquids as a solution of Kauzmann's paradox. The off-equilibrium dynamics below Tsp corresponds to fast nucleation of small, but stable, crystal droplets, followed by extremely slow growth, due to the presence of pinning energy barriers. In the early time region, which is longer the lower the temperature, this crystal-growth phase is indistinguishable from an off-equilibrium glass, both from a structural and a dynamical point of view: crystal growth has not advanced enough to be structurally detectable, and a violation of the fluctuation-dissipation theorem (FDT) typical of structural glasses is observed. On the other hand, for longer times crystallization reaches a threshold beyond which crystal domains are easily identified, and FDT violation becomes compatible with ordinary domain growth.Comment: 25 page

EU accession and Poland's external trade policy

No description supplie

On Dynamics of Integrate-and-Fire Neural Networks with Conductance Based Synapses

We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some \textit{finite} precision, we propose a model where spikes are effective at times multiple of a characteristic time scale $\delta$, where $\delta$ can be \textit{arbitrary} small (in particular, well beyond the numerical precision). We make a complete mathematical characterization of the model-dynamics and obtain the following results. The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the "edge of chaos", a notion mathematically well defined in the present paper. Furthermore, except at the edge of chaos, there is a one-to-one correspondence between the membrane potential trajectories and the raster plot. This shows that the neural code is entirely "in the spikes" in this case. As a key tool, we introduce an order parameter, easy to compute numerically, and closely related to a natural notion of entropy, providing a relevant characterization of the computational capabilities of the network. This allows us to compare the computational capabilities of leaky and Integrate-and-Fire models and conductance based models. The present study considers networks with constant input, and without time-dependent plasticity, but the framework has been designed for both extensions.Comment: 36 pages, 9 figure

Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence

This review reports on the research done during the past years on violations of the fluctuation-dissipation theorem (FDT) in glassy systems. It is focused on the existence of a quasi-fluctuation-dissipation theorem (QFDT) in glassy systems and the currently supporting knowledge gained from numerical simulation studies. It covers a broad range of non-stationary aging and stationary driven systems such as structural-glasses, spin-glasses, coarsening systems, ferromagnetic models at criticality, trap models, models with entropy barriers, kinetically constrained models, sheared systems and granular media. The review is divided into four main parts: 1) An introductory section explaining basic notions related to the existence of the FDT in equilibrium and its possible extension to the glassy regime (QFDT), 2) A description of the basic analytical tools and results derived in the framework of some exactly solvable models, 3) A detailed report of the current evidence in favour of the QFDT and 4) A brief digression on the experimental evidence in its favour. This review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the QFDT as well as for the more expert readers who may be interested in more specific results.Comment: 120 pages, 37 figures. Topical review paper . Several typos and misprints corrected, new references included and others updated. to be published in J. Phys. A (Math. Gen.

Sensory and Cognitive Declines in Older Adults: A Longitudinal Study

In a recent cross-sectional study, as has been found in numerous previous studies, Sommers et al.: 2011) found that age-related declines in hearing, as assessed by pure-tone thresholds, begin around age 20 and continue across the lifespan. In another article published from the same cross-sectional dataset, Hale et al.: 2011) found that working memory ability also begins declining around age 20 and continues throughout life. The present study is a longitudinal follow-up of these two studies in which a sub-sample of older adults: ≥65 years old at the time of original testing approximately four years ago) were re-tested on sensory and cognitive measures. The goal was to examine the extent to which older adults experience longitudinal declines on sensory and cognitive abilities over a relatively short period of time, and whether declines in one domain accompany declines in the other. In reference to sensory abilities, participants experienced declines for pure-tone thresholds and speech perception in noise. Additionally, they experienced declines for most cognitive abilities. They did not experience declines on the two simple verbal working memory tasks or on the two visuospatial processing speed tasks. Despite extensive longitudinal sensory and cognitive declines, there was only partial evidence for a common cause underlying these declines. Given the paucity of longitudinal studies investigating these abilities, the present results provide important information about the sensory-cognitive profile of aging

Spectra of large time-lagged correlation matrices from Random Matrix Theory

We analyze the spectral properties of large, time-lagged correlation matrices using the tools of random matrix theory. We compare predictions of the one-dimensional spectra, based on approaches already proposed in the literature. Employing the methods of free random variables and diagrammatic techniques, we solve a general random matrix problem, namely the spectrum of a matrix $\frac{1}{T}XAX^{\dagger}$, where $X$ is an $N\times T$ Gaussian random matrix and $A$ is \textit{any} $T\times T$, not necessarily symmetric (Hermitian) matrix. As a particular application, we present the spectral features of the large lagged correlation matrices as a function of the depth of the time-lag. We also analyze the properties of left and right eigenvector correlations for the time-lagged matrices. We positively verify our results by the numerical simulations.Comment: 44 pages, 11 figures; v2 typos corrected, final versio

Ground-state configuration space heterogeneity of random finite-connectivity spin glasses and random constraint satisfaction problems

We demonstrate through two case studies, one on the p-spin interaction model and the other on the random K-satisfiability problem, that a heterogeneity transition occurs to the ground-state configuration space of a random finite-connectivity spin glass system at certain critical value of the constraint density. At the transition point, exponentially many configuration communities emerge from the ground-state configuration space, making the entropy density s(q) of configuration-pairs a non-concave function of configuration-pair overlap q. Each configuration community is a collection of relatively similar configurations and it forms a stable thermodynamic phase in the presence of a suitable external field. We calculate s(q) by the replica-symmetric and the first-step replica-symmetry-broken cavity methods, and show by simulations that the configuration space heterogeneity leads to dynamical heterogeneity of particle diffusion processes because of the entropic trapping effect of configuration communities. This work clarifies the fine structure of the ground-state configuration space of random spin glass models, it also sheds light on the glassy behavior of hard-sphere colloidal systems at relatively high particle volume fraction.Comment: 26 pages, 9 figures, submitted to Journal of Statistical Mechanic

Implicit Bias in Daily Perceptions and Legal Judgments

In today’s demonstration, we explored the audience’s positive and negative associations with blacks and whites. The demonstration is an adaptation of the Implicit Association Test (www.projectimplicit.net), a computer-based task designed to explore mental connections between various concepts. Participants were presented with a list of concepts (stereotypically black and white names, pleasant and unpleasant concepts) in a column down the middle of a screen along with the response categories (black/white or Pleasant/Unpleasant) along the left and right sides. When reading a word, participants were asked to categorize it by slapping the knee (left or right) that corresponds to the category displayed on the left or right side of the screen. Their task was to do this as fast as possible, correcting any mistakes before going forward, and raising their hand after completing the last word in the list. We then noted the amount of time for a critical mass of participants (approximately seventy-five percent) to complete each trial. In simple trials, either names or valenced words are displayed. In two critical trials, both names and valenced words were presented simultaneously in the middle of the screen. The trials differ based on the pairings of the response categories, and these trials tend to show a drastic difference in completion times. When participants were required to use the same hand to categorize black names and unpleasant words or white names and pleasant words, they tended to respond almost twice as quickly as when using the same hand to categorize black names and pleasant words or white names and unpleasant words. While there are individual differences among the respondents, the demonstration provided audible and visceral evidence of the trend. We then asked the audience to interrogate the methodological and cultural implications of the task, ultimately concluding that the test potentially reveals the fairly widespread implicit negative associations with blacks. With this working hypothesis, we next discussed the nature of racial bias and its implications for judgment in legal domains

Slater-Pauling Behavior of the Half-Ferromagnetic Full-Heusler Alloys

Using the full-potential screened Korringa-Kohn-Rostoker method we study the full-Heusler alloys based on Co, Fe, Rh and Ru. We show that many of these compounds show a half-metallic behavior, however in contrast to the half-Heusler alloys the energy gap in the minority band is extremely small. These full-Heusler compounds show a Slater-Pauling behavior and the total spin-magnetic moment per unit cell (M_t) scales with the total number of valence electrons (Z_t) following the rule: M_t=Z_t-24. We explain why the spin-down band contains exactly 12 electrons using arguments based on the group theory and show that this rule holds also for compounds with less than 24 valence electrons. Finally we discuss the deviations from this rule and the differences compared to the half-Heusler alloys.Comment: 10 pages, 8 figures, revised figure 3, new text adde